Probabilistic Robust Control System Design by Stochastic Optimization

Open Access
Author:
Li, Xiang
Graduate Program:
Electrical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 26, 2004
Committee Members:
  • Constantino Manuel Lagoa, Committee Chair
  • Mario Sznaier, Committee Member
  • David Jonathan Miller, Committee Member
  • Tom Michael Cavalier, Committee Member
Keywords:
  • probabilistic algorithms
  • stochastic optimization
  • robust control
Abstract:
This dissertation concentrates on recent results on probabilistic robust controller design. In contrast to approaches taken in classical robustness theory, probabilistic robust controller design allows for a small risk of performance violation. This results, in many cases, in a significant reduction of the computational complexity of the controller design cycle and/or a significant reduction of the controller complexity even for a low level of risk of performance violation. In contrast to several of the probabilistic approaches in the control literature, we explore the problems' structure, i.e., convexity, to design more efficient algorithms. For a class of design problems which are convex in controller parameters, we introduce stochastic optimization methods to solve them. For a large class of non-convex problems, we provide a new approach which is shown to converge to the desired robust controller. This is accomplished by choosing an appropriate set of intermediate optimization variables at each iteration. Most of the results provided address the problem of designing robust output feedback controllers, where one directly determines the transfer function of the controller. Preliminary results are also presented on the design of robust static linear state feedback controllers.