Sampled-Data Consensus for High-Order Multiagent Systems under Fixed and Randomly Switching Topology

Niu Jie,Li Zhong

doi:10.1155/2014/598965

Abstract

This paper studies the sampled-data based consensus of multiagent system with general linear time-invariant dynamics. It focuses on looking for a maximum allowable sampling period bound such that as long as the sampling period is less than this bound, there always exist linear consensus protocols solving the consensus problem. Both fixed and randomly switching topologies are considered. For systems under fixed topology, a necessary and sufficient sampling period bound is obtained for single-input multiagent systems, and a sufficient allowable bound is proposed for multi-input systems by solving theH∞optimal control problem of certain system with uncertainty. For systems under randomly switching topologies, tree-type and complete broadcasting network with Bernoulli packet losses are discussed, and explicit allowable sampling period bounds are, respectively, given based on the unstable eigenvalues of agent’s system matrix and packet loss probability. Numerical examples are given to illustrate the results.

Highlights

In recent years, coordination of distributed dynamic systems operating over relative sensing/communication networks has attracted the attention of researchers in system theory, biology, and statistical physics, and so forth [1–5]
Zhang and Tian [22] studied the influence of packet loss probabilities on the consensus ability of discrete-time high-order multiagent systems and provided a maximum allowable sampling period bound
This paper studies the consensus problem for high-order multiagent systems with sampled data and packet losses and focuses on looking for a maximum allowable sampling period such that as long as the sampling period is less than this period bound, there always exists a state feedback protocol solving the consensus problem

Summary

Introduction

Coordination of distributed dynamic systems operating over relative sensing/communication networks has attracted the attention of researchers in system theory, biology, and statistical physics, and so forth [1–5]. Zhang and Tian [14] pointed out that for high-order multiagent systems the sampling period should be bounded and proposed an allowable bound based on Discrete Dynamics in Nature and Society given consensus protocol. Zhang and Tian [22] studied the influence of packet loss probabilities on the consensus ability of discrete-time high-order multiagent systems and provided a maximum allowable sampling period bound. This paper studies the consensus problem for high-order multiagent systems with sampled data and packet losses and focuses on looking for a maximum allowable sampling period such that as long as the sampling period is less than this period bound, there always exists a state feedback protocol solving the consensus problem. Pr(⋅) and E(⋅) denote the probability and expected value of a random process, respectively. ‖x‖P is the Euclidian norm (xTPx)1/2

Preliminaries

Problem Formulation

MASPB of Systems under Fixed Undirected Topology

MASPB of Systems under Randomly Switching Topologies

Simulation Examples