预设时间下的分布式优化和纳什均衡点求解

Prescribed-time distributed optimization and Nash equilibrium seeking

本文研究了预设时间下的分布式优化和纳什均衡点求解问题.假设每个智能体只能通过局部的信息更新自身的状态,设计了一类预设时间下的分布式协议.该协议可以在任意预设的时间内实现收敛,并且不需要依赖智能体的初始状态和系统参数.当目标函数是强凸函数时,通过选取一个适当的Lyapunov函数,利用代数图论和凸分析理论等工具严格的证明了多智能体系统在预设时间下能够收敛到优化问题的最优解和非合作博弈问题的纳什均衡点.最后,通过仿真算例进一步验证了本文所设计协议的有效性.

In this paper,prescribed-time distributed optimization and Nash equilibrium seeking problems are investigated.Assuming that each agent can only have access to its local information,we design a distributed protocol within the prescribed-time.The protocol can achieve convergence in any prescribed-time,which renders the convergence time fully independent of the initial conditions and any other parameters.When the objective function is strongly convex,selecting an appropriate Lyapunov function,by utilizing algebraic graph theory and convex analysis theory strictly proves that the multi-agent can converge to the optimal solution of optimization problem and the Nash equilibrium of noncooperative game problem within the prescribed-time.Finally,simulation examples verify the effectiveness of the proposed protocols.