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

This paper delves into the fixed-time bipartite consensus control problem of stochastic nonlinear multi-agent systems (MASs) under performance constraints. A constraint scaling function is put forward to model the performance constraints characterized by user-predefined steady-state accuracy and settling time, independent of the initial condition. Technically, the local synchronization error of each follower is mapped to a new error variable employing the constraint scaling function and an error transformation function prior to being utilized for controller design. To attain fixed-time convergence of the local tracking error, a barrier function transforms the scaled synchronization error to a new variable to ensure the prescribed performance. Subsequently, an adaptive fuzzy fixed-time bipartite consensus controller is developed. The fuzzy logic system handles the uncertainties in the designing procedures, and only 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 consensus error of the antagonistic network evolves within the user-predefined performance constraints. The simulation results evaluate the effectiveness of the developed control scheme.