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

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 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 ' 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 ' 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. 1. Introduction Adaptive control theory (Goodwin and Sin 1984) can be used to provide solutions to a variety of control design problems where model uncertainty is due to imprecise knowledge of various parameters. However, it is generally recognised that a specific parametric plant description will never exactly describe a practical system's response, regardless of the choice of the parameters. This is primarily due to neglected dynamics that is not captured by uncertain real parameters. This has motivated the study of the robust adaptive control problem with various approaches. A number of robust adaptive control results have already been obtained (e. 2001) provides another methodology for designing a linear time-invariant feedback controller that optimally reduces the effect of uncertainty on the system, whether …