Adaptive Fuzzy Nonsingular Fixed-Time Bipartite Consensus Tracking Using Adding Power Integration Technique for Stochastic Nonlinear Constrained MASs

In this article, the adaptive fuzzy fixed-time bipartite consensus tracking control problem is studied for stochastic nonlinear multi-agent systems with unknown control gains and time-varying output constraints. First, in order to address the difficulties arising from the unknown control gains, the Nussbaum technique is employed. In the meantime, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$tan$</tex-math></inline-formula>-type nonlinear mapping function is introduced, which guarantees the predefined output constraints are not violated. Then, different from the previous control strategies in which they only focused on the balanced directed topology, the classification optimization algorithm is presented to accomplish the bipartite consensus tracking control according to the structurally unbalanced directed topology. Besides, by combining the adaptive backstepping technique with the adding power integration methodology, the nonsingular fixed-time control strategy is proposed. The proposed adaptive fuzzy fixed-time control strategy ensures that the bipartite consensus tracking errors converge to a region near zero in fixed time and all the signals in the closed-loop system are bounded in probability. Last, the effectiveness of the presented control scheme is demonstrated with a simulation example.