Adaptive fuzzy fixed-time bipartite consensus control for stochastic nonlinear multi-agent systems with performance constraints

This paper investigates the fixed-time bipartite consensus control problem of stochastic nonlinear multi-agent systems (MASs) with performance constraints. A constraint scaling function is proposed to model the performance constraints with user-predefined steady-state accuracy and settling time without relying on the initial condition. Technically, the local synchronization error of each follower is mapped to a new error variable using the constraint scaling function and an error transformation function before being used to design the controller. To achieve fixed-time convergence of the local tracking error, a barrier function transforms the scaled synchronization error to a new variable to guarantee the prescribed performance. Then, an adaptive fuzzy fixed-time bipartite consensus controller is developed. The fuzzy logic system handles the uncertainties in the designing procedures, and one adaptive parameter needs to be estimated online. It is shown that the closed-loop system has practical fixed-time stability in probability, and the antagonistic network's consensus error evolves within user-predefined performance constraints. The simulation results evaluate the effectiveness of the developed control scheme.