Practically fixed-time adaptive consensus control for multiagent systems with prescribed performance

In this paper, the fixed-time consensus tracking control problem of multiagent systems (MASs) subject to unknown nonlinearities and performance constraints is investigated. Initially, an improved fixed-time performance function is designed, which enables the consensus tracking errors to converge to the preset region in fixed time, and alleviates the initial error conditions by setting the parameters appropriately. Moreover, the unknown nonlinearities of MASs are approximated by the radial basis function neural network (RBF NN). Subsequently, a fixed-time prescribed performance controller is designed, which excludes the fractional power of tracking error to prevent potential singularity problems existing in stability proof. Additionally, a fixed-time dynamic surface filter is formulated to eliminate the "explosion of complexity" issue, meanwhile, the filter errors are bounded in fixed time. Utilizing the Lyapunov stability theory, it can be guaranteed that all signals in MASs exhibit practically fixed-time stability, and the consensus errors all approach a small region centered on origin within the prescribed bounds. Finally, simulations are presented to verify the validity of the proposed control strategy.