演化博弈的鲁棒稳定与镇定

On robust stability and stabilization of evolutionary games

中文关键词  演化博弈  干扰  稳定与镇定  鲁棒Nash均衡  矩阵半张量积

英文关键词  evolutionary games  disturbances  stability and stabilization  robust Nash equilibrium  semi-tensor product of matrices

中文摘要

      本文研究了干扰影响下演化博弈的稳定与镇定问题. 首先, 文章给出了干扰博弈、控制–干扰博弈以及鲁棒 Nash均衡等概念, 并在此基础上提出了干扰演化博弈与控制–干扰演化博弈鲁棒稳定与镇定的定义. 其次, 利用矩 阵半张量积工具, 得到了干扰演化博弈与控制–干扰演化博弈的代数状态空间表示, 将鲁棒稳定与镇定问题转化为 一个辅助系统的集合稳定与集合镇定问题. 紧接着, 文章建立了干扰演化博弈与控制–干扰演化博弈鲁棒稳定与镇 定的充分必要条件, 并进一步设计了状态反馈控制器. 最后, 通过两个例子验证了所得结论的有效性.

英文摘要

      This paper investigates the stability and stabilization problems of evolutionary games with disturbances. First, based on several concepts, including disturbed game, controlled-disturbed game and robust Nash equilibrium, the definitions of robust stability and stabilization of disturbed evolutionary game and controlled-disturbed evolutionary game are specified, respectively. Second, by virtue of semi-tensor product, the algebraic state space representation of disturbed evolutionary game and controlled-disturbed evolutionary game are derived. Meanwhile, the robust stability and stabilization problems are converted into the set stability and set stabilization problems of an auxiliary system. Then, necessary and sufficient conditions for the robust stability and stabilization problems are presented, and the state feedback controller is designed as well. Finally, two examples are given to verify the effectiveness of the obtained results.