Guaranteed Cost Consensus for Fuzzy Multi-Agent Systems With Switching Topologies

Jiafeng Yu,Chunsong Han,Qinsheng Li,Jian Wang,Wen Xing

doi:10.1109/access.2020.2980296

Abstract

This paper concentrates on guaranteed cost consensus problem for nonlinear multi-agent systems (MASs) under directed switching topologies. First, a novel polynomial fuzzy model is constructed for describing the nonlinear error MASs that are formulated by follower agents and a leader agent. Then, a consensus tracking protocol is devised to ensure that the MASs with changing topologies can achieve agreement. For the established fuzzy MASs, guaranteed cost function is introduced based on error states and control inputs. By the multiple polynomial Lyapunov function, we present relaxed sufficient condition to reach consensus with a guaranteed cost for the fuzzy MASs. Moreover, the designed consensus protocol can realize guaranteed cost by the upper bound for any initial error state. The obtained condition is converted to sum of squares and solved numerically. Finally, an example is given to illustrate the validity of the proposed consensus technique.

Highlights

The Takagi-Sugeno (T-S) fuzzy models can efficiently approximate any smooth nonlinear function with arbitrary precision, which have gained widespread attention in the past decades
Control problems of guaranteed cost consensus are investigated for linear multi-agent systems (MASs) under switching undirected topologies in [30]
Motivated by the aforementioned discussions, we aim to study the guaranteed cost consensus issue of polynomial fuzzy MASs with switching topologies in this paper

Summary

INTRODUCTION

The Takagi-Sugeno (T-S) fuzzy models can efficiently approximate any smooth nonlinear function with arbitrary precision, which have gained widespread attention in the past decades. Control problems of guaranteed cost consensus are investigated for linear MASs under switching undirected topologies in [30]. Few result is reported on guaranteed cost consensus for polynomial fuzzy MASs under changing directed communication topologies. (ii) Consensus protocols are designed to ensure that polynomial fuzzy MASs can achieve a guaranteed cost consensus for a given cost function established by the error states and control inputs. (iii) Based on multiple Lyapunov analysis, new relaxed sufficient condition is proposed to ensure the guaranteed cost consensus for polynomial fuzzy MASs with switching directed topologies, respectively. Different from the previous works, instead of utilizing state information, a guaranteed cost function based on error states and control inputs is employed for polynomial fuzzy MASs in this paper, because convergence states of agents may be nonzero when MASs achieve consensus.

CONSENSUS CONDITION UNDER

CONCLUSION