Consensus of Switched Multiagent Systems under Relative State Constraints

Qingling Wang

doi:10.1155/2017/5767495

Abstract

The consensus problem is presented for the switched multiagent system (MAS), where the MAS is switched between continuous- and discrete-time systems with relative state constraints. With some standard assumptions, we obtain the fact that the switched MAS with relative state constraints can achieve consensus under both fixed undirected graphs and switching undirected graphs. Furthermore, based on the absolute average value of initial states, we propose sufficient conditions for consensus of the switched MAS. The challenge of this study is that relative state constraints are considered, which will make the consensus problem much more complex. One of the main contributions is that, for the switched MAS with relative state constraints, we explore the solvability of the consensus problem. Finally, we present two simulation examples to show the effectiveness of the results.

Highlights

Inspired by the works of [1, 2], the attention to the consensus problem of the multiagent system (MAS) has grown in the research community
One of the main contributions is that, for the switched MAS with relative state constraints, we explore the solvability of the consensus problem
The consensus problem was first discussed for first order [12,13,14,15] and generalized to second order [16, 17], general linear dynamics [18, 19], and nonlinear dynamics [20, 21] in communication networks and sensor networks

Summary

Introduction

Inspired by the works of [1, 2], the attention to the consensus problem of the MAS has grown in the research community. Many dynamical systems interact with the environment or have physical limitations As such, they are often affected by saturation constraints that can disrupt consensus. [31] studied the stability problem of single switched systems, while the consensus of a switched MAS was presented in [32, 33]. By using some standard assumptions, the consensus shall be reached for the switched MAS under fixed undirected graph with the assumption that the absolute value of initial states is bounded. The main contributions are stated as follows: Firstly, compared with existing results [32], the challenge of this study is Complexity that state constraints are considered in the switched MAS, which increases the complexity.

Problem Formulation

Main Results

Simulations

Conclusions