Distributed Time-Varying Nash Equilibrium Seeking Algorithm for Target Protection of MultiUSVs With Conflicting Goals

In this article, a target protection problem of multiunmanned surface vessels (multiUSVs) with conflicting individual and group goals is formulated and investigated. In the present problem, the group goal of the USVs is to cooperatively protect a given moving global target by maintaining it at the center of the formation formed by the USVs, whereas each USV has an individual goal of tracking its designated target. Striking a balance between inherently conflicting goals poses a significant challenge, especially in the face of the unknown aggregated information about the center of the formation. This article aims to determine trajectories for USVs to achieve a balance between conflicting individual and group goals. To fulfill this objective, the target protection problem is first transformed into a time-varying aggregative game. Then, a distributed multiround prediction-correction algorithm (DMPCA) is designed to track the unique Nash equilibrium trajectory (NET) of the time-varying aggregative game. It is theoretically proved that the trajectory generated by DMPCA could linearly converge to a bounded domain of NET if the underlying undirected communication graph among the USVs is connected and the algorithm parameters are appropriately selected. Finally, experimental studies are performed to verify the effectiveness of the algorithm.