| 引用本文: | 赵荣,冯俊娥.演化博弈的鲁棒稳定与镇定[J].控制理论与应用,2021,38(11):1793~1800.[点击复制] |
| ZHAO Rong,FENG Jun-e.On robust stability and stabilization of evolutionary games[J].Control Theory and Technology,2021,38(11):1793~1800.[点击复制] |
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| 演化博弈的鲁棒稳定与镇定 |
| On robust stability and stabilization of evolutionary games |
| 摘要点击 1421 全文点击 596 投稿时间：2021-08-07 修订日期：2021-11-14 |
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| DOI编号 10.7641/CTA.2021.10716 |
| 2021,38(11):1793-1800 |
| 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 |
| 基金项目 国家自然科学基金项目(61773371, 61877036), 山东省自然科学基金项目(ZR2019MF002)资助. |
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| 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. |
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