Event-triggered H∞ consensus for uncertain nonlinear systems using integral sliding mode based adaptive dynamic programming

Abstract

This paper studies a robust optimal consensus problem for uncertain nonlinear multi-agent systems, where the uncertainties include both input and external disturbances. Adaptive distributed observer, integral sliding mode control and H_∞ adaptive dynamic programming are integrated to obtain a sub-optimal control protocol for each follower. Firstly, an adaptive distributed observer is designed for state estimation of the leader, which serves as the reference of the ADP algorithm. Then, an H_∞ ADP algorithm is presented to make each follower track the reference in real-time. An integral sliding manifold-based discontinuous control is designed to eliminate the matched uncertainty, and continuous control is obtained by solving the Hamilton-Jacobi-Isaac equation under the H_∞ tracking framework. Two event-triggered rules are developed to relieve the communication pressure. For simplicity, a critic-only structure is used to numerically implement the proposed algorithm, and a concurrent learning technique is employed to update weights of neural networks. All signals in the closed-loop system are proven to be uniformly ultimately bounded. Finally, a simulation is conducted to demonstrate demonstrates the effectiveness of the method.

Keywords: control; Adaptive dynamic programming; Concurrent learning; Event-triggered control; Multi-agent systems.