Fully-Distributed Neural-Network-Based Approaches for Monotonic Game With Finite-Time Disturbance Rejection

In this article, the variational GNE-nps (vGNE) seeking problem for general monotonic game with multiple coupling constraints involving dynamical players is explored. Specifically, a distributed vGNE-seeking neural network (vGSNN) with a feedback controller is designed based on high-pass filter, which efficiently transforms players' high-order dynamics into equivalent second-order ones. To further relax the requirement on parameter predesign, we propose a controller that uses adaptive weights to replace the traditional fixed gains, which realizes the full distribution of the vGSNN. Furthermore, to enhance the robustness of the vGSNN against disturbances, a novel sliding-mode controller is incorporated to ensure finite-time disturbance rejection while maintaining the full distribution of the vGSNN. Finally, an uncrewed aerial vehicle (UAV) swarm game is put forward to verify the effectiveness of the vGSNNs.