Bipartite Consensus for Takagi-Sugeno Fuzzy Uncertain Multi-Agent Systems With Gain Fluctuations

This paper examines the problem of bipartite consensus for Takagi-Sugeno fuzzy multi-agent systems subject to uncertainties. The principal intention of this work is to develop a non-fragile controller through which the considered multi-agent system can achieve bipartite consensus. An undirected signed graph is considered to describe the cooperative and competitive interaction among neighboring agents. On this circumstance, we propose a consensus protocol by the utilization of graph theory. Further, with the aid of Lyapunov stability theory, the sufficient conditions are derived in the form of linear matrix inequalities which ensures the bipartite consensus of the considered multi-agent system. At last, two numerical examples are provided with their simulations to describe the viability of the developed theoretical findings.

Introduction

Multi-agent systems (MASs) are a special kind of complex dynamical systems which consists of multiple individual interacting agents. Generally, for an isolated system, it is very challenging to accomplish complex tasks. However, MASs can solve complex problems in a cooperative manner which is beyond the capability of isolated systems. Especially, MASs have several benefits such as cost reduction, flexibility and reliability when compared with isolated systems. During recent years, cooperative control of MASs has emerged as an important research topic among the research community. This fact is due to its far-ranging real-world applications but not limited to mobile robots [1] and unmanned aerial vehicles [2]. The authors in [3] developed cooperative control for MASs under both actuator bias faults and partial loss of actuator effectiveness. Using the adaptive backstepping technique, the authors in [4] studied cooperative control for MASs under the influence of unknown control directions.