Asymptotic State Regulation of Fully Actuated Systems With Time-Varying Parameters and Perturbed Input Matrices

Asymptotic state regulation of fully actuated systems (FASs) with time-varying unknown parameters, perturbed input matrices, and nonlinear uncertainties is considered. Compared to the closely related results on FASs with time-varying parameters, the requirement that the time-varying parameters are differentiable and the assumptions imposed on their derivatives in those works are no longer needed in this article, which means that many types of time-varying parameters that were difficult to handle by previous methods, such as those that are continuous and bounded but not differentiable, can now be handled. Furthermore, inspired by the congelation of variables method, a novel robust adaptive method is proposed, which achieves the global asymptotic convergence of the state variables instead of the global boundedness obtained in previous methods, and guarantees the global boundedness of the estimation. In the developed controller, the adaptive part compensates for time-varying parameters, and the robust part overcomes the effects of incomplete compensation and other remaining uncertainties. Moreover, a parallel extension of the developed method to the disturbed case and a discussion on parameter selection are given. Finally, the proposed method is successfully applied to the control of resonant circuit systems and Norrbin ship steering systems.