Optimal Control of Switched Systems with Application to Networked Embedded Control Systems

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Logos Verlag Berlin GmbH, 2012 - Computers - 201 pages
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This thesis addresses optimal control of discrete-time switched linear systems with application to networked embedded control systems (NECSs). Part I focuses on optimal control and scheduling of discrete-time switched linear systems. The objective is to simultaneously design a control law and a switching (scheduling) law such that a cost function is minimized. This optimization problem exhibits exponential complexity. Taming the complexity is a major challenge. Two novel methods are presented to approach this optimization problem: Receding-horizon control and scheduling relies on the receding horizon principle. The optimization problem is solved based on relaxed dynamic programming, allowing to reduce complexity by relaxing optimality within predefined bounds. The solution can be expressed as a piecewise linear (PWL) state feedback control law. Stability is addressed via an a priori stability condition based on a terminal weighting matrix and several a posteriori stability criteria based on constructing piecewise quadratic Lyapunov functions and on utilizing the cost function as a candidate Lyapunov function. Moreover, a region-reachability criterion is derived. Periodic control and scheduling relies on periodic control theory. Both offline and online scheduling are studied. The optimization problem is solved based on periodic control and exhaustive search. The online scheduling solution can again be expressed as a PWL state feedback control law. Stability is guaranteed inherently. Several methods are proposed to reduce the online complexity based on relaxation and heuristics. Part II focuses on optimal control and scheduling of NECSs. The NECS is modeled as a block-diagonal discrete-time switched linear system. Various control and scheduling codesign strategies are derived based on the methods from Part I regarding the structural properties of NECSs. The methods presented in Part I and II are finally evaluated in a case study.
 

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Contents

Introduction
3
FiniteHorizon Control and Scheduling
21
Periodic Control and Scheduling
61
26
66
42
72
Conclusions and Future Work
95
Optimal Control of Networked Embedded Control Systems101 6 Introduction
103
Modeling
111
Control and Scheduling Codesign
121
Case Study
137
Conclusions and Future Work
149
A Supplementary Material
155
Bibliography
161
Zusammenfassung
179
Copyright

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