ADAPTIVE OUTPUT-FEEDBACK CONTROL OF NONLINEAR-SYSTEMS REPRESENTED BY INPUT-OUTPUT MODELS

We consider a single-input-single-output nonlinear system which can be represented globally by an input-output model, The system is input-ou tput linearizable by feedback and is required to satisfy a minimum pha se condition, The nonlinearities are not required to satisfy any globa l growth condition, The model depends linearly on unknown parameters w hich belong to a known compact convex set. We design a semiglobal adap tive output feedback controller which ensures that the output of the s ystem tracks any given reference signal which is bounded and has bound ed derivatives up to the nth order, where n is the order of the system , The reference signal and its derivatives are assumed to belong to a known compact set, It is also assumed to be sufficiently rich to satis fy a persistence of excitation condition, The design process is simple , First we assume that the output and its derivatives are available fo r feedback and design the adaptive controller as a state feedback cont roller in appropriate coordinates. Then we saturate the controller out side a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that wh en the speed of the high-gain observer is sufficiently high, the adapt ive output feedback controller recovers the performance achieved under the state feedback one.