Minimax guaranteed cost control for linear continuous-time systems with large parameters uncertainty

Thls paper presents a method for designing a robust controller for linear systems with structured time-varymg uncertainty The proposed robustness design method results in a simple linear output feedback control law which not only guarantees the asymptotic stability of the closed-loop system, but also minimizes the maximal performance bound over all possible parameter perturbations The problem is solved by employing a constrained optimgatlon method using analytical gradients A comparative study of an example shows the improvements and advantages of the proposed method over previous ones 1 lntroducuon THE DESIGN OF a feedback controller for systems wRh uncertain parameters has been an important sublect in the literature of automatic control theory for many years The robust controller design approach is supenor to other controller design approaches in vanous aspects, which have been well documented by Chang and Peng (1972) Recently, a number of robust controller design methods have been presented (e g Chang and Peng, 1972, Vinkler and Wood, 1978, Thorp and Barmlsh, 1981, Noldus, 1982, Petersen and Hollot, 1986, Wang et al, 1987, Mori and Kokame, 1988, Schmitendorf, 1988, Tsay et al, 1991) Among different methods the Guaranteed Cost Control (GCC) approach, first described by Chang and Peng (1972), has the advantage of giwng a guaranteed cost (GC) of the prescnbed performance index, and thus the system performance degradation incurred by the time-varying uncertainties is guaranteed to be less than this upper bound Vinkler and Wood (1978) have developed a multlstep version of GCC However, the explicit performance bound corresponding to a fixed performance mdex ms not available from their method, losing the most important feature of GCC In this paper the Minimax Guaranteed Cost Control (MGCC) law is proposed The results of the MGCC go beyond the results of previous methods (e g Chang and Peng, 1972, Petersen and Hollot, 1986, Wang et al, 1987, SchmRendorf, 1988, Tsay et al, 1991), in two aspects First, the MGCC, using the Lyapunov