Keywords: Multi-Agent Systems, Networked Control Systems, Power Electronics
Abstract: The increasing diffusion of artificial intelligence, i.e., embedding microprocessors and software in commonly used devices, and the understanding that emerging behaviours arise in the presence of interconnected systems are the motivations of the increasing interest of researchers on control, estimation and robustification of complex systems. These systems are often modelled by a set of dynamical agents connected by links representing their interactions. Such a modelling naturally leads to the graph theory as the main tool for both defining the properties of the overall system and designing effective approaches to the control and estimation of multi agent systems (MASs). The distributed control scheme for MASs has been recognised as an effective compromise between the centralised and fully decentralised ones. In this approach the local controllers/estimators are connected just with some neighbourhoods such that the amount of transferred data on the network is decreased and the control is not completely lost even in the case of communication faults. An usual approach to control and estimation in MASs is based on consensus, where the control law is designed to achieve specific tasks (e.g., steering the state of each agent to the same value, flocking, leader following) and it relies on proper interaction rules among neighbourhoods. One interesting application is the control of electrical networks which require that the frequency is everywhere the same and voltages in the nodes must fulfil specific requirements. Because of the intrinsic uncertainty in modelling as well as the presence of external unknown disturbances, the integration of the consensus approach with control techniques having intrinsic robustness property is welcome. Since Variable Structure Control with Sliding Modes has well stated robustness properties, in this talk some of the control and estimation schemes based on this technique are presented and discussed to highlight their pros and possible cons. In particular, the approach based on consensus will be discussed and an application to the control of electrical networks will be presented. Some hints for discussion and open problems will be given as well.

Keywords: First Order Sliding Mode, Application of Sliding Mode Control to other theoretical problems, Automotive Systems
Abstract: To Anti-lock Braking System (ABS) is a widely used device, with applications in a variety of automotive applications. Its operation consists in controlling the wheel slip, thus preventing the wheels from locking up during braking, maximizing the friction force and shortening the braking distance while maintaining maneuverability. The nonlinear nature of the road-tire interaction as well as the uncertainties related to each particular road condition make this a challenging problem. In this paper, a new design is proposed to control the wheel slip. An extremum seeking controller strategy for the external loop is designed to estimate the optimum slip value to each road condition in real time, and a sliding mode control aproach for the internal loop is employed to regulate the desired slip value. The stability analysis of the closed-loop system is developed. Numerical simulations show a good performance of the proposed control scheme.

Keywords: Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Application of Sliding Mode Control to other theoretical problems, First Order Sliding Mode
Abstract: In this paper, a new multivariable extremum seeking control approach based on sliding mode and cyclic search for static nonlinear maps is proposed. Classical and even similar methods are characterized by slow convergence rates and local or semi-global convergence/stability properties. Whereas the proposed approach guarantees global and fast convergence to a neighborhood of the extremum of the objective function, because (1) it does not employ averaging and singular perturbation analysis tools and (2) in the control law, a sliding manifold with integral action is designed, which allows the output rapidly to track the reference signal regardless of recurrent changes of the searching direction. Stability and convergence properties are demonstrated using non-linear systems' analysis tools. Furthermore, a rigorous analysis of the residual oscillations around the extremum is carried out. Numerical simulations are performed to illustrate the theoretical results and highlight the advantages of the proposed strategy in terms of robustness, fast convergence and small residual errors.

Keywords: Sliding Mode based Observation, First Order Sliding Mode, Fault Detection
Abstract: For uncertain linear system subjected to uniformly bounded unknown inputs it is presented a novel finite-time unknown input first-order sliding-mode observer. The strategy involves the design of a pair of quadratically stable first-order sliding-mode observers, aimed to guarantee the robustness to non-smooth unknown inputs and the finite-time convergence to zero of the output estimation errors. Then, the exact estimation of the unmeasured states is achieved in a fixed-time since the sliding motion is established through the design of an auxiliary output consisting of a delayed linear-combination of the estimations provided by the above-mentioned pair of observers. To confirm the effectiveness of the proposed scheme, along with a sketch of the proof of its convergence characteristics, a detailed numerical comparison analysis with the existing first-order sliding-mode competitor observers is illustrated.

Keywords: Sliding Mode based Observation, Higher Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control
Abstract: The present paper proposes a novel specified-time stable second-order sliding-mode dynamic system, formulated through a modification of the super-twisting algorithm. A broader definition of finite-time stability with specified convergence time, denominated here as specified-time stability, is provided. We devise a state observer for a damped simple pendulum to test the proposed algorithm’s efficacy. The simulations illustrate that the estimation errors are taken to the origin at the specified settling time, with proper choice of the observer parameters.

Keywords: Networked Control Systems, Higher Order Sliding Mode
Abstract: This paper presents the drive-response synchronization problem for competitive neural networks (CNNs) in predefined time. The CNN response system is considered in presence of deterministic disturbances satisfying Lipschitz conditions and in presence of both stochastic white noises and deterministic disturbances satisfying Lipschitz conditions. The effect of deterministic disturbances and stochastic noises is suppressed by designing a time-varying continuous control input driving the CNN synchronization error at the origin for an a priori predefined time, independently of the CNN initial conditions, deterministic disturbances, and stochastic noises. Finally, numerical simulations are conducted to demonstrate validity of the obtained theoretical results and effectiveness of the presented synchronization scheme.

Keywords: First Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Fault Detection
Abstract: Several biomedical applications can be achieved using two-magnet driving microrobots since they are easy to manipulate and can be accessed within complex microenvironments. To precisely control the movement of microrobots actuated by two permanent magnets, an event-triggered sliding mode control (SMC) technique is presented. This technique uses a minimal amount of control force and eliminates the external disturbances. It shows the microrobots are attracted toward the sliding surface and remain within it despite disturbances. In addition, this paper explores the stabilization of microrobots under input constraint. Finally, simulation results are used to demonstrate the efficiency of the proposed theory.

Keywords: Higher Order Sliding Mode, Application of Sliding Mode Control to other theoretical problems, Homogeneity Methods for Variable Structure Systems & Sliding Mode Control
Abstract: Two recent results on earthquake control are summarized. A simplified model of an earthquake phenomenon is addressed by means of a cascade system of a 1D wave equation, representing the fault slip and wave propagation, and a 1D diffusion equation, representing the actuator dynamics as a diffusion process. In order to avoid a fast slip (earthquake-like behaviour), the control is designed to follow a slow reference. The control strategies are presented separately for both Partial Differential Equations (PDEs). For the wave PDE, a homogeneous boundary tracking control is developed to achieve exponential Input to State Stability (eISS) of the error closed-loop dynamics. For the diffusion PDE, Proportional Integral (PI) and a discontinuous integral term are coupled to exponentially stabilize the error origin despite model uncertainties and perturbations. Simulations are additionally conducted to support the robustness and stability properties of the proposed control algorithms, by separately, obtaining critical remarks that will lead to the design of the single control for the cascade system in a future stage.

Keywords: Process Industry, First Order Sliding Mode, Application of Sliding Mode Control to other theoretical problems
Abstract: This paper proposes the combination of a sliding-mode controller (SMC) with a proportional and integral controller (PI) for moisture in the soil, aiming at precision irrigation. The dynamics of the water propagation into the soil is modeled by the Richards equation, that is a nonlinear parabolic partial differential equation (PDE). The SMC of the average moisture in a layer near the interface with the atmosphere allows the rejection of external disturbances such as water evaporation or rain. A master PI control loop allows the non-collocated sensor and actuator, such that the moisture can be controlled at any desired depth. Simulation results illustrate the nonlinear dynamics of the water infiltration in the soil, and the performance of the moisture controllers.

Keywords: First Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Power Electronics
Abstract: The use of fractional operators in control theory is recent and new approaches are emerging more and more. The existing literature shows improvement in control performance when using fractional controllers. One of the main reasons for this improvement is due to the greater number of control parameters, inserted by the exponents that represents the fractional-order of the integral or derivative operators. Another interesting feature of fractional calculus is that it is often used to describe phenomena with memory. In this context, this paper proposes a comparison between Sliding Mode Controls of Integer-Order (SMC) and Fractional-Order (FOSMC). Sliding Mode Control is one of the most successful approaches in dealing with uncertainties and one of the most efficient in nonlinear dynamics. The problem chosen for the application of the controllers is a nonlinear bi-stable vibration energy harvesting system, since controlling this system makes the relationship between generated energy and consumed energy (control effort) very important, being an ideal situation to evaluate and compare the performance of the two methods. A novelty in this paper is the use of the Cross Entropy optimization method to obtain the set of optimal parameters (best performance) in the SMC and FOSMC controllers. The result of the optimization tests reinforces the improvement in the use of the fractional operator reducing the control effort by up to 93% when compared to the integer-order controller. The Cross Entropy method was also very effective for controllers with a large number of adjustment parameters.

Keywords: Homogeneity Methods for Variable Structure Systems & Sliding Mode Control, Mobile Robots, Application of Sliding Mode Control to other theoretical problems
Abstract: A novel controller based on variable-structure principle is proposed for satellite attitude control. This variable-structure controller does not lead to a sliding mode and, respectively, to chattering, which makes it suitable for practical implementation. Comparative analysis based on numerical simulations shows that significant improvement over the classical PD controller in transient performance is possible using the proposed controller.

Keywords: Higher Order Sliding Mode, Multi-Agent Systems, Application of Sliding Mode Control to other theoretical problems
Abstract: Control of perturbed coupled nonlinear six degree-of-freedom systems, such as that of a spacecraft formation, augmented by actuator dynamics is considered. In a space environment, significant uncertainty may exist, leading to inadequate information on disturbance torques and forces and their unknown associated bounds. Thus, the methods of adaptive continuous higher-order sliding mode control (ACHOSM) are explored to solve these problems. In this work, we show that ACHOSM methods are superior as compared to PD-plus controller through simulations.

Keywords: Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Application of Sliding Mode Control to other theoretical problems, First Order Sliding Mode
Abstract: This paper introduces optimal sliding mode control with a predefined upper bound of settling time (PUBST) for stabilizing uncertain nonlinear dynamical systems. Sufficient conditions for optimality are given, which involve a Lyapunov function that satisfies a certain differential inequality guaranteeing PUBST. Further, for guaranteeing optimality it also satisfies the Hamilton–Jacobi–Bellman equation. Moreover, an integral sliding mode control is integrated with the optimal PUBST control to make the system insensitive to the matched type of bounded perturbations. The validity of the proposed method is demonstrated with a practical example of a rigid body aircraft system.

Keywords: Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Application of Sliding Mode Control to other theoretical problems, First Order Sliding Mode
Abstract: Stability and stabilization with predefined upper bounded settling time (PUBST) for the nonlinear nonautonomous systems are studied in this paper. The concepts of input to state stability are extended to the control problems exhibiting the property of convergence with PUBST (PUBSTC). The Lyapunov functions for depicting the presence of PUBST are introduced and reffered to as PUBSTC Lyapunov functions. Furthermore, a robust sliding mode control allowing the convergence with PUBST is designed for the nonlinear systems with matched disturbances and referred to as PUBSTC-SMC. These developments are accompanied by several academic examples for better understanding.

Keywords: First Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control
Abstract: This paper considers the problem of placing all the poles arbitrarily for a linear time-invariant plant with (the linear part of) sliding mode control. We solve this problem in two ways. In the first approach, we design a sliding mode control by specifying the desired pole locations. The closed-loop system under this control law has all eigenvalues at the desired places. In the second approach, the sliding mode control is designed from a given state feedback gain so that all the poles of the closed-loop system are placed at the same location as that of the state feedback controller. Here, we provide a necessary and sufficient condition for the existence of a linear gain using the sliding mode control to achieve the desired pole assignment. This condition is always fulfilled for the single input case whereas it is only applicable for certain multi-input scenarios that meet the conditions stated in the paper. In both the approaches, one can place the closed-loop poles with the proposed sliding mode control at any arbitrary location in the left half of the complex plane, unlike with traditional design, where m poles are at the origin with m being the number of control inputs. A numerical example illustrates the proposed design methodology for sliding mode control.

Keywords: Adaptive Sliding Mode, First Order Sliding Mode, Chattering Analysis
Abstract: In this paper, an explicit Euler discretization scheme is used to obtain a discrete-time version of the indirect adaptive sliding mode control for an uncertain scalar linear system with an unknown parameter. The unknown parameter is linear in the state, the input disturbance is assumed to be bounded. An improper discretization of indirect adaptive sliding mode algorithms may lead to unbounded parameter estimates, which then result in an unbounded state. We modify the algorithm by using a priori knowledge of the location of the unknown parameter such that boundedness of the trajectory can be guaranteed. This entails obtaining a stabilizing condition on the sampling interval and calculating the bound of the state trajectory. The proposed discretization is illustrated by simulation results of an academic scalar system.

Keywords: Adaptive Sliding Mode
Abstract: Industrial environments are full of phenomena that represent enormous challenges to control engineers. Sometimes, a simple process such as the liquid level control in an arrangement of cylindrical tanks imposes several constraints that require continuous human supervision. Most of the traditional control techniques in the industry are linear, although the industrial plant is nonlinear. This fact, associated with disturbances, uncertainties in the parameters, and coupling, among others, imposes constraints on the traditional controllers, which, sometimes, allows them to show good response in a limited operation point. Thus, this work presents a robust nonlinear controller for industrial cylindrical tanks. It does not have constraints related to operation points and is robust to several industrial phenomena. To verify the performance of the proposed controller, we applied it for the quadruple tank process. The work beyond the proposed controller presents results of stability analysis and simulations.

Keywords: Fault Detection, Electric Drives And Actuators, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control
Abstract: In this paper, a sliding-mode fault tolerant control (FTC) based on actuator switching is proposed for a class of n-link robotic manipulators with actuator failures and disturbances, for which, each joint is driven by an actuator with several healthy actuators as backups. First, a sliding-mode controller is designed, and then based on the value of the sliding surfaces, a set of monitoring functions (MFs) is constructed to tackle those serious actuator failures. It is shown that with the proposed scheme, all signals of the closed-loop system are bounded. A two-link robotic manipulator example is used to verify the effectiveness of the control scheme.