Nash Equilibrium Seeking for General Linear Systems With Disturbance Rejection
研究了受外部干扰的一般线性系统网络中的聚合博弈，提出了基于内部模型的分布式策略更新规则，在完美和不完美信息下均能驱使策略收敛到纳什均衡，并通过李雅普诺夫稳定性等理论分析了收敛性。
This article explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on the internal model are proposed for the case with perfect and imperfect information, respectively. Different from the existing algorithms based on gradient dynamics, by introducing the integral of the gradient of cost functions on the basis of the passivity theory, the rules are proposed to force the strategies of all agents to evolve to the Nash equilibrium, regardless of the effect of disturbances. The convergence of the two strategy-updating rules is analyzed via the Lyapunov stability theory, passivity theory, and singular perturbation theory. Simulations are performed to illustrate the effectiveness of the proposed methods.