Distributed Cooperative Control of Singular Multi-agent Systems Based on Fuzzy Logic Approach

This paper studies the consensus issue of nonlinear singular multi-agent systems under undirected graphs based on fuzzy logic systems. The main objective is to develop a novel collaborative control algorithm to achieve consensus and impulse free for each agent described by nonlinear singular systems while only knowing local information, namely the state information of the agent itself and its neighbors. To overcome the analysis limitation of nonlinear singular multi-agent systems, the fuzzy logic system method is applied to deal with nonlinear items. Specifically, the consensus issue of singular multi-agent systems with fuzzy logic systems is equivalently simplified to an asymptotic stability analysis process for error systems. To achieve this objective, a novel distributed adaptive collaborative controller is designed, where the adaptive rate adjusts the coupling weight between each agent. In the research of the singular linear multi-agent system, a tolerance region is introduced, and stability of the closed-loop system is established according to Lyapunov theory. Then, fuzzy approximation theory is used to transform unknown nonlinear functions into fuzzy functions satisfying Lipschitz conditions, and the stability and impulse-free property are addressed by constructing LMI conditions. Finally, the effectiveness of the presented approach is demonstrated through two numerical examples.