TAILIEUCHUNG - AdaptiveControlSystemsp2

| 7 Active identification for control of discrete-time uncertain nonlinear systems J. Zhao and I. Kanellakopoulos Abstract The problem of controlling nonlinear systems with unknown parameters has received a great deal of attention in the continuous-time case. In contrast its discrete-time counterpart remains largely unexplored primarily due to the difficulties associated with utilizing Lyapunov design techniques in a discretetime framework. Existing results impose restrictive growth conditions on the nonlinearities to yield global stability. In this chaper we propose a novel approach which removes this obstacle and yields global stability and tracking for systems that can be transformed into an output-feedback strict-feedback or partial-feedback canonical form. The main novelties of our design are i the temporal and algorithmic separation of the parameter estimation task from the control task and ii the development of an active identification procedure which uses the control input to actively drive the system state to points in the state space that allow the orthogonalized projection estimator to acquire all the necessary information about the unknown parameters. We prove that our algorithm guarantees complete for control purposes identification in a finite time interval whose maximum length we compute. Thus the traditional structure of concurrent on-line estimation and control is replaced by a two-phase control strategy first use active identification and then utilize the acquired parameter information to implement any control strategy as if the parameters were known. 160 Active identification for control of discrete-time uncertain nonlinear systems Introduction In recent years a great deal of progress has been made in the area of adaptive control of continuous-time nonlinear systems 1 2 . In contrast adaptive control of discrete-time nonlinear systems remains a largely unsolved problem. The few existing results 3 4 5 6 can only guarantee global stability under

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