Robust Gradient-Based Adaptive Control of Nonlinearly Parametrized Plants

Abstract

Most of the contributions in adaptive control literature assume that the system dynamics is linearly parametrizable, and a certainty equivalence principle is exploited to guarantee global stability and asymptotic convergence of tracking error to zero. Although linear-in-the-parameters (LIP) assumption is reasonable for a large class of dynamics, there exists a considerable number of real world systems, involving complex dynamics, where nonlinear parametrizations are inevitable. Previous research has shown that classical gradient-based adaptive designs with the certainty equivalence principle do not perform satisfactorily for nonlinear-in-the-parameter (NLIP) systems, and may, in fact, cause instability in many situations. This letter is an attempt toward addressing this issue by a novel non-certainty equivalence adaptive control design, where the classical gradient-based adaptive algorithm is used to tackle the LIP component of the NLIP dynamics, while a robust compensator, appended to the controller, accounts for the linearization error. The designed controller ensures global uniformly ultimately bounded stability of the error dynamics. Simulation results on a model of biochemical process, involving NLIP dynamics, are provided to validate the theoretical development.