Adaptive prescribed‐time control for nonlinear systems with uncertain time‐varying parameters and control gains

Abstract This article investigates the adaptive prescribed‐time dynamic surface control (PTDSC) problem for a class of nonlinear strict‐feedback systems with uncertain time‐varying parameters and unknown control gains. First, the spatiotemporal transformation method is employed to eliminate the effect of the unknown control gains in the nonlinear systems. Then, to deal with the problem of “complexity explosion” in the backstepping design framework, a novel dynamic surface control (DSC) strategy is proposed by adding a time‐varying gain to the nonlinear filter. Furthermore, under the Lyapunov stability theory, the rational adaptive laws are cleverly designed to eliminate the influence of the unknown time‐varying parameters. The PTDSC strategy proposed in this paper can guarantee that all the states of the nonlinear systems and the estimate errors of the nonlinear filters converge to zero within the prescribed time. Lastly, a simulation example is provided to demonstrate the effectiveness of the proposed control algorithm.