Distributed Time-Varying Nash Equilibrium Algorithm Based on Prediction-Correction Technique with Set Constraints

In this paper, a class of time-varying noncooperative game problems with set constraints is investigated. A distributed time-varying Nash equilibrium seeking algorithm based on the prediction-correction technique is designed to track the time-varying Nash equilibrium, in which the prediction term based on the Newton’s method is employed to offset the changes of the Nash equilibrium and the correction term enhances the convergence performance. The projection operator is also introduced to settle the set constraints. It is theoretically demonstrated that the proposed algorithm can be tracked within the bounded neighborhood of the time-varying Nash equilibrium under the undirected connectivity graph when appropriate parameters are chosen. Finally numerical simulations validate the effectiveness of the algorithm by applying it to solve the formation tracking problem of a multi-USV system.