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

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(1) 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.