Adaptive Control Design for a Class of Uncertain High-Order Nonlinear Systems with Time Delay

TLDR: In this article, a continuous adaptive state-feedback controller for a class of uncertain high-order nonlinear systems with time delays is proposed, under somewhat necessary restrictions on the system nonlinearities, by the method of adding a power integrator and the related adaptive technique.

Abstract: This paper is concerned with adaptive stabilization for a class of uncertain high-order nonlinear systems with time delays. To the authors' knowledge, there has been no analogous result. Hence during investigation, the conditions on delay effect and the control design framework should be established for the first time. In this paper, under somewhat necessary restrictions on the system nonlinearities, by the method of adding a power integrator and the related adaptive technique, a procedure is developed to design the continuous adaptive state-feedback controller without overparametrization. Moreover, the uniform stability and convergence of the resulting closed-loop system are rigorously proven, with the aid of a suitable Lyapunov-Krasovskii functional. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical result.