Consensus of Uncertain Linear Multi-agent Systems with Granular Fuzzy Dynamics

This paper is devoted to investigate the distributed consensus problem for multi-agent systems with uncertain agent models. The uncertainty in the agents' dynamics is considered as granular fuzzy numbers and consequently the consensus error is a granular fuzzy number. It is proven that this error converges to zero asymptotically using the proposed fuzzy consensus protocol. Additionally, the definition of granular fuzzy consensus surface is proposed which determines the robustness of the consensus protocol to changes in the communication topology. Necessary and sufficient conditions are proposed to ensure that an unbounded fuzzy consensus surface can be reached with the proposed consensus protocol. The final consensus value as a fuzzy number is also calculated in presence of uncertainty. Simulation examples corroborate the efficiency of the presented method.