Robust tracking control of uncertain nonlinear systems using adaptive dynamic programming

Abstract

In this paper, we develop an adaptive dynamic programming-based robust tracking control for a class of continuous-time matched uncertain nonlinear systems. By selecting a discounted value function for the nominal augmented error system, we transform the robust tracking control problem into an optimal control problem. The control matrix is not required to be invertible by using the present method. Meanwhile, we employ a single critic neural network (NN) to approximate the solu­tion of the Hamilton-Jacobi-Bellman equation. Based on the developed critic NN, we derive optimal tracking control without using policy iteration. Moreover, we prove that all signals in the closed-loop system are uniformly ultimately bounded via Lyapunov’s direct method. Finally, we provide an example to show the effectiveness of the present approach.