Consensus of Uncertain Multiagent Systems Under Granular Differentiability Concept

Abstract

In this paper, the problem of consensus of linear multi-agent systems with both uncertain dynamics and uncertain switching topology is investigated. Uncertainties are considered as granular fuzzy numbers whicharerepresentedvia horizontalmembership functions (HMFs) and Relative Distance Measurement (RDM) arithmetic. It is first proved that there exists a crisp solution to a fuzzyLinear Matrix Inequality(LMI) problem. This proof creates a bridge such that multidimensional RDM arithmetic that has been devoted to linear functions so far could be entered into some problems with nonlinear functions. Then an algorithm is proposed for the consensus of the multi-agent systems with uncertainty. Here, by proving the existence of a crisp solution for fuzzy LMI, we are able to prove that the proposed algorithm can ensure achieving consensus. Furthermore, the gain coefficients obtained for this fuzzy system are crisp numbers and can be applied to real systems in practical applications. Finally, the final value of consensus is calculated as a fuzzy number to present a better understanding of the effect of uncertaintyon the final value of consensus. In addition, the efficiency of the proposed algorithm is shown in a simulation example.