A Distributed Fixed-Time Neurodynamic Algorithm and Its Application in Multi-Autonomous Underwater Vehicle Collaborative Escorting

In this paper, a distributed fixed-time neurodynamic algorithm (DFxTNA) is designed for solving distributed optimization problem with time-varying (TV) objective function and constraints. The DFxTNA consists of consensus part based on sliding-mode control technique and optimization part based on Hessian matrix and penalty function. In contrast to existing distributed TV algorithms, DFxTNA based on fixed-time sliding mode control can effectively improve the convergence performance of the algorithm and has better stability with the addition of TV disturbance. In addition, the consistency and fixed-time convergence of DFxTNA are proved by Lyapunov theory and fixed-time stability, respectively. The effectiveness of DFxTNA is verified by numerical experiments. Finally, a distributed TV optimization problem model is established for a multi-autonomous underwater vehicle (AUV) cooperative escort scenario, and DFxTNA is applied to solve the problem. Simulation results confirm the effectiveness and stability of DFxTNA in target tracking, formation control, and dynamic obstacle avoidance.