Fuzzy Adaptive Bipartite Consensus of Stochastic Multiagent Systems: A Singularity-Free Prescribed Performance Control Approach

This article explores the fuzzy adaptive bipartite consensus problem of stochastic multiagent systems (MASs) using a singularity-free prescribed performance control (PPC) approach. When bipartite consensus errors approach constraint boundaries under the effect of adverse factors, the conventional PPC method may encounter a singularity issue, which can degrade system performance or lead to system instability. To address this issue, this article generalizes the concept of shear mapping to the PPC approach of stochastic MASs. Subsequently, a reference performance function is designed to guide the evolution trend of bipartite consensus errors, which effectively decreases the overshoot of bipartite consensus errors. Moreover, a scaling function is designed to remove the feasibility conditions in the existing PPC results. The proposed approach ensures that all signals of the closed-loop systems are semiglobally ultimately uniformly bounded in probability. Finally, a set of simulation results is provided to confirm the effectiveness of the proposed approach.