Robust adaptive control for a class of mimo nonlinear systems

Abstract

The design of stabilizing controllers for nonlinear plants with unknown nonlinearities is a challenging problem. The inability to identify the nonlinearities on-line or off-line accurately motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant nonlinearities. The price paid in such case, could be lack of theoretical guarantees for global stability, and/or nonzero tracking or regulation error at steady state. In this paper a nonlinear robust adaptive control algorithm is designed and analyzed for a class of multi-input multi-output nonlinear systems with unknown nonlinearities. The controller guarantees closed loop semi-global stability and convergence of the tracking error to a small residual set. The size of the residual set for the tracking error depends solely on design parameters, which can be chosen to meet desired upper bounds for the tracking error. Consequently the proposed methodology provides a design procedure to meet apriori specified performance guarantees for the steady state tracking error.