Finite-Horizon $H_{\infty }$ Consensus Control of Discrete Time-Varying Multiagent Systems: A Dynamic Event-Based Learning Approach

Abstract

This paper addresses the finite-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus problem for general discrete time-varying multi-agent systems with energy-bounded external disturbances and limited network bandwidth resource. A dynamic event-based learning approach is proposed to produce a dynamic discrete-time event-triggered scheme and a dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol. Based on the local state information, the dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol is developed to guarantee the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus of the general discrete time-varying multi-agent systems with external disturbances. Besides, a novel criterion is established by employing the Lyapunov theory and considering the special dynamic triggering constraint, and the corresponding recursive learning algorithm is developed. In contrast with the previous works, the proposed dynamic event-based approach results in less network bandwidth utilization, and the novel recursive algorithm brings less conservatism of the designed controller. Finally, the effectiveness of the corresponding algorithm and the advantages of the proposed dynamic event-based approach are testified by a numerical simulation.