Norm Based Optimally Robust Control of Constrained Discrete Time Linear Systems

Abstract

Most realistic control problems involve both some type of time-domain constraints and model uncertainty. However, the majority of controller design procedures currently available focus only on one aspect of the problem, with only a handful of method capable of simultaneously addressing, albeit in a limited fashion, both issues. In this paper we propose a simple design procedure that takes explicitly into account both time domain constraints and model uncertainty. Specifically, we use a operator norm approach to define a simple robustness measure for constrained systems. The available degrees of freedom are then used to optimize this measure subject to additional performance specifications. We believe that the results presented here provide a useful new approach for designing controllers capable of yielding good performance under substantial uncertainty while meeting design constraints.