Event-triggered Containment Control for a Class of High-order Nonlinear Multi-agent Systems

This paper addresses the event-triggered containment control for a class of multi-agent systems, where the dynamics of agents are described by high-order nonlinear systems. Due to the complexity of high-order nonlinear systems, the event-triggered containment control problem is hard to solve, and the main difficulty lies in how to exclude the Zeno behavior. To this end, optimized event-triggered conditions are designed by applying the error threshold for centralized and decentralized cases, respectively. It is proven that under the designed protocols, all the followers can asymptotically converge to the convex hull spanned by multiple leaders and the Zeno behavior can be avoided. Finally, a numerical simulation is given to verify the effectiveness of the presented protocols.

1 Introduction

In the past decades, cooperative control of multi-agent systems (MASs) has raised considerable concern due to the inspiration from animal group behaviors and its widespread application in various fields. So far great progress has been made in this area, such as consensus control, leader-following control, containment control, and so on [1]–[3]. As is known to all, the consensus problem is one of the most fundamental and critical subject in the study of MASs. Consensus control aims to make a group of agents reach an agreement on a common value by designing appropriate protocols. MASs can be classified into leaderless systems and leader-following systems. For a system which includes multiple leaders, the consensus-liked problem will be extended to the containment control problem.