Stabilization of Time Delay Evolutionary Congestion Game Based on Semi-tensor Product Method

doi:10.19678/j.issn.1000-3428.0054594

Abstract

Abstract: To address the stabilization problem of evolutionary congestion game with time delay,this paper proposes a stabilization method based on semi-tensor product for evolutionary congestion game with time delay.The semi-tensor product method of matrix is used to describe the evolutionary congestion game with time delay as a logical dynamic system,and an equivalent algebraic form is given.On this basis,the dynamic behavior of evolutionary congestion game with time delay is analyzed,and it is proved that the fixed point of the game is the Nash equilibrium point.The necessary and sufficient conditions for the game to evolve from global stabilization to Nash equilibrium under open-loop control and state feedback control are presented,as well as the design process of control.Analysis results show that the dynamic system of evolutionary congestion game with time delay can evolve from global stabilization to Nash equilibrium under open-loop control and state feedback control,which shows the effectiveness of the method.

Key words: time delay, evolutionary game, congestion game, matrix semi-tensor product, open-loop control, state feedback control

摘要： 针对带有时滞作用的演化拥塞博弈的镇定问题，提出一种基于半张量积的时滞演化拥塞博弈的镇定方法。利用矩阵的半张量积方法将时滞演化拥塞博弈描述为逻辑动态系统，并给出等价的代数形式。在此基础上，分析时滞演化拥塞博弈的动态行为，证明该博弈的不动点即为纳什均衡点，给出其在开环控制和状态反馈控制下全局镇定到纳什均衡的充要条件和控制设计的过程。算例分析结果表明，时滞演化拥塞博弈的动态系统在开环控制和状态反馈控制下能全局镇定到纳什均衡，证明了该方法的有效性。

关键词: 时滞, 演化博弈, 拥塞博弈, 矩阵半张量积, 开环控制, 状态反馈控制

CLC Number:

TP393

WANG Guilin, XU Yong. Stabilization of Time Delay Evolutionary Congestion Game Based on Semi-tensor Product Method[J]. Computer Engineering, 2020, 46(7): 300-305.

王桂林, 徐勇. 基于半张量积方法的时滞演化拥塞博弈镇定[J]. 计算机工程, 2020, 46(7): 300-305.

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