Robust adaptive control of uncertain systems with guaranteed robust stability and asymptotic performance

摘要

This article presents a robust adaptive control scheme for a discrete-time plant that is subjected to both coprime factor perturbations and unknown exogenous disturbances. With the proposed control scheme, all the variables in the closed-loop system are bounded in the presence of the perturbations and disturbances, and an a priori computable upper bound on the size of the nonparametric dynamical uncertainty, for which stability is ensured, is provided. Moreover, one can guarantee a priori bound on the asymptotic performance of the overall adaptive system which is arbitrarily close to that of the corresponding nonadaptive control system. In addition, it is shown that the l optimal robust controller design is continuous as a map from the plant to the optimal closed-loop solution. Furthermore, if the set of plants is compact, then the l_1 optimal robust controller design is uniformly continuous on the set of plants. These properties are necessary for analysing the interplay between identification and control in the overall adaptive system.