Probabilistic robust design with linear quadratic regulators

✍ Scribed by B.T. Polyak; R. Tempo

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 126 KB
• Volume: 43
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(01)00117-7

✦ Synopsis

In this paper, we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators (LQR). We consider systems a ected 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 ÿrst generate a random sample and then we perform a subgradient step for a convex constraint deÿned 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 ÿnite number of steps. In addition, at a ÿxed step, we compute a lower bound of the probability that a quadratically stabilizing controller is found.