ADAPTIVE CONTROLLER-DESIGN FOR TRACKING AND DISTURBANCE ATTENUATION IN PARAMETRIC STRICT-FEEDBACK NONLINEAR-SYSTEMS

The authors develop a systematic procedure for obtaining robust adapti ve controllers that achieve asymptotic tracking and disturbance attenu ation for a class of nonlinear systems that are described in the param etric strict-feedback form and are subject to additional exogenous dis turbance inputs, Their approach to adaptive control is performance-bas ed, where the objective for the controller design is not only to find are adaptive controller, but also to construct an appropriate cast fun ctional, compatible with desired asymptotic tracking and disturbance a ttenuation specifications, with respect to which the adaptive controll er is ''worst case optimal.'' In this respect, they also depart from t he standard worst case (robust) controller design paradigm where the p erformance index is fixed priori. Three main ingredients of the paper are the backstepping methodology, worst case identification schemes, a nd singular perturbations analysis. Under full state measurements, clo sed form expressions have been obtained for are adaptive controller an d the corresponding value function, where the latter satisfies a Hamil ton-Jacobi-Isaacs equation (or inequality) associated with the underly ing cost function, thereby leading to satisfaction of a dissipation in equality for the former. An important by-product of the analysis is th e finding that the adaptive controllers that meet the dual specificati ons of asymptotic tracking and disturbance attenuation are generally n ot certainty-equivalent, but are asymptotically so as the measure quan tifying the designer's confidence in the parameter estimate goes to in finity. To illustrate the main results, the authors include a numerica l example involving a third-order system.