A composite adaptive robust control for nonlinear systems with model uncertainties

Abstract

AbstractThis article is concerned with a composite adaptive robust control (CARC) for non‐strict feedback nonlinear systems with model uncertainties including parametric uncertainties and uncertain nonlinearities. It is assumed that the model uncertainties of the nonlinear system are bounded but unknown. Firstly, prescribed tracking performance is achieved by the CARC control law even the unknown parameters are time‐varying. This is accomplished firstly by designing a discontinuous projection that confines the unknown parameters in an estimated region. Then the robustness of the closed‐loop system is guaranteed by leveraging the deterministic robust control philosophy. Also, a command filter has been designed to avoid computing complex derivatives of virtual control law in the backstepping procedure. Secondly, a composite adaptation law that intelligently integrates information of both tracking error and prediction error is constructed for improving the performance of controllers. The high adaptation gain of CARC leads to higher parameter convergence speed and smaller tracking errors. Moreover, if the actual parameters are within the design range, asymptotic stability can be achieved in presence of parametric uncertainties only. In addition, exponential convergence of tracking errors and parameters can be shown under certain conditions. Finally, numerical examples are made to validate the superiority and effectiveness of the proposed control scheme.