Distributed Nash equilibrium seeking strategies via bilateral bounded gradient approach

This paper investigates distributed Nash equilibrium (NE) seeking problems. A bilateral bounded gradient approach, a novel optimization algorithm, is utilized to solve strongly convex problems. Furthermore, for a strongly monotone game, the NE can be obtained in finite time by the bilateral bounded gradient algorithm. In the distributed manner, two types of algorithms are proposed for seeking the NE: consensus-based strategy and passivity-based strategy. For each player, nonlinear protocols are proposed to estimate the actions of their rivals, enabling these estimations to converge to the actual actions in fixed time. To solve the optimization problem, the bilateral bounded gradient algorithm is employed, ensuring that all players' actions converge to the NE in finite time. Moreover, to reduce the communication consumption, event-triggered schemes are introduced in the information exchange of players. Finally, swarm roundup behavior is analyzed by a non-cooperative game in which the proposed algorithms drive all tanks to hunt the target in finite time. The roundup effectiveness is verified by the simulations.