DocumentCode :
2970990
Title :
Probabilistic robust design with linear quadratic regulators
Author :
Polyak, B.T. ; Tempo, R.
Author_Institution :
Inst. of Control Sci., Acad. of Sci., Moscow, Russia
Volume :
2
fYear :
2000
fDate :
2000
Firstpage :
1037
Abstract :
In this paper, we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators. We consider systems affected by random bounded nonlinear uncertainty so that classical optimization methods based on linear matrix inequalities cannot be used without conservatism. The approach followed here is a blend of randomization techniques for the uncertainty together with convex optimization for the controller parameters. In particular, we propose an iterative algorithm for designing a controller which is based upon subgradient iterations. At each step of the sequence, we first generate a random sample and then we make a subgradient step for a convex constraint defined by the LQR problem. The main result of the paper is to prove that this iterative algorithm provides a controller which quadratically stabilizes the uncertain system with probability one in a finite number of steps. In addition, at a fixed step, we compute a lower bound of the probability that a quadratically stabilizing controller is found
Keywords :
control system synthesis; convex programming; iterative methods; linear quadratic control; probability; randomised algorithms; robust control; uncertain systems; LMI; LQ regulators; LQR problem; controller design; convex constraint; convex optimization; iterative algorithm; linear matrix inequalities; linear quadratic regulators; probabilistic robust design; quadratic stabilization; random bounded nonlinear uncertainty; randomization techniques; subgradient iterations; uncertain system; uncertain systems; Algorithm design and analysis; Control systems; Iterative algorithms; Linear matrix inequalities; Optimization methods; Regulators; Robust control; Robustness; Uncertain systems; Uncertainty;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
ISSN :
0191-2216
Print_ISBN :
0-7803-6638-7
Type :
conf
DOI :
10.1109/CDC.2000.911987
Filename :
911987
Link To Document :
بازگشت