This article investigates differential graphical games for linear multiagent systems with a leader on fixed communication graphs. The objective is to make each agent synchronize to the leader and, meanwhile, optimize a performance index, which depends on the control policies of its own and its neighbors. To this end, a distributed adaptive Nash equilibrium solution is proposed for the differential graphical games. This solution, in contrast to the existing ones, is not only Nash but also fully distributed in the sense that each agent only uses local information of its own and its immediate neighbors without using any global information of the communication graph. Moreover, the asymptotic stability and global Nash equilibrium properties are analyzed for the proposed distributed adaptive Nash equilibrium solution. As an illustrative example, the differential graphical game solution is applied to the microgrid secondary control problem to achieve fully distributed voltage synchronization with optimized performance.

中文翻译：

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微分图形博弈的分布式自适应纳什均衡解


本文研究了具有固定通信图领导者的线性多智能体系统的微分图形博弈。目标是使每个代理同步到领导者，同时优化性能指标，这取决于它自己和邻居的控制策略。为此，针对微分图形博弈提出了分布式自适应纳什均衡解。与现有的解决方案相比，该解决方案不仅是纳什解决方案，而且是完全分布式的，因为每个代理仅使用其自己及其直接邻居的本地信息，而不使用通信图的任何全局信息。此外，还分析了所提出的分布式自适应纳什均衡解的渐近稳定性和全局纳什均衡特性。作为说明性示例，将差分图形游戏解决方案应用于微电网二次控制问题，以实现具有优化性能的完全分布式电压同步。