Keywords: Autonomous systems, Autonomous robots
Abstract: When robots are to be deployed over long time scales, optimality should take a backseat to “survivability”, i.e., it is more important that the robots do not break or completely deplete their energy sources than that they perform certain tasks as effectively as possible. For example, in the context of multi-agent robotics, we have a fairly good understanding of how to design coordinated control strategies for making teams of mobile robots achieve geometric objectives, such as assembling shapes or covering areas. But, what happens when these geometric objectives no longer matter all that much? In this talk, we consider this question of long duration autonomy for teams of robots that are deployed in an environment over a sustained period of time and that can be recruited to perform a number of different tasks in a distributed, safe, and provably correct manner. This development will involve the composition of multiple barrier certificates for encoding tasks and safety constraints through the development of non-smooth barrier functions, as well as a detour into ecology as a way of understanding how persistent environmental monitoring can be achieved by studying animals with low-energy life-styles, such as the three-toed sloth.

Keywords: Optimal control, Optimization, Automotive
Abstract: This paper presents a bi-level optimization framework to compute the maximum-distance stint and charging strategies for a fully electric endurance race car. Thereby, the lower level computes the minimum-stint-time Powertrain Operation (PO) for a given battery energy budget and stint length, whilst the upper level leverages that information to jointly optimize the stint length, charge time and number of pit stops, in order to maximize the driven distance in the course of a fixed-time endurance race. Specifically, we first extend a convex lap time optimization framework to capture multiple laps and force-based electric motor models, and use it to create a map linking the charge time and stint length to the achievable stint time. Second, we leverage the map to frame the maximum-race-distance problem as a mixed-integer second order conic program that can be efficiently solved to the global optimum with off-the-shelf optimization algorithms. Finally, we showcase our framework on a 6 h race around the Zandvoort circuit. Our results show that a flat-out strategy can be extremely detrimental, and that, compared to when the stints are optimized for a fixed number of pit stops, jointly optimizing the stints and number of pit stops can increase the driven distance of several laps.

Keywords: Automotive, Optimal control, Electrical machine control
Abstract: This paper presents a modeling and optimization framework to minimize the energy consumption of a fully electric powertrain by optimizing its design and control strategies whilst explicitly accounting for the thermal behavior of the Electric Motor (EM). Specifically, we first derive convex models of the powertrain components, including the battery, the EM, the transmission and a Lumped Parameter Thermal Network (LPTN) capturing the thermal dynamics of the EM. Second, we frame the optimal control problem in time domain, and devise a two-step algorithm to accelerate convergence and efficiently solve the resulting convex problem via nonlinear programming. Subsequently, we present a case study for a compact family car, optimize its transmission design and operation jointly with the regenerative braking and EM cooling control strategies for a finite number of motors and transmission technologies. We validate our proposed models using the high-fidelity simulation software Motor-CAD, showing that the LPTN quite accurately captures the thermal dynamics of the EM, and that the permanent magnets' temperature is the limiting factor during extended driving. Furthermore, our results reveal that powertrains equipped with a continuously variable transmission (CVT) result into a lower energy consumption than with a fixed-gear transmission (FGT), as a CVT can lower the EM losses, resulting in lower EM temperatures. Finally, our results emphasize the significance of considering the thermal behavior when designing an EM and the potential offered by CVTs in terms of downsizing.

Keywords: Automotive, Optimization, Statistical learning
Abstract: The torsional oscillations of the driveline represent a well-known issue in electric powertrains. In order to dampen such oscillations, active damping control is usually employed to suitably modulate the requested torque. However, on the one hand, the modelling inaccuracies due to the presence of nonlinear elements in the driveline system might lead to an ineffective model-based calibration. On the other hand, model-free iterative data-driven calibration overcomes the above problem at the cost of possible safety issues. In fact, unsafe controllers might be tested producing potential system failures. This paper presents a safe model-free calibration framework based on Bayesian optimization. Results on a full-fledged vehicle simulator shows that the performance is improved as compared to model-based calibration, while at the same time the experimental effort is concentrated in safe operating regions.

Keywords: Electrical machine control, Modeling, Automotive
Abstract: Interior Permanent Magnet Synchronous Machines (IPMSMs) are the preferred choice for battery electric vehicles. Knowledge of the permanent magnet temperatures is crucial for ensuring safe operation and optimal use of these machines, as the reversible and irreversible demagnetization of the magnet material is temperature dependent. Accurate knowledge of the temperature of the permanent magnets can both extend the overload range, thus increasing the power density of the machine and exploit the effect of thermal field weakening in high-speed regions. Therefore, we present a method for estimating the permanent magnet temperature using a lumped parameter thermal network (LPTN) model. Consisting of 17 nodes, the LPTN represents the IPMSM components with a low level of discretization and separates heat transfer mechanisms within the entire machine in radial and axial direction with T-structure thermal elements. An electromagnetic-thermal Finite Element Analysis (FEA) model is used to fit the LPTN and adapt the control software to the electrical machine at an early design stage. In addition, this FEA model is used to validate the LPTN, since a prototype with measurement data is not yet available. Finally, the method is verified with five different operating points, ranging from nominal speed to high speed and from low load to high load. This LPTN can be used in model-in-the-loop control application before an actual prototype of the IPMSM is available, resulting in an optimal use of development time.

Keywords: Optimal control, Automotive, Adaptive control
Abstract: Low ambient temperatures, cold starts and city drives interrupted by still stand phases represent major challenges for energy and emission management of hybrid-electric vehicles (HEVs). Large time constants of battery and thermal systems, require long horizons to optimize overall system performance and avoid constraint violations, such as battery energy or real-world emission targets. In this work, a local online controller is extended with a coarse global optimization to predict optimal state trajectories. Manageable computational demand of this upper level optimization is achieved by a combination of model approximations, dimension reduction and coarse sampling. An online adaptation mechanism is implemented for the low-level controller to deal with imprecise predictions and system uncertainty.

The proposed multi-level control strategy provides performance within 5% of the global optimum for 100 real world driving cycles using a constant parametrization without cycle-specific tuning.

Keywords: Optimal control, Automotive, Optimization
Abstract: This paper presents a convex optimization framework to compute the minimum-lap-time control strategies of all-wheel drive (AWD) battery electric race cars, accounting for the grip limitations of the individual tyres. Specifically, we first derive the equations of motion (EOM) of the race car and simplify them to a convex form. Second, we leverage convex models of the electric motors (EMs) and battery, and frame the time-optimal final-drives design and EMs control problem in space domain. The resulting optimization problem is fully convex and can be efficiently solved with global optimality guarantees using second-order conic programming algorithms. Finally, we validate our modeling assumptions via the original non-convex EOM, and showcase our framework on the Formula Student Netherlands endurance race track. Thereby, we compare a torque vectoring with a fixed power split configuration, showing that via torque vectoring we can make a better use of the individual tyre grip, and significantly improve the achievable lap time by more than 4%. Finally, we present a design study investigating the respective impact of the front and rear EM size on lap time, revealing that the rear motor sizing is predominant due to the higher vertical rear tyre load caused by the center of pressure position and rearwards load transfer under acceleration.

Keywords: Hybrid systems, Optimization, Optimal control
Abstract: The Toyota Prius system has an excellent fuel economy (FE), but a mediocre acceleration performance (AP), especially at high speed. In order to enhance its AP while maintaining a good FE, this paper investigates the addition of multi-mode capabilities to this benchmark system with a focus on the incorporation of fixed gear modes, which are able to achieve a good AP at high speed. Firstly, candidate clutches and gears were systematically added to the single-mode Prius system. Secondly, 63 candidate multi-mode architectures were generated through the enumeration of the different clutch combinations, and their AP was evaluated. Then, AP screening criteria aiming to select systems with an outstanding AP and feasible gradeability were applied and a total of 3300 systems were selected. Lastly, the FE was assessed for these selected multi-mode systems and the ‘best’ systems with good FE and AP were selected. The results revealed that the addition of fixed gear modes significantly enhances the AP of this benchmark system, which is also able to maintain an outstanding FE thanks to its input-split mode.

Keywords: Optimal control, Aerospace
Abstract: This paper exposes a method to handle inaccurate modeling and/or initial state errors during the Powered Descent Guidance (PDG), a critical phase of atmospheric rocket landing. For this, we develop a replanification method having reliable online computational capabilities. From a reference descent scenario, an optimal correction problem is formulated. After revisiting results on Non Linear Programming sensitivity for degenerate optimization problems, we conclude that Quadratic Programming (QP) provides a local solution to the replanification problem. Using three illustrative PDG scenarios, we stress degeneracy and show how QP is used to evaluate the upper Dini derivatives at stake. Further, we discuss to what extent QP also provides a quantitatively reasonable solution outside a small neighboorhood of the reference scenarios.

Keywords: Optimal control, Nonlinear system theory
Abstract: A Hamiltonian system associated with an infinite horizon optimal control problem has a local stable manifold under appropriate assumptions. Hence, characteristics, candidates of solutions to the optimal control problem, pass through the local stable manifold of the corresponding Hamiltonian system. This paper employs a graph of the local stable manifold as a terminal condition characteristic satisfies, which leads to the two-point boundary value problem with an iterative procedure for computing a point of the local stable manifold. It contributes to forming a bundle of characteristics around a neighborhood of given a reference characteristic with no conjugate points.

Keywords: Optimal control, Predictive control for linear systems, Linear parameter-varying systems
Abstract: Model predictive control is a control approach that minimizes a stage cost over a predicted system trajectory based on a model of the system and is capable of handling state and input constraints. For uncertain models, robust or adaptive methods can be used. Because the system model is used to calculate the control law, the closed-loop behavior of the system and thus its performance, measured by the sum of the stage costs, are related to the model used. If it is adapted online, a performance bound is difficult to obtain and thus the impact of model adaptation is mostly unknown. This work provides a (worst-case) performance bound for a linear adaptive predictive control scheme with a specific model parameter estimation. The proposed bound is expressed in terms of quantities such as the initial system parameter error and the constraint set, among others and can be calculated a priori. The results are discussed in a numerical example.

Keywords: Optimal control, Stability of nonlinear systems, Lyapunov methods
Abstract: Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered disturbances. In this paper, the converse optimality theory is extended to the class of affine systems with disturbances in continuous time while considering norm constraints on both control inputs and disturbances. The admissibility theorem and the design of the internal dynamics model are generalized in this context. A robust stabilizability condition is added for the initial converse optimality problem using inverse optimality’s tool: the robust control Lyapunov function. A design for nonlinear class of systems that are both robustly stabilizable and globally asymptotically stable in open loop is obtained. A case study illustrates the presented theory.

Keywords: Optimal control, Computational methods, Nonlinear system theory
Abstract: Symbolic optimal control is a powerful method to synthesize algorithmically correct-by-design state-feedback controllers for nonlinear plants. Its solutions are (near-)optimal with respect to a given cost function. In this note, it is demonstrated how symbolic optimal control can be used to calculate controllers for an optimized routing guidance of vehicle systems in continuous state space. In fact, the capacitated vehicle routing problem and a variant of travelling salesman problem are investigated. The latter problem has a relevant application in case of loss of vehicles during mission. A goods delivery scenario and a reconnaissance mission, involving bicycle and aircraft dynamics respectively, are provided as examples.

Keywords: Optimal control, Differential algebraic systems, Linear systems
Abstract: In this paper we deal with the linear matrix inequality (LMI) arising from a singular linear quadratic regulator (LQR) problem. The maximal rank-minimizing solution K_{max} of the LMI plays a central role in obtaining a proportional-derivative feedback law for the optimal input. The optimal cost of the LQR, too, depends on this solution K_{max}. In this paper, we provide a method to compute this maximal rank-minimizing solution K_{max} of the singular LQR LMI. We compute this solution using the notions of the weakly unobservable or the slow space and the strongly reachable or the fast space of the Hamiltonian system arising from the singular LQR problem. In this process, we also provide a novel characterization of the fast space in terms of the system matrices.

Keywords: Optimal control, Emerging control applications, Energy systems
Abstract: We consider the problem of dispatching power from (or into) several fleets of heterogeneous batteries, of prescribed power rating and initial or, respectively, target energy, in the absence of cross-charging. The fleets are possibly localised in different network nodes and their individual maximum transmission power to meet a given demand signal is limited. The theory effectively generalizes an optimal dispatch policy originally developed for the case of fleets without transmission capacity constraints.

Keywords: Game theoretical methods, Network analysis and control, Control over networks
Abstract: In this paper we formulate a two-player game-theoretic problem on resilient graphs. An attacker is capable to disable some of the edges of the network with the objective to divide the agents into clusters by emitting jamming signals while, in response, the defender recovers some of the edges by increasing the transmission power for the communication signals. We consider repeated games between the attacker and the defender where the optimal strategies for the two players are derived in a rolling horizon fashion based on the number of agents in each cluster. The players' actions at each discrete-time steps are constrained by their energy for transmissions of signals. Simulation results are provided to demonstrate the effects of the values of horizon lengths and game periods on the players' performance.

Keywords: Game theoretical methods, Optimization
Abstract: In this paper, we consider a privacy signaling game problem for binary alphabets where a transmitter has a pair of messages one of which is a casual message that needs to be conveyed whereas the other message contains sensitive data and needs to be protected. The receiver wishes to estimate both messages with the aim of acquiring as much information as possible. For this setup, we study the interactions between the transmitter and the receiver with non-aligned information theoretic objectives (modeled by mutual information and hamming distance) due to the privacy concerns of the transmitter. We derive conditions under which Nash and/or Stackelberg equilibria exist and identify the optimal responses of the encoder and decoders strategies for each type of game. One particularly surprising result is that when both type of equilibria exist, they admit the same encoding and decoding strategies. We corroborate our analysis with simulation studies.

Keywords: Robotics, Cooperative autonomous systems, Emerging control applications
Abstract: Multi-robot task allocation is a practical way to identify synergies between robots. When all the robots within a system fall under the auspices and authority of a single organization, they can simply be compelled to share their information and participate in cooperative protocols. But when, for instance, they are rivals vying in the marketplace, their own private data may be copyrighted or sensitive, so that disclosing information may erode a competitive advantage. Yet, even limited cooperation, by offering some arbitrage of common resources (such as shared infrastructure), often reduces costs for all parties; indeed, competition and cooperation are not mutually exclusive. We examine the question of how to allocate robots to tasks optimally while ensuring that no task valuations, utilities, positions, or related data are released. We do this via an auction-based assignment algorithm implemented using secure multi-party computation operations, without requiring any trusted auctioneer. The approach offers precise and effective privacy guarantees that are stronger than present methods. We demonstrate the feasibility of the approach via tests in a case study inspired by autonomous driving. First, we tested the approach in a single-computer setup, using parties with virtual network interfaces, where we studied the effects of varying the number of parties and the associated parameters of the auction. Next, we tested the approach in a decentralized, physical test-bed using single board computers running over a WiFi LAN network. Finally, we conducted a small proof-of-concept experiment using two autonomous mobile robots performing a decentralized, private auction.

Keywords: Agents and autonomous systems, Cooperative autonomous systems, Concensus control and estimation
Abstract: In this paper, we develop and analyze a gossip-based average consensus algorithm that enables all of the components of a distributed system, each with some initial value, to reach (approximate) average consensus on their initial values after executing a finite number of iterations, and without having to reveal to other curious components the specific value they contribute to the average calculation. We consider a fully-connected (undirected) network in which curious components do not interfere in the computation in any other way, but can collaborate arbitrarily and are aware of the privacy-preserving strategy. We characterize precisely conditions on the information exchange that guarantee privacy preservation for a specific node. The protocol also provides a criterion that allows the nodes to determine, in a distributed manner (while running the proposed gossip protocol), when to terminate their operation because approximate average consensus has been reached.

Keywords: Emerging control applications, Control over networks, Robust adaptive control
Abstract: Wireless communication offers many benefits for control such as substantially reduced deployment costs, higher flexibility, as well as easier data access. It is thus not surprising that smart and wireless sensors and actuators are increasingly used in industry. With these enhanced possibilities, exciting new technologies such as Control-as-a-Service arise, where (for example) controller design or tuning based on input-output-data can be outsourced to a cloud or mobile device. This implies, however, that sensitive plant information may become available to service providers or, possibly, attackers. Against this background, we focus on privacy preserving optimal PID tuning as-a-Service here. In particular, we combine homomorphic encryption with extremum seeking in order to provide a purely data-driven and confidential tuning algorithm. The encrypted realization requires several adaptions of established extremum seekers. These encompass relative parameter updates, stochastic gradient approximations, and a normalized objective function. As a result, and as illustrated by various numerical examples, the proposed encrypted extremum seeker is able to tune PID controllers for a wide variety of plants without being too conservative.

Keywords: Safety critical systems, Optimization, Stochastic systems
Abstract: In this manuscript, we provide a set of tools (in terms of semidefinite programs) to synthesize Gaussian mechanisms to maximize privacy of databases. Information about the database is disclosed through queries requested by (potentially) adversarial users. We aim to keep part of the database private (private sensitive information); however, disclosed data could be used to estimate private information. To avoid an accurate estimation by the adversaries, we pass the requested data through distorting (privacy-preserving) mechanisms before transmission and send the distorted data to the user. These mechanisms consist of a coordinate transformation and an additive dependent Gaussian vector. We formulate the synthesis of distorting mechanisms in terms of semidefinite programs in which we seek to minimize the mutual information (our privacy metric) between private data and the disclosed distorted data given a desired distortion level -- how different actual and distorted data are allowed to be.

Keywords: Machine learning, Lyapunov methods, Optimization
Abstract: Control barrier functions (CBFs) have become a popular tool to enforce safety of a control system. CBFs are commonly utilized in a quadratic program formulation (CBF-QP) as safety-critical constraints. A class mathcal{K} function in CBFs usually needs to be tuned manually in order to balance the trade-off between performance and safety for each environment. However, this process is often heuristic and can become intractable for high relative-degree systems. Moreover, it prevents the CBF-QP from generalizing to different environments in the real world. By embedding the optimization procedure of the exponential control barrier function based quadratic program (ECBF-QP) as a differentiable layer within a deep learning architecture, we propose a differentiable safety-critical control framework that enables generalization to new environments for high relative-degree systems with forward invariance guarantees. Finally, we validate the proposed control design with 2D double and quadruple integrator systems in various environments.

Keywords: Robotics, Constrained control, Nonlinear system theory
Abstract: We revisit the trajectory planning problem for general N-link robotic manipulators. Our approach focuses on characterising the whole set of states that can be transferred to a target set of velocities without violating constraints. To achieve this, we work in the commonly utilized two dimensional projected space of the Lagrangian dynamics on a specific predefined path. The produced dynamics is a double integrator, with nonlinearities being pushed into a non-convex and state-dependent input constraint set. We approach the problem as a special emph{reach-avoid} set computation problem using ordering properties of the trajectories generated by a suitably parameterised state feedback control law. %As a byproduct of the algorithm, we provide simple, continuous state-feedback controllers that solve the reachability problem. Our results are illustrated in simulation using a realistic model of the UR5{texttrademark} commercial robot.

Keywords: Identification for control, Robotics, Predictive control for linear systems
Abstract: This paper presents a method for identifying the parameters of a ballbot (a robot balancing on a ball) from proper input/output measurements and by exploiting available information about its model structure. To avoid biased parameter estimations, the method adopts a so-called indirect closed-loop identification, where a linearized model of the system dynamics is identified. Owing to the special structure of the linearized model, the parameters of the nonlinear model, which are nonlinear combinations of it physical parameters, can be extracted by solving a set of linear equations. These identified parameters could be used to initialize any suitable optimization tool for further enhancing their values. One important feature of the method is that it allows the use of highly developed off-the-shelf algorithms of system identification, which can give unbiased/consistent estimates. For evaluating the identified model, it has been employed to design a combination of two controllers, a linear quadratic regulator (LQR) and a model predictive control (MPC) for balancing the ballbot. The experimental results demonstrate that the ballbot can be balanced with such a composition control based on the identified model.

Keywords: Robotics, Agents networks, Network analysis and control
Abstract: A problem of transformation of a planar formation of a robot swarm to another formation is considered. Robots are placed in the vertices of a polygon, so the goal is to transform the entire polygon in a continuous way. The proposed solution is based on the topological concept of homotopy. It describes a continuous passage from one closed curve to another one. During the passage the basic structure of the curved is preserved: at each instant it is a closed curve, but not necessarily a polygon, with robots occupying some places on it. In order to provide a constructive solution, it is assumed that the region bounded by the polygon is star-shaped.

Keywords: Robotics, Safety critical systems, Robust control
Abstract: In this paper, we show how to realize robust safety-critical control laws for robotic manipulators with large constraint inequalities (>100). In particular, we use control barrier functions (CBFs) formulated via the kinetic energy terms to represent constraints like joint position and velocity limits both in configuration and task space. By using the kinetic energy terms, we can realize model-free constraints in a quadratic program (QP), which can be solved in real-time, thereby demonstrating fast computation time despite the presence of large constraints. We will consider two types of CBFs, the reciprocal and the zeroing type, and integrate with Control Lyapunov Function (CLF) based constraints to yield a multi-objective QP. Further, we will provide feasibility and continuity guarantees, thereby yielding a continuous, robust and a safe control law for a broad class of robotic systems. Towards the end, we will demonstrate two types of QP formulations in a 6-DOF manipulator, where one uses 109 constraints through the reciprocal type and the other uses 61 constraints using the zeroing type of CBFs.

Keywords: UAV's, Autonomous robots, Robotics
Abstract: The use of unmanned aerial vehicles (UAVs) for autonomous inspection tasks has become more prominent in recent years. To make the most of the autonomous inspection, the parameters governing control, perception and navigation of the robot should be tuned precisely to the necessary task. Currently, the use of motion capture (mocap) systems is the norm when performing the stringent evaluation of simultaneous localization and mapping (SLAM) and advanced controllers. In this paper, we address the use of a cost-effective solution to ground-truthing and evaluation of said algorithms in large industrial environments. To this end, we use fiducial markers, deployed in known locations, in order to estimate the pose of the vehicle in 6 degrees-of-freedom (6DOF) and test them against a state-of-the-art mocap system. We additionally test the method in the field, by deploying the markers to the environment of interest and applying widely used SLAM implementations to confirm its efficacy by evaluating their performance in two emulated inspection task scenarios. We find that our method is comparable in performance to the state-of-the-art mocap systems without the need for laborious calibration and is capable of providing a pose estimate for evaluating SLAM and underlying UAV control methods.

Keywords: UAV's, Autonomous systems, Autonomous robots
Abstract: Event-based vision has already revolutionized the perception task for robots by promising faster response, lower energy consumption, and lower bandwidth without introducing motion blur. In this work, a novel deep learning method based on gated recurrent units utilizing sparse convolutions for detecting gates in a race track is proposed using event-based vision for the autonomous drone racing problem. We demonstrate the efficiency and efficacy of the perception pipeline on a real robot platform that can safely navigate a typical autonomous drone racing track in real-time. Throughout the experiments, we show that the event-based vision with the proposed gated recurrent unit and pretrained models on simulated event data significantly improve the gate detection precision. Furthermore, an event-based drone racing dataset consisting of both simulated and real data sequences is publicly released.

Keywords: UAV's, Cooperative control, Robotics
Abstract: This paper integrates cooperative localization with continuum deformation coordination of a multi-quadcopter system {(MQS) to assure safety and optimality of the quadcopter team coordination in the presence of position uncertainty. We first consider the MQS as a finite number of particles of a deformable triangle in a 3-D motion space and define their continuum deformation coordination as a leader-follower problem in which leader quadcopters} can estimate (know) their positions but follower quadcopters rely on relative position measurements to localize themselves and estimate the leaders' positions. We then propose a navigation strategy for the MQS to plan and acquire the desired continuum deformation coordination, in the presence of measurement noise, disturbance, and position uncertainties, such that collision is avoided and rotor angular speeds of all quadcopters remain bounded. We show the efficacy of the proposed strategy by simulating the continuum deformation coordination of an MQS with eight quadcopters.

Keywords: Linear systems, LMI's/BMI's/SOS's, Optimization
Abstract: Inspired by recent work on data-driven control, this work presents data-driven event-triggered control strategies for discrete-time linear time-invariant (LTI) systems. The results presented do not require explicit identification of the system parameters and are based on the input and state data collected from the system during an open-loop experiment. The design of event-triggered control consists of two stages: finding a state feedback controller that exponentially stabilizes the system and designing an event-triggered policy that determines the instances at which the control law needs to be updated. The proposed designs in both stages involve solving semi-definite programs with data-dependent linear matrix inequalities (LMIs) as constraints. For the event-triggered implementation, we employ a relative thresholding mechanism and the range of the thresholding parameter is derived using S-procedure. Conditions on the thresholding parameter are derived that ensure both pre-specified exponential convergence and non-trivial event-triggering. We present simulation results for an illustrative example that validates the proposed methods.

Keywords: Linear systems, LMI's/BMI's/SOS's, Switched systems
Abstract: The Carleman bilinearization is an approach that performs an exact conversion of a finite-dimensional nonlinear system into an infinite-dimensional bilinear system. A finite-dimensional system is later obtained through a truncation for analysis and control purposes. This paper investigates the linear matrix inequality (LMI)-based design of a switched state-feedback control law for the model obtained via Carleman bilinearization of a first-order nonlinear system. It is shown that in order to obtain feasible design conditions, the performance requirements must be relaxed in a neighborhood of the zero equilibrium point, so that problems arising from the uncontrollability of the linear part of the model can be avoided. The effectiveness of the proposed approach is shown using a numerical example and experimental results using a multi-input tank system.

Keywords: Behavioural systems, Distributed parameter systems, Linear systems
Abstract: The notion of bisimulation of dynamical systems described by ordinary differential and difference equations is well established in the literature. However, a notion of bisimulation for systems described by partial differential and difference equations is visibly nonexistent. In this paper, we formulate a notion of bisimulation, namely S-bisimulation, for a special class of dynamical systems described by partial differential equations with real constant coefficients. An algebraic characterization of S-bisimulation and an algorithm for computing the maximal S-bisimulation relation is provided.

Keywords: Linear systems, Markov processes, Optimization
Abstract: In this paper, we examine the robust regulation problem of Markov jump linear systems with transition probabilities matrix subject to polytopic uncertainties. Based on penalty function and dynamic programming concepts, we define an unconstrained least-squares optimization problem from a polytopic perspective. In this sense, we minimize the states, whereas the underlying Markov jump system undergoes the worst-case effects of uncertainties. We propose a recursive solution in the form of a symmetrical matrix arrangement, from which we attain robust feedback gains. Moreover, the solution exists for any positive penalty parameter, whose a priori tuning is thus straightforward. For validation purposes, we provide a numerical example and compare the results to those obtained with a robust H-infinity controller. The proposed approach outperforms the robust H-infinity controller in terms of computational time required to yield the feedback gains.

Keywords: Linear systems, Optimal control, Constrained control
Abstract: We show how the recent works on data driven open-loop minimum-energy control for linear systems can be exploited to obtain closed-loop piecewise-affine control laws, by employing a state-space partitioning technique which is at the basis of the static relatively optimal control. In addition, we propose a way for employing portions of the experimental input and state trajectories to recover information about the natural movement of the state and dealing with non-zero initial conditions. The same idea can be used for formulating several open-loop control problems entirely based on data, possibly including input and state constraints.

Keywords: Neural networks, LMI's/BMI's/SOS's, Linear systems
Abstract: This paper is concerned with the analysis of the L_{2} induced norm of continuous-time LTI systems where the input signals are restricted to be nonnegative. This induced norm is referred to as the L_{2+} induced norm in this paper. It has been shown very recently that the L_{2+} induced norm is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinear elements only provide nonnegative signals. For the upper bound computation of the L_{2+} induced norm, an approach with copositive programming has also been proposed. It is nonetheless true that this approach becomes effective only for multi-input systems, and for single-input systems this approach does not bring any improvement over the trivial upper bound, the standard L_2 norm. To overcome this difficulty, we newly introduce positive filters to increase the number of positive signals. This enables us to enlarge the size of the copositive multipliers so that we can obtain better (smaller) upper bounds with copositive programming.

Keywords: Uncertain systems, Linear systems
Abstract: Propagation of uncertainty in the initial conditions of a dynamical system is necessary in various control applications. While several generally applicable methods based on Monte Carlo simulation and surrogate modeling exist for this task, they can be computationally intensive or difficult to set up for complex initial distributions. Here, we propose an approach for studying the propagation of initial condition uncertainty, tailored to linear dynamical systems. Our approach uses a class of maximum entropy probability distributions to track the state probability density in time. For deterministic linear systems with initial state distributions belonging to this distribution class, our method results in set of ODEs that allow the exact calculation of the state distribution at any time point in time, generalizing the results known for Gaussian initial distributions. For systems perturbed by noise, we show that the state distribution can be efficiently approximated in a maximum entropy sense via the moment equations. Our results provide a powerful computational alternative to commonly used uncertainty propagation methods, and can be exploited in the construction of filtering and control methods for linear systems with uncertain initial conditions.

Keywords: Biological systems, Modeling, Observers for nonlinear systems
Abstract: In the design of smart irrigation systems, there are several open challenges, among which: i) the modeling of heterogeneity of cropping land, and ii) the estimation of non-measured state variables to control crop development. This work addresses both challenges by an agent-based model (ABM) of a discretized field and by using state estimation techniques. For the last challenge, two software sensors, i.e., an extended Kalman filter (EKF) and an unscented Kalman filter (UKF), are used and compared to estimate online the states of homogeneous portions of land assigned to the agents of an ABM model. The agent-based crop model is presented and simulated under two different climatic scenarios to assess the performance of the estimation techniques. Simulation results of a testbed in Colombia show the advantages of UKF over the EKF.

Keywords: Neural networks, Identification for control, Mechatronics
Abstract: Performance of model–based feedforward controllers is typically limited by the accuracy of the model describing the inverse system dynamics. Physics–guided neural networks (PGNN), where a known physical model cooperates in parallel with a neural network, were recently proposed as a method to achieve high accuracy of the identified inverse dynamics. However, the flexible nature of neural networks can create overparameterization when employed in parallel with a physical model, which results in a parameter drift during training. This drift may result in parameters of the physical model not corresponding to their physical values, which increases vulnerability of the PGNN to operating conditions not present in the training data. To address this problem, this paper proposes a regularization method via identified physical parameters, in combination with an optimized training initialization that improves training convergence. The regularized PGNN framework is validated on a real–life industrial linear motor, where it delivers better tracking accuracy and extrapolation.

Keywords: Stability of nonlinear systems, Lyapunov methods, Robotics
Abstract: This paper presents a novel energy shaping-based integral action for mechanical systems with unknown dissipative forces and matched disturbances. The proposed approach builds on the simultaneous interconnection and damping assignment method and takes advantage of the representation of the dissipative forces in the port-Hamiltonian dynamics. We consider dissipative forces that cannot be written in the classical dissipation structure of the port-Hamiltonian systems. We show that the proposed design ensures the stability of the equilibrium and is robust against dissipative force uncertainty, and rejects constant matched disturbances. Two case studies are presented, and simulation results show the closed-loop performance.

Keywords: Feedback linearization, Identification for control, Power plants
Abstract: This study proposes a feedback linearization based-control using a dynamic neural network to control a pressurized water-type nuclear power plant. The nonlinear plant model adopted in this study is characterized by five inputs, five outputs and, 38 state variables. The model is linearized through dynamic neural network-based system identification and feedback linearization. The proportional–integral–derivative (PID) controller is subsequently applied to the linearized process. The effectiveness of the proposed approach is demonstrated by simulations on different subsystems of a pressurized water reactor nuclear power plant model. Simulation results show that the proposed strategy offers good performance and is capable of effectively tracking the reference under disturbances.

Keywords: Flexible structures, Hybrid systems, Mechatronics
Abstract: Active vibration control (AVC) is crucial for the structural integrity, precision, and speed of industrial machines. Despite advancements in nonlinear control techniques, most AVC techniques predominantly employ linear feedback control due to their simplicity and ability to be designed in the frequency domain. In this paper, we introduce a reset-based nonlinear bandpass filter that uses velocity feedback to improve transient damping of vibrating structures. The approach is motivated from an energy-based mechanistic analysis, which incentivizes the use of reset. A novel feature of our approach is that it works for non-ideal, naturally damped systems, and enables control design in the frequency domain, in line with industrial practice. We demonstrate the effectiveness of this new filter by numerical simulations and experimental validation on a single degree-of-freedom flexure stage.

Keywords: Intelligent systems, Neural networks, Traffic control
Abstract: We propose a Predictive Group Elevator Scheduler by using predictive information of passengers arrivals from a Transformer based destination predictor and a linear regression model that predicts remaining time to destinations. Through extensive empirical evaluation, we find that the savings of Average Waiting Time (AWT) could be as high as above 50% for light arrival streams and around 15% for medium arrival streams in afternoon down-peak traffic regimes. Such results can be obtained after carefully setting the Predicted Probability of Going to Elevator (PPGE) threshold, thus avoiding a majority of false predictions for people heading to the elevator, while achieving as high as 80% of true predictive elevator landings as early as after having seen only 60% of the whole trajectory of a passenger.

Keywords: Medical signal processing, Applications in neuroscience, Filtering
Abstract: In this paper, we explore the Dynamic Neural Fields (DNFs) in the presence of model uncertainties, i.e. the stochastic DNF equations. The model describes a neural tissue affected by external stimulus where the interaction of neurons population is treated as a continuum. This yields a stochastic nonlinear integro-differential equation. The working memory mechanism modeled by the DNFs should allow the system to cope with missing sensors' information. The goal of this paper is to design an accurate reconstruction methodology of the pattern formation in a neural tissue from an incomplete data available from the sensors. We assume that the measurements are partially observed in both domains that are the time and the spatial domains. For that, we explain how the state-space representation can be adopted for the stochastic DNFs and, next, we derive the filtering method based on the Ito-Taylor expansion of order 1.5 within the Extended Kalman Filter. The numerical experiments are also provided.

Keywords: Control education, Manufacturing processes, Electrical power systems 
Abstract: Introduction of IFAC Industry Committee, the facilitators and session objectives: 1: To sharpen the insights among researchers and students on the real needs in industry. 2. To provide industrial practitioners a framework to translate their day-to-day problems into a research agenda relevant for their industry cluster.

Keywords: Control education, Manufacturing processes, Electrical power systems 
Abstract: Overview of the concepts and framework presented in the Control Engineering Practice paper. Verification with tutorial attendees.

Keywords: Control education, Manufacturing processes, Electrical power systems
Abstract: See Part 1.

Keywords: Control education, Manufacturing processes, Electrical power systems
Abstract: See Part 1.

Keywords: Manufacturing processes
Abstract: Case Study: Process Industry: In-depth treatment of this industry cluster and its characteristic control problems. Purpose is to give the audience a feeling on what it really means to identify control problems for an industry cluster, and how to generate interest in industry on innovative ideas.

Keywords: Electrical power systems
Abstract: Case Study - Energy and Power Conversion: In-depth treatment of this cluster and its characteristic control problems. Purpose: same as above.

Keywords: Control education, Manufacturing processes, Electrical power systems
Abstract: Wrap up and verification of the previous via online questioning. For the research people: what are key learnings from this? For the industrial people: to what extent does this help you in establishing the business case for automatic control in your industry cluster?

Keywords: Control education, Manufacturing processes, Electrical power systems
Abstract: See Part 1.

Keywords: Linear systems, Statistical learning, Signal processing
Abstract: This module introduces the area of compressed sensing and motivates the role of sparsity in discrete-time linear dynamical systems.

Keywords: Linear systems, Statistical learning, Signal processing
Abstract: This module presents the NP-hard problem of sparse initial state estimation and approximate algorithms to efficiently recover the sparse state.

Keywords: Linear systems, Statistical learning, Signal processing
Abstract: See Part 1.

Keywords: Emerging control theory, Linear systems, Statistical learning
Abstract: This module discusses the role of sparsity in the observability of a linear dynamical system and the related mathematical tools and results. For example, the results show that if the initial state vector admits a sparse representation, the number of measurements can be significantly reduced by using random projections to obtain the measurements.

Keywords: Emerging control theory, Linear systems, Constrained control
Abstract: This module explores the aspects of controllability and stabilizability of a linear dynamical system using sparse control inputs. The key result discussed here is the compact algebraic controllability test of the system, which is elucidated using the example of manipulating network opinion by an external budget-constrained agent.

Keywords: Emerging control theory, Linear systems, Constrained control
Abstract: See Part 1.

Keywords: Emerging control theory, Linear systems, Statistical learning, Constrained control, Signal processing
Abstract: This module discusses the new sparsity models and sparse recovery problems that uniquely arise in the study of linear dynamical systems, namely, piecewise sparsity and temporal correlation. The focus is on efficient algorithms for designing sparse control inputs exploiting these underlying structures.

Keywords: Emerging control theory, Linear systems, Statistical learning
Abstract: See Part 1.

Keywords: Adaptive control
Abstract: For mission-critical systems, a redundant set of actuators bears the promise of enhanced performance, fault-tolerance, and increased robustness. Input redundancy is typically approached by means of finite-horizon optimization (MPC) or via static control allocation strategies. MPC resolves the redundancy via on-line optimization seamlessly with the actual control policy, but leads to solutions that are difficult to be retrofitted to existing controllers. In classic control allocation, standing assumptions prescribe the definition of a virtual control input with the same dimensionality of the regulated output. A control strategy designed for this virtual input is then “distributed” across the redundant set of actuators via on-line optimization. Reality is more complex: While it is desirable to devise allocation strategies that can be merged into existing control architectures, the setup of classic control allocation is unduly restrictive and does not hold for many technological systems of interest. In this talk, we present an approach to the systematic design of dynamic control allocation schemes for general classes of input-redundant systems that results in plug-in modules for existing or desired control architectures. The enabling methodology is a geometric characterization that leads to the exploitation of input redundancy in the system inverse, rather than in the plant model itself. The steady-state behavior of the system is shaped through adaptation of free parameters stemming from dynamic optimization of selected performance criteria penalizing both the control input and the state trajectory, all while maintaining invariance of the error-zeroing manifold. The method is applied to fault-tolerant control of over-actuated aircraft, where results from flight tests are presented alongside simulation studies.

Keywords: Control education
Abstract: In this session, Prof. Kerrigan will present some examples of how they have used various digital learning tools in the 3rd year Control Systems module in the Department of Aeronautics at Imperial College London. To provide formative feedback for students during interactive problem classes, MATLAB Live Scripts were used that were based on solving some basic control problems. To enable students to learn how to solve more realistic problems from applications in aerospace, a set of MATLAB Grader assignments was developed that students could submit in their own time and were automatically graded with feedback on which parts need correcting. In order to encourage students to be fully engaged during the in-person laboratory experiment, a corresponding pre-laboratory exercise was developed based on a virtual laboratory in Simulink and MATLAB Grader assignment. The presentation will also reflect on what has worked well and not so well, both from an instructor and student viewpoint.

Keywords: Predictive control for linear systems, Optimal control, Robust control
Abstract: Tube-based model predictive control (MPC) methods leverage tubes to bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. This paper presents a novel tube-based MPC formulation based on system level disturbance reachable sets (SL-DRS), which leverage the affine system level parameterization (SLP). We show that imposing a finite impulse response (FIR) constraint on the affine SLP guarantees containment of all future deviations in a finite sequence of SL-DRS. This allows us to formulate a system level tube-MPC (SLTMPC) method using the SL-DRS as tubes, which enables concurrent optimization of the nominal trajectory and the tubes, while using a positively invariant terminal set. Finally, we show that the SL-DRS tubes can also be computed offline.

Keywords: Cellular dynamics, Optimal control, Process control
Abstract: In bacteria, the mechanisms behind the allocation of resources to different cellular functions (i.e. growth or nutrient uptake) have been tuned to optimally adjust cell composition to changing environments. Simple dynamical models of bacterial growth have been key in predicting these mechanisms through a resource allocation perspective. This approach has also been applied to the production of added-value compounds, to determine how to externally adjust the cellular composition in order to maximize metabolite over biomass synthesis. This paper presents a resource allocation perspective of a fed-batch process, based on a multi-scale mechanistic model considering intracellular concentrations of the main cellular components, as well as the dynamics of the bioreactor. The model presented here is a simple coarse-grained self-replicator model of E. coli, accounting for empirical cellular trade-offs observed in previous experimental works. The problem of maximizing an added-value metabolite of interest is written as an Optimal Control problem, in terms of the internal resource allocation parameter and the feeding rate of the bioreactor. Numerical results are provided to better understand the role of cellular composition in fed-batch processing.

Keywords: Computational methods, Optimization algorithms, Optimal control of communication networks
Abstract: This paper proposes a comparative assessment between gradient-based and LMI (Linear Matrix Inequality)- based computational methods for coalitional feedback controllers. The analysis is performed in the context of multi-agent networked systems with bidirectional communication links. In particular, we compare three methods based on gradient optimisation, which use different strategies to compute the feedback gain, with LMI-based methods typically employed to compute this type of controllers. The simulation results show that the proposed gradient-based methods can outperform the LMI-based methodology, but at the expense of higher computational cost.

Keywords: Optimal control, Markov processes, Delay systems
Abstract: We deal with the recursive robust control problem for uncertain discrete-time Markovian jump linear systems with Markov time-delay. We assume all matrices of the system are subject to norm-bounded parametric uncertainties. By application of the lifting method and modeling of time-varying delay as a mode-dependent Markov chain, the delay system is converted to an augmented delay-free Markovian jump linear system. The delay-independent state-feedback control is then deduced by the robust regularized least-squares approach. The proposed solution is given in terms of augmented coupled Riccati equations presented through a symmetric matrix arrangement. With a numerical example, we evaluate the proposed control and compare its performance with a control approach.

Keywords: Optimal control, Optimization, UAV's
Abstract: In this paper, we address a minimum-time steering problem for a drone modeled as point mass with bounded acceleration, across a set of desired waypoints in the presence of gravity. We first present a method to calculate the minimum-time control input to steer the drone between two waypoints based on a continuous-time problem formulation that is solved using Pontryagin's Minimum Principle. Subsequently, we use this two-point solution to find a minimum-time trajectory across multiple waypoints. We solve for the time-optimal trajectory across a given set of waypoints by discretizing in the time domain and formulating the minimum-time problem as a nonlinear program (NLP). The velocities at each waypoint obtained from solving the NLP are then used as boundary conditions to extend our two-point solution across those multiple waypoints. We apply this planning methodology to execute a surveying task that minimizes the time taken to completely explore a target area or volume. Numerical simulations and theoretical analyses of this new planning methodology are presented. The results from our approach are also compared to traditional polynomial trajectories like minimum snap planning.

Keywords: Aerospace, Optimal control
Abstract: The problem of guiding a pursuer against multiple evaders, one of which is finally engaged by the pursuer, is considered. Contrary to the existing approach of guiding the pursuer before allocation using a complex time-weighted average of individual guidance commands, a simplified virtual target approach is proposed. Prior to the allocation decision at the prescribed decision time, the pursuer is guided using a conventional one-on-one guidance law towards a stationary virtual target with a set of associated terminal constraints. The proposed approach allows realizing a complex engagement using a guidance law with a fixed structure and a scalable algorithm to compute an optimal virtual target.

Keywords: UAV's, Optimal control
Abstract: This paper deals with the hierarchical real–time control of unmanned aerial vehicles (UAV) with rule–based strategy for mission time and energetic references generator based on optimal control theory. The objective of this work is to design a control which ensures an energy consumption close to the optimality, and easily implementable thanks to its low computational cost. The first part of the work deals with the extraction of simple and immediate rules for the determination of the optimal mission time, and the generation of ‘energetic trajectories’ from the analysis of the optimal control strategy, to minimize the consumption over a high heterogeneous amount of simulations. Then, a hierarchical real–time controller is proposed to track desired energetic trajectories, identified as optimal. The results provided are validated through numerical experiments and compared in terms of energy performance with the optimal solution.

Keywords: Concensus control and estimation, Control over networks, Agents networks
Abstract: This paper proposes a resilient distributed control scheme that ensures average consensus in multi-agent systems with continuous-time single-integrator kinematics in the presence of cyber-attacks. Potential cyber-attacks considered on such systems are in the form of unknown uniformly bounded false data injection (FDI) to control input channels (actuators) and also eavesdropping attacks. The purpose of such cyber-attacks is to disturb the average consensus in multi-agent systems and also to disclose the states of agents. The proposed resilient distributed average consensus protocol includes a set of virtual variables/states being exchanged via a communication network given by a general directed graph (digraph) and is designed to make the closed-loop system stable and preserve the average consensus regardless of the existence of cyber-attacks. Unlike the existing literature, the proposed distributed average consensus framework does not require any conditions on directed graphs to be strongly connected, balanced, or symmetric. A graph-theoretical approach, Lyapunov direct method, and LaSalle's invariance principle are used to guarantee the rigorous stability of multi-agent systems augmented with the proposed distributed algorithm. Simulation results validate the theoretical contributions of this paper.

Keywords: Distributed control, Cooperative autonomous systems, Agents and autonomous systems
Abstract: This paper presents a distributed resilient consensus protocol based on competitive interaction design method to solve consensus problem on general digraphs containing directed spanning tree in the presence of cyber-attacks. The attacker aims at destabilizing the consensus dynamics by intercepting the system’s communication network. The competitive interaction method allows us to design a virtual network that protects the multi-agent systems from adversaries without requiring high network connectivity and global information about the number of adversaries. In fact, the proposed distributed consensus protocol enables agents to achieve consensus in the presence of any number of bounded adversaries and also when the virtual network is being attacked. In addition, the proposed virtual network also improves the performance of consensus algorithm in the absence of attacks. Simulations are presented to illustrate our theoretical results.

Keywords: Fault detection and identification, Fault estimation, Autonomous systems
Abstract: The paper studies the problem of leakage localization in water distribution networks. For the case of a single pipe that suffers from a single leak, by taking recourse to pressure and flow measurements, and assuming those are noiseless, we provide a closed-form expression for leak localization, leak exponent and leak constant. For the aforementioned setting, but with noisy pressure and flow measurements, an expression for estimating the location of the leak is provided. Finally, assuming the existence of a single leak, for a network comprising of more than one pipe and assuming that the network has a tree structure, we provide a systematic procedure for determining the leak location, the leak exponent, and the leak constant.

Keywords: Fault tolerant systems, Safety critical systems, Linear systems
Abstract: Actuator injection attacks pose real threats to all industrial plants controlled through communication networks. In this manuscript, we study the possibility of constraining the controller output (i.e. the input to the actuators) by means of a dynamic filter designed to prevent reachability of dangerous plant states -- preventing thus attacks from inducing dangerous states by tampering with the control signals. The filter synthesis is posed as the solution of a convex program (convex cost with Linear Matrix Inequalities constraints) where we aim at shifting the reachable set of control signals to avoid dangerous states while changing the controller dynamics as little as possible. We model the difference between original control signals and filtered ones in terms of the H-infinity norm of their difference, and add this norm as a constraint to the synthesis problem via the bounded-real lemma. Results are illustrated through simulation experiments.

Keywords: Transportation systems, Fault tolerant systems, Sensor and signal fusion
Abstract: In this paper, a localization solution for railway and tramway vehicles, relying on low-cost on-board sensor technology and on a Kalman-based data fusion scheme, is tested against failures in GPS measurement acquisition. Such failures can be caused by either non-favorable operating conditions (e.g, the presence of tunnels), or intentional/accidental service disruptions. Our analysis, carried out through simulation of a three-dimensional multi-body vehicle, highlights failure conditions under which the localization solution is shown to be resilient with respect to an acceptable performance level, as well as situations that the original framework is not able to cope with. In the latter case, a variant solution, still based on low-cost on-board technology, is shown to be able to recover satisfactory performance.

Keywords: Predictive control for linear systems, Network analysis and control
Abstract: In this paper, a robust model predictive control strategy is developed for networked cyber-physical systems subject to false data injections. The aim of the proposed resilient architecture consists in quickly detecting data integrity anomalies and implementing adequate countermeasures. One of its relevant features is the capability to mitigate the use of periodic software rejuvenation procedures. This is achieved by on-line updating an initial sequence of admissible control moves via perturbations analysis and sequential quadratic arguments that are formally incorporated with detection and control phases.

Keywords: Observers for linear systems, Electrical power systems, Sliding mode control
Abstract: In this paper, a novel scheme inspired by the Super-Twisting Sliding Mode Algorithm (STA) is proposed to detect, reconstruct and mitigate resonance load altering cyber attacks in smart grids. In the existing literature, it has been shown that these attacks are difficult to be detected by the control centre, as they are often characterised by relatively small power oscillations. Nonetheless, they can degrade the energy balance of the smart grid by making the frequency oscillating outside the tolerable limits. These attacks can further bring disruptive consequences, such as widespread blackouts and the disconnection of an area from the grid. In this study, it is shown that Battery Energy Storage Systems (BESSs) controlled by an observer-based STA can effectively mitigate the impact of these attacks on a smart grid. Specifically, an STA observer is created to detect and reconstruct in real-time load altering cyber attacks in a decentralised fashion. The estimation of the attack is then utilised as a set-point for a decentralised STA-based controller to dynamically regulate the output power of the BESS. The simulation results, which account for three possible scenarios, demonstrate the effectiveness of the proposed scheme.

Keywords: Iterative learning control, Stochastic systems, Stochastic filtering
Abstract: Many repetitive control problems are characterized by the fact that disturbances have the same effect in each successive execution of the same control task. Such disturbances comprise the lumped representation of unmodeled parts of the open-loop system dynamics, a systematic model-mismatch or, more generally, deterministic yet unknown uncertainty. In such cases, well-known strategies for iterative learning control are based on enhancing the system behavior not only by exploiting data gathered during a single execution of the task but also using information from previous executions. The corresponding dual problem, namely, iterative learning state and disturbance estimation has not yet received the same amount of attention. However, it is obvious that improved estimates for the aforementioned states and disturbances which periodically occur in each execution will be a means to achieve an improved accuracy and, therefore, in future work also to optimize the control accuracy. In this paper, we present a joint design procedure for observer gains in two independent dimensions, a gain for processing information in the temporal domain during a single execution of the task (also named trial) and a gain for learning in the iteration domain (i.e., from trial to trial).

Keywords: Iterative learning control, Statistical learning, Predictive control for nonlinear systems
Abstract: In this paper, we propose an iterative learning-based optimal control strategy for unknown systems. The system model is assumed to be initially unknown and learned by the Gaussian process regression (GPR) with the historical data collected in the previous iterations. To impose the constant improvement on the control performance and strict constraint satisfaction on the state of the system, we derive a multi-step ahead deterministic bound of the error between the prediction via a learned model and the state of the system, and then use it in the control design. The result from the numerical experiment shows the effectiveness of our method.

Keywords: Process control, Iterative learning control, Manufacturing processes
Abstract: Selective laser melting is a promising additive manufacturing technology enabling the fabrication of highly customizable products. A major challenge in selective laser melting is ensuring the quality of produced parts, which is influenced greatly by the thermal history of printed layers. We propose a Batch-Model Predictive Control technique based on the combination of model predictive control and iterative learning control. This approach succeeds in rejecting both repetitive and non-repetitive disturbances and thus achieves improved tracking performance and process quality. In a simulation study, the selective laser melting dynamics is approximated with a reduced-order control-oriented linear model to ensure reasonable computational complexity. The proposed approach provides convergence to the desired temperature field profile despite model uncertainty and disturbances.

Keywords: Optimal control, Iterative learning control, Sampled data control
Abstract: In this paper, we propose a Policy Gradient method (PGM) to design an optimal controller for discrete-time partially observable systems. The proposed method utilizes the fact that the state of the system can be statically estimated as an algebraic map of finite-length input-output history data. We show that the PGM including the estimation of this map is globally linear convergent for discrete-time partially observable systems. The proof consists of two-steps: First, we show it for SISO systems by using the fact that the covariance matrix of input-output history for SISO systems is invertible. MIMO systems, however, do not have this property because the state estimation from the history is redundant, in other words, the aforementioned map has to be a horizontal matrix. To overcome this problem, we next introduce the modal decomposition to the convergence analysis, thereby guaranteeing the global linear convergence for generic MIMO systems. The effectiveness of the proposed method is shown through a numerical simulation.

Keywords: Transportation systems, Traffic control, Iterative learning control
Abstract: Traffic congestion has become a nightmare to modern life in metropolitan cities. textit{On average, a driver spending textit{X} hours a year stuck in traffic} is one of most common sentences we often read regarding traffic congestion. Our aim in this article is to provide a method to control this seemingly ever-growing problem of traffic congestion. We model traffic dynamics using a continuous-time mass-flow conservation law, and apply optimal control techniques to control traffic congestion. First, we apply the mass-flow conservation law to specify traffic feasibility and present continuous-time dynamics for modeling traffic as a network problem by defining a network of interconnected roads (NOIR). The traffic congestion control is formulated as a boundary control problem and we use the concept of state-transition matrix to help with the optimization of boundary flow by solving a constrained optimal control problem using quadratic programming. Finally, we show that the proposed algorithm is successful by simulating on a NOIR.

Keywords: Predictive control for nonlinear systems, Iterative learning control, Uncertain systems
Abstract: This paper considers a risk-constrained infinite-horizon optimal control problem and proposes to solve it in an iterative manner. Each iteration of the algorithm generates a trajectory from the starting point to the target equilibrium state by implementing a distributionally robust risk-constrained model predictive control (MPC) scheme. At each iteration, a set of safe states (that satisfy the risk-constraint with high probability) and a certain number of samples of the uncertainty governing the risk constraint are available. These states and samples are accumulated in previous iterations. The safe states are used as terminal constraint in the MPC scheme and samples are used to construct a set of distributions, termed ambiguity set, such that it contains the underlying distribution of the uncertainty with high probability. The risk-constraint in each iteration is required to hold for all distributions in the ambiguity set. We establish that the trajectories generated by our iterative procedure are feasible, safe, and converge asymptotically to the equilibrium. Simulation example illustrates our results for the case of finding a risk-constrained path for a mobile robot in the presence of an uncertain obstacle.

Keywords: Optimal control, Iterative learning control, Mechatronics
Abstract: A novel architecture based on the use of two independently actuated wheels is proposed for a rehabilitation exoskeleton with swinging legs. First, the equations of motion of the exoskeleton are derived via Euler-Lagrange principles yielding, by the structure of the mechanics, a purely continuous-time model without impacts. To impose a gait-like motion suitable for rehabilitation purposes, a two-step control scheme is envisioned: a reference generator unit is combined with a low-level feedback control for the individual wheels. For the latter, the dynamical model is employed for emulating, initially via simulation, a Reinforcement Learning approach to compute the optimal scheduling of different (stabilizing) PID controllers, hence paving the way for the future extension to a purely model-free framework for the actual prototype.

Keywords: Aerospace, H2/H-infinity methods, LMI's/BMI's/SOS's
Abstract: The problem of rigid-body attitude tracking in the presence of exogenous disturbances is addressed. Attitude is parameterized using the rotation matrix, an element of the Special Orthogonal Group SO(3), as it provides a singularity-free and unambiguous attitude description. The closed-loop stability and robustness properties of a PD-type state-feedback control law, proposed in literature for attitude tracking using rotation matrices, are investigated using the nonlinear H_{infty} control framework. Starting from a dissipation inequality, sufficient conditions are derived which ensure that the closed-loop energy gain from bounded, finite-energy exogenous disturbances to a specified error signal respects a given upper bound. Then, the sufficient conditions are reformulated using the state and input matrices for the translational double integrator, and recast as linear matrix inequalities (LMIs). Lastly, the reformulated LMIs are used to synthesize controller gains for the proportional and derivative state-feedback terms in the original SO(3) control law. The problem of controller synthesis for a microsatellite is considered as a case study, and the proposed LMI-based procedure is used to synthesize a robust PD-type attitude controller on SO(3).

Keywords: Robust adaptive control, Optimization, Safety critical systems
Abstract: We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive control, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.

Keywords: Electrical power systems, Robust control, Optimization
Abstract: Commercial buildings show a great potential for participating in demand response (DR) programs due to their extensive use of energy-intensive flexible loads such as heating, ventilation, and air conditioning (HVAC) systems. The capability of HVAC systems for responding to automated control and intelligent energy scheduling strategies makes them essential flexibility sources in commercial DR. This capability, in combination with the use of local energy storage systems (ESSs), can substantially enhance the energy management performance. This paper proposes a novel robust model predictive control (MPC) approach for online energy scheduling of multiple commercial buildings comprising individual HVAC systems, ESSs, and non-controllable loads. The proposed approach aims at minimizing the total expected energy costs while ensuring the occupants’ thermal comfort under the presence of uncertainties in electricity market pricing. Moreover, operational constraints of the power grid and buildings’ components are considered. To this aim, we firstly formulate the energy scheduling problem as a min-max robust optimization problem which is transformed into a mixed-integer linear programming problem using duality. Next, we apply MPC to solve the robust optimization problem iteratively based on the receding horizon concept. Finally, we assess the performance of the proposed approach on a simulated realistic case study.

Keywords: Robust adaptive control, H2/H-infinity methods, Linear time-varying systems
Abstract: Due to its simplicity and inexpensive computation, the gradient descent algorithm is one of the most used tools in adaptive control and system identification. Although it has been studied for decades, little has been achieved in terms of tuning methods in the presence of disturbances. One of the main difficulties in its analysis is the time-varying nature of the algorithm. In this work, we contribute in such direction by providing LMI tools for tuning the gradient descent algorithm gain such that a guaranteed upper bound on the L2-gain with respect to parameter variations and measurement noise is achieved. Two academic examples are provided to illustrate the efficient application of the method.

Keywords: Robust control, Uncertain systems, Feedback linearization
Abstract: We study the robust control problem for nonlinear systems using a model-following control (MFC) scheme. The MFC architecture is a two degrees-of-freedom structure consisting of two control loops: the model control loop (MCL) including a nominal model of the process, and the process control loop~(PCL) accounting for modelling errors and disturbances. Both control loops are designed using (partial) feedback linearisation. We design a set-point controller in the MCL and apply a high-gain state feedback in the PCL. We analyse the stability of the overall system and derive robustness bounds for a class of locally Lipschitz uncertainties. We analyse and compare robustness and performance properties to various different control designs. It turns out that the proposed controller is able to stabilise significantly larger uncertainties, while requiring less control effort and shows better tracking performance.

Keywords: Output feedback
Abstract: In this paper, we formalize the Robust Mean Square Stability problem in the presence of deterministic LTI perturbations. In particular, we extend the robust stability notion of mu to include both deterministic and stochastic uncertainties and provide a computable sufficient condition that guarantees Robust Mean Square Stability of the closed-loop. We use an inverted pendulum example where the sensor is subject to link/attention dropout and find the trade-off between the amount of attention and fragility to model uncertainty expressed as the size of the disk margin.

Keywords: Uncertain systems, Robust control, Game theoretical methods
Abstract: A problem of designing reduced order robust dynamic output feedback controller for uncertain linear systems is considered. The controller design aims to guarantee an upper bound on the considered disturbance attenuation performance of the system. For all admissible uncertainties and the worst case of external disturbances, the designed controller ensures finite-time boundedness of system trajectories, while minimizing the upper bound of the considered objective function. Sufficient conditions for the existence of such an output feedback controller are derived in terms of differential matrix inequalities. An iterative algorithm is proposed to synthesize the desired controller.

Keywords: Sliding mode control, Constrained control
Abstract: In plants with saturated actuators, discontinuous integral controllers, such as the super-twisting controller, suffer from a windup effect. In this paper, an anti-windup method for a multivariable super-twisting controller based on the conditioning technique is proposed. The conditioned controller is applied to a thermal multi-input multi-output system. Experimental results show the effectiveness of the proposed approach.

Keywords: Output feedback, Optimization algorithms, Process control
Abstract: Predictive Functional Control (PFC), a simplified and low-cost MPC algorithm, has gained considerable attention for industrial process control in the last two decades. Although with PFC, controller tuning is relatively simple and more meaningful than a PID controller, its efficacy turns poorer for larger prediction horizons--a necessity for over-damped ad non-minimum phase dynamics. This paper proposes a conceptually novel tuning mechanism based on a single choice which is: how much faster or slower than open-loop would you like the closed-loop to converge? Simulations demonstrate that this is a cheap and simple way of effective tuning, by suitably over or under actuating the open-loop control action.

Keywords: Energy systems, Differential algebraic systems, Uncertain systems
Abstract: Abstract—The foundation of advanced battery management is computationally efficient control-oriented models that can capture the key battery characteristics. The selection of an appropriate battery model is usually focused on model order, whereas the effects of input and parameter uncertainties are often overlooked. This work aims to pinpoint the minimum model complexity for health-conscious fast charging control of lithiumion batteries in relation to sensor biases and parameter errors. Starting from a high-fidelity physics-based model that describes both the normal intercalation reaction and the dominant side reactions, Pad e approximation and the finite volume method are employed for model simplification, with the number of control volumes as a tuning parameter. For given requirements on modeling accuracy, extensive model-based simulations are conducted to find the simplest models, based on which the effects of current sensor biases and parameter errors are systematically studied. The results show that relatively loworder models can be well qualified for the control of voltage, state of charge, and temperature. On the other hand, highorder models are necessary for health management, particularly during fast charging, and the choice of the safety margin should also take the current sensor biases into consideration. Furthermore, when the parameters have a certain extent of uncertainties, increasing the model order will not provide improvement in model accuracy.

Keywords: Linear systems, Coverage control, Aerospace
Abstract: The robustness of a class of saturated feedback controllers for a double integrator perturbed by large disturbances with bounded moving average is studied. It is shown, using a Lyapunov-like analysis, that the trajectories of the closed-loop system are ultimately bounded.

Keywords: Control over networks, Biological systems, Autonomous systems
Abstract: The paper studies the spread of a virus over a (possibly) time-varying graph, with the spread being (possibly) worsened by the presence of a shared resource. We propose a time-varying susceptible-infected-water-susceptible (SIWS) model, with the water compartment representing the contamination level in the shared resource. We say that the system is in the disease-free equilibrium (DFE) if none of the nodes (representative of sub-populations, such as cities, districts, etc.) are infected, and the shared resource is contaminant-free. We identify multiple sufficient conditions for exponential convergence to the DFE. Based on one of the aforementioned sufficient conditions, an on/off lockdown strategy that eradicates the infection spread is also proposed. More specifically, we design a switching rule between lockdown and free (i.e., no lockdown) modes to guarantee exponential convergence to the DFE.

Keywords: Cooperative control, Autonomous robots, Robotics
Abstract: Inspired by natural swarm collective behaviors such as colonies of bees and schools of fish, coordination strategies in swarm robotics have received significant attention in recent years. In this paper, a mixed formation control design based on edge and bearing measurements is proposed for networked multi-vehicle systems. Although conventional edge-based controllers have been widely used in many formation tasks, the tracking accuracy may not be guaranteed in some extreme environments as it depends on the quality of the sensors and requires the exact position data of each vehicle. To overcome this limitation, we combine the edge-based controller with a bearing-based method where only relative bearings among the vehicles are required. Depending on the sensing-ability of the robotic platform, this mixed control method can provide an efficient solution to maximise the tracking performance. Both leaderless and leader-follower cases are considered in the protocol design. The stability of the networked multi-vehicle systems under the proposed mixed formation approach is ensured by Lyapunov theory. Finally, we present simulation results to verify the effectiveness of the theoretical results.

Keywords: Robotics, Autonomous robots, Predictive control for nonlinear systems
Abstract: This work aims at designing a visual predictive control (VPC) scheme for a mobile manipulator. It consists in combining image-based visual servoing with model predictive control to benefit from the advantages of both control structures. Two challenges are addressed in this paper: the choice of the visual features and the closed-loop stability. The first ones rely on image moments to improve the end effector positioning precision. The second one is tackled through a terminal constraint coupled with suitable input constraints to reduce the computational burden. Simulation results using ROS and Gazebo validate the proposed approach.

Keywords: Manufacturing processes, Reduced order modeling, Large-scale systems
Abstract: Selective Laser Melting (SLM) is an additive manufacturing technology that builds three dimensional parts by melting layers of metal powder together with a laser that traces out a desired geometry. SLM is popular in industry, however the inherent melting and re-solidification of the metal during the process can, if left uncontrolled, cause excessive residual stress, porosity, and other defects in the final printed parts. This paper presents a control-oriented thermal model of a multi-layer SLM process and proposes a structured model reduction methodology with an associated reduced order model based in-layer controller to track temperature references. Simulation studies demonstrate that the controller is able to prevent layer-to-layer heat buildup and that good closed-loop performance is possible using relatively low-order models.

Keywords: Reduced order modeling, Model/Controller reduction, Differential algebraic systems
Abstract: We present an approach for the regularization of underconstrained interpolants constructed in the Loewner framework for nonlinear descriptor systems. This is accomplished by building a family of systems preserving the property of Loewner equivalence. It is then shown that if the Loewner function is surjective the family contains a subfamily of well-posed interpolants.

Keywords: Reduced order modeling, Identification
Abstract: In this work, we propose a time-domain data-driven technique for model reduction by moment matching of linear systems. We propose an algorithm, based on the so-called swapped interconnection, that (asymptotically) approximates an arbitrary number of moments of the system from a single time-domain sample. A family of reduced-order models that match the estimated moments is derived. Finally, the use of the proposed algorithm is demonstrated on the problem of model reduction of a building model.

Keywords: Cooperative autonomous systems, Modeling, Network analysis and control
Abstract: In this paper we propose a mathematical model for a Transactive Memory System (TMS) involved in the cooperative process of learning a task. The model is based on an intertwined dynamics involving both the individuals level of expertise and the interaction network among the cooperators. The model shows that if all the agents are non-stubborn, then all of them are able to acquire the competence of the most expert members of the group, asymptotically reaching their level of proficiency. Conversely, when dealing with all stubborn agents, the capability to pass on the task depends on the connectedness properties of the interaction graph.

Keywords: Model/Controller reduction
Abstract: We propose a steady-state based moment matching method for model reduction of quadratic-bilinear systems. Considering a large-scale quadratic-bilinear system possessing a stable equilibrium at the origin, the goal of this paper is to design a reduced order model which maintains certain properties of the original system. More precisely, it is required that the reduced order model also possesses a stable equilibrium at the origin and, further, it may be desirable that its relative degree matches that of the original system. We use the notion of nonlinear moments and exploit a formal power expansion to solve this problem. Two different families of reduced order models are provided in this paper and their use is demonstrated on an illustrative numerical example.

Keywords: Identification, Sliding mode control, Algebraic/geometric methods
Abstract: This paper addresses the parameter estimation problem of a non-stationary sinusoidal signal with a time-varying amplitude, which is given by a known function of time multiplied by an unknown constant coefficient. A robust estimation algorithm is proposed for identifying the unknown frequency and the amplitude coefficient in real-time. The estimation algorithm is constructed based on the Volterra integral operator with suitably designed kernels and sliding mode adaptation laws. It is shown that the parameter estimation error converges to zero within an arbitrarily small finite time, and the robustness against bounded additive disturbances is certified by bounded-input-bounded-output arguments. The effectiveness of the estimation technique is evaluated and compared with other existing tools through numerical simulations.

Keywords: Large-scale systems, Modeling, Filtering
Abstract: Reservoir model update is an ill-posed inverse problem that has been considered challenging due to the high-dimensionality (∽ 10⁵ to 10⁶) and the high-nonlinearity of the reservoir dynamics. Recently, the ensemble Kalman filter (EnKF) has been efficiently employed as a feasible alternative to the extended Kalman filter in reservoir history matching and large-scale problems in general. The EnKF is a Monte Carlo implementation of the standard Kalman filter algorithm that reduces the required computational power by searching the solution in an ensemble subspace that is much smaller than the original state-space. Consequently, the performance of the algorithm depends fundamentally on the members of the ensemble. In this paper, a systemic observability-based strategy to sample the EnKF is introduced as an efficient alternative to random sampling. The proposed method is described and assessed on the basis of a twin experiment of a 2D two-phase reservoir, and the results are compared with the original random sampling strategy. In addition, an algorithmic-differentiation-based approach is derived to obtain the linearized model of the extended (augmented state/parameter) nonlinear model directly from the numerical simulator. Numerical experiments show promising results for the proposed observability-based sampling strategy over the random sampling strategy in terms of estimating the permeability fields of the subsurface porous media from noisy sparse production data.

Keywords: Nonlinear system theory
Abstract: In this talk, several key notions of dynamical systems subject to constraints, and more specifically to isolated nonlinearities, are discussed. These constraints can be due to physical, safety or technological constraints affecting the control actuators and/or sensors and it is clear that neglecting these constraints can be a source of undesirable or even catastrophic behavior for the closed-loop dynamical system. Hence, dealing first with nonlinear actuators, we discuss how to account for the nonlinearities to address the stability/performance analysis or controller synthesis. Leveraging on this, we then illustrate how this framework can be expanded and adapted to handle different kinds of nonlinearities, potentially leading to other analysis and synthesis problems, as for example in the context of mechanical and communication constraints. This talk will present some recent elements related to the proposed techniques and illustrate their potential on some applications as the control of anesthesia. Furthermore, it will discuss how to take inspiration from the proposed tools in order to handle other kinds of problems as for example the convergence of some optimization algorithms.

Keywords: Robotics
Abstract: There is a growing demand for robotic systems to be used in environments which can be considered ‘extreme’ or ‘challenging’. The focus of this presentation will be on some of the robotic challenges that are faced in the nuclear industry and an overview of the robots that have been developed at the University of Manchester to address these challenges. Many of the robotic challenges in demanding environments can be divided into either inspection and characterisation or remote handling. Inspection typically requires a mobile robotic platform to be developed that has appropriate sensors integrated on to it, such as LiDARS to provide simultaneous localisation and mapping, and environmental sensors to measure variables of interest, such as radiation and temperature. The presentation will discuss some of the platforms that have been developed and the low-level systems that have been integrated onto the robots. This will include an analysis of the control systems that have been used and the higher-level optimisation systems linked to mission planning. Details of deployments of these robots into active nuclear facilities at Sellafield and Dounreay in the UK, as well as overseas will also be provided. To support the remote handling work, we have been working collaboratively with the UK Atomic Energy Agency’s RACE centre to design a remote glovebox capability. This system enables robotic manipulators to be inserted into a glovebox, rather than human arms, allowing humans to be kept a safe distance away from what might be a radioactive environment within the glovebox. Whilst the initial system was designed to be tele-operated, many of the low-level systems, such as grasping, can now be automated. Finally, a summary of some of the immediate, as well as long-term robotic and control challenges, will be discussed.