Asymptotic Full Actuation Control for A Class of Nonlinear Systems

Abstract

This paper addresses the issue of full actuation control for a class of nonlinear systems, commonly seen in engineering applications. The class of nonlinear systems involves unknown and uncertain parameters, rendering the design of feed-back controllers very challenging, especially for the full actuation control. To tackle the design issue in the presence of parameter uncertainties, the asymptotic full actuation control is proposed, aimed at achieving the full actuation control asymptotically. We first develop an adaptive control algorithm, reminiscent to the well-known backstepping control, to achieve the asymptotic global stabilization for the class of nonlinear systems, in the absence of convergence for the parameter estimates to their respective true values. The well-known recursive least-squares algorithm is then employed to estimate system parameters via sampling the output and other system signals. The asymptotic convergence of the estimates to the true system parameters and hence the asymptotic full actuation are then shown to hold for the class of nonlinear systems under some mild assumptions.