Abstract

This paper studies the scaled consensus control problem of networked multi-agent systems with linear coupling dynamics and external disturbances. A state feedback based distributed H∞ sliding mode control (SMC) approach is firstly established by designing integral-type sliding function, and a linear matrix inequality (LMI) based sufficient condition is given, which can guarantee the states of all agents achieving scaled consensus with H∞ disturbance attenuation index on sliding surface. A distributed adaptive SMC law with adaptive updated law is proposed such that the sliding surface is reachable. Then, the output feedback based distributed H∞ SMC is considered by designing distributed observer, and a SMC law is synthesized for the reaching motion based on the state estimates. A LMI based sufficient condition for the scaled consensus with H∞ disturbance attenuation index of the overall closed-loop system is derived. At last, the proposed distributed H∞ SMC is further extended to solve the scaled consensus control problem of networked multi-agent systems under switching topology. An example is included to show the effectiveness of the proposed methods.

Introduction

Over the last few years, cooperative control of multi-agent systems has been paid to much attention due to its potential applications in satellite formation flying, cooperative unmanned air vehicles, distributed sensor networks, and so forth [1–۳]. One of the most considered coordination control issues for multi-agent systems is to design a protocol based only on local relative information between neighboring agents to make the states of all agents reach an agreement on a state, which is known as the consensus problem. Du et al. [4–۲۴] investigated the distributed consensus control problems for multi-agent systems by combining the graph theory with system control theories.