Neural-network-based adaptive fixed-time control for stochastic multi-agent systems

This article deals with the fixed-time control design issue for stochastic multi-agent systems (MASs). First of all, a new practical fixed-time stability criterion in probability is proposed. Compared with existing works, the settling time is exclusively determined by design parameters, signifying that it can be calculated with precision. Utilizing this stability criterion, a fixed-time control strategy for stochastic MASs is designed, principally leveraging the backstepping control techniques and the radial basis function neural networks (RBF NNs). Additionally, the singularity problem in the control scheme is avoided by exploiting L'Hôpital's rule. With the designed control strategy, the stochastic MASs achieve practical fixed-time stability. Furthermore, the tracking errors converge to an adjustable range near zero. The effectiveness of the proposed control strategy is verified by a series numerical simulation.