GLOBAL ADAPTIVE OUTPUT-FEEDBACK CONTROL OF NONLINEAR-SYSTEMS .2. NONLINEAR PARAMETERIZATION

This paper addresses the problem of designing global output-feedback robust stabilizing controls for a class of single-input, single-output minimum phase uncertain nonlinear systems with known and constant relative degree. They are assumed to be linear with respect to the input and nonlinear with respect to an unknown constant parameter vector belonging to a known compact set. The class of nonlinear systems is determined by geometric conditions. The nonlinearities are restricted to depend, in suitable coordinates, on the output only: growth conditions, such as sector or Lipschitz, are not required. The nonlinearities may be uncertain and are only required to be bounded by known smooth functions. The order of the robust compensator is equal to the relative degree minus one and is static when the relative degree is one. A self-tuning version of the robust control capable of achieving set point regulation is then developed in which the control gains are tuned by an output-feedback adaptive algorithm. When the parameter vector enters linearly, the self-tuning regulator does not require the knowledge of parameter bounds and guarantees set point regulation for the same class of systems considered in the companion paper [9]: under the same set of assumptions the algorithm in [9] still has the advantage of guaranteeing tracking, while the self-tuning regulator is simpler and more robust with respect to uncertain nonlinearities.