Last updated on July 3, 2015. This conference program is tentative and subject to change
For Lurye systems this work culminated in the class of multipliers proposed by O'Shea in 1966 and formalised by Zames and Falb in 1968. The superiority of this class was quickly and widely accepted. Nevertheless the result was ahead of its time as graphical techniques were preferred in the absence of readily available computer optimization. Its first systematic use as a stability criterion came twenty years after the initial proposal of the class. A further twenty years have been required to develop a proper understanding of the different techniques that can be used. In this long gestation some significant knowledge has been overlooked or forgotten. Most significantly, O'Shea's contribution and insight is no longer acknowledged; his papers are barely cited despite his original parameterization of the class.
This tutorial paper aims to provide a clear and comprehensive introduction to the topic from a user's viewpoint. We review the main results: the stability theory, the properties of the multipliers (including their phase properties, phase-equivalence results and the issues associated with causality), and convex searches. For clarity of exposition we restrict our attention to continuous time multipliers for single-input single-output results. Nevertheless we include several recent significant developments by the authors and others. We illustrate all these topics using an example proposed by O'Shea himself.
This paper also proposes an ellipsoidal outer approximation of the manipulator's workspace. This approximation can be utilized in an inverse kinematics algorithm. Some numerical experiments will show the validity of the proposed approximation algorithm.
Using recent results of X. Dai on the asymptotic growth rate of such systems, we introduce the concept of multinorm as an algebraic tool for stability analysis.
We conjugate this tool with two families of multiple quadratic Lyapunov functions, parameterized by an integer T >= 1, and obtain converse Lyapunov Theorems for each.
Lyapunov functions of the first family associate one quadratic form per state of the automaton defining the switching sequences. They are made to decrease after every T successive time steps. The second family is made of the textit{path-dependent} Lyapunov functions of Lee and Dullerud. They are parameterized by an amount of memory (T-1) >= 0.
Our converse Lyapunov theorems are finite. More precisely, we give sufficient conditions on the asymptotic growth rate of a stable system under which one can compute an integer parameter T >= 1 for which both types of Lyapunov functions exist.
As a corollary of our results, we formulate an arbitrary accurate approximation scheme for estimating the asymptotic growth rate of switching systems with constrained switching sequences.
We formulate the trajectory planning as an optimal control problem (OCP) which is discretized into a large scale nonlinear program (NLP) solved by direct multiple-shooting using the CasADi toolkit and the NLP solver IPOPT. The optimal solution is compared to a classical jerk limited bang-bang solution based on the rigid body model but not taking into account the vibrational modes.
The comparison of both approaches leads to a paradigm shift: instead of focusing on the classical trade-off between performance (cycle time) and precision (residual vibrations), it is more appropriate to deal with trade-offs between modeling uncertainties and residual vibrations. The residual vibrations can be completely eliminated if its model is perfectly known.
While MPC can produce an improved performance over standard strategies, many approaches taken in the literature are not easily scalable and do not allow for intuitive reconfiguration. Two possible MPC strategies for control of a building heating system are designed and compared here. In the first strategy, the thermal comfort of the occupants of the building is balanced with the energy use in a single objective function. In the second strategy, a lexicographic, multi-objective formulation is used to split the competing goals of energy reduction and thermal comfort. The strategies are assessed in a validated simulation platform in terms of energy efficiency, comfort performance, scalability and reconfigurability in times of system changes or faults.
Tools for CCS include gramian-based Interaction Measures (IMs), initially defined for linear systems. Since a trending research topic is the derivation of IMs for nonlinear systems, a decision of the designer is therefore the approach to the problem in the linear or nonlinear framework.
For this end, a method is discussed that determines the degree of nonlinearity of a system based on a specially tailored experiment, and thus enables the selection of the correct framework for the analysis.
The novelty is in the estimation of two gramian-based IMs with confidence bounds from the tailored experiment which is applicable if the process is revealed to be weakly nonlinear.
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