Neural Adaptive <i>H</i>_∞ Sliding-Mode Control for Uncertain Nonlinear Systems with Disturbances Using Adaptive Dynamic Programming

Abstract

This paper focuses on a neural adaptive H∞ sliding-mode control scheme for a class of uncertain nonlinear systems subject to external disturbances by the aid of adaptive dynamic programming (ADP). First, by combining the neural network (NN) approximation method with a nonlinear disturbance observer, an enhanced observer framework is developed for estimating the system uncertainties and observing the external disturbances simultaneously. Then, based on the reliable estimations provided by the enhanced observer, an adaptive sliding-mode controller is meticulously designed, which can effectively counteract the effects of the system uncertainties and the separated matched disturbances, even in the absence of prior knowledge regarding their upper bounds. While the remaining unmatched disturbances are attenuated by means of H∞ control performance on the sliding surface. Moreover, a single critic network-based ADP algorithm is employed to learn the cost function related to the Hamilton–Jacobi–Isaacs equation, and thus, the H∞ optimal control is obtained. An updated law for the critic NN is proposed not only to make the Nash equilibrium achieved, but also to stabilize the sliding-mode dynamics without the need for an initial stabilizing control. In addition, we analyze the uniform ultimate boundedness stability of the resultant closed-loop system via Lyapunov’s method. Finally, the effectiveness of the proposed scheme is verified through simulations of a single-link robot arm and a power system.

Keywords

• adaptive dynamic programming
• disturbance observer
• neural networks
• optimal control
• sliding-mode control