  This paper focuses on the optimal coverage problem (OCP) for multi-agent
systems with decentralized optimization. A game based distributed decision
approach for the the multi-agent OCP is proposed. The equivalence between the
equilibrium of the game and the extreme value of the global performance
objective is strictly proved. Then, a distributed algorithm only using local
information to obtain the global near-optimal coverage is developed, and its
convergence is proved. Finally, the proposed method is applied to maximize the
covering time of a satellite constellation for a target. The simulation results
under different scenarios show our method costs much less computation time
under some level index than traditional centralized optimization.
