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

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

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Daniel Görges, Optimal Control of Switched Systems with Application to Networked Embedded Control Systems (2012), Logos Verlag, Berlin, ISBN: 9783832597009

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Beschreibung / Abstract

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.

Inhaltsverzeichnis

  • BEGINN
  • 1 Introduction
  • 1.1 Hybrid Systems
  • 1.2 Switched Systems
  • 1.3 Stability and Stabilization of Switched Systems
  • 1.4 Optimal Control of Switched Systems
  • 2 Finite-Horizon Control and Scheduling
  • 2.1 Problem Formulation
  • 2.2 Dynamic Programming Solution
  • 2.3 Complexity Reduction via Pruning
  • 2.4 Relaxed Dynamic Programming Solution
  • 3 Receding-Horizon Control and Scheduling
  • 3.1 Problem Formulation
  • 3.2 Explicit Solution
  • 3.3 Stability Analysis
  • 3.4 Reachability Analysis
  • 4 Periodic Control and Scheduling
  • 4.1 Offline Scheduling
  • 4.2 Online Scheduling
  • 5 Conclusions and Future Work
  • 5.1 Conclusions
  • 5.2 Future Work
  • 6 Introduction
  • 6.1 Networked Embedded Control Systems
  • 6.2 Implementation-Aware Control
  • 6.3 Control and Scheduling Codesign
  • 7 Modeling
  • 7.1 NECS Architecture
  • 7.2 Computation and Communication Model
  • 7.3 NECS Model
  • 7.4 Cost Function
  • 8 Control and Scheduling Codesign
  • 8.1 Problem Formulation
  • 8.2 Structural Properties of the NECS Model
  • 9 N0-Step Receding-Horizon Control and Scheduling
  • 9.1 Problem Formulation
  • 9.2 Dynamic Programming Solution
  • 9.3 Suboptimality Analysis
  • 9.4 Explicit Solution
  • 9.5 Stability Analysis
  • 9.6 Reachability Analysis
  • 10 Case Study
  • 10.1 Introduction
  • 10.2 Modeling
  • 10.3 Control and Scheduling Codesign
  • 10.4 Conclusions
  • 11 Conclusions and Future Work
  • 11.1 Conclusions
  • 11.2 Future Work

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