Guaranteed cost neural tracking control for a class of uncertain nonlinear systems using adaptive dynamic programming

Abstract

This paper presents an adaptive dynamic programming-based guaranteed cost neural tracking control algorithm for a class of continuous-time matched uncertain nonlinear systems. By introducing an augmented system and employing a modified cost function with a discount factor, the guaranteed cost tracking control problem is transformed into an optimal tracking control problem. Unlike existing optimal tracking control algorithms often requiring the control matrix to be invertible, the developed control algorithm relaxes this restrictive condition under the assumption that the system is controllable. A single critic neural network (NN) is constructed to approximate the solution of the modified Hamilton–Jacobi–Bellman equation corresponding to the nominal augmented error dynamics. Utilizing the newly developed critic NN, the optimal tracking control can be derived without policy iteration. All signals in the closed-loop system are proved to be uniformly ultimately bounded via Lyapunov׳s direct method. In addition, the developed control scheme is verified to guarantee that the tracking errors converge to an adjustable neighborhood of the origin. Two numerical examples are provided to illustrate the effectiveness and applicability of the developed approach.