网络化演化博弈的建模和策略调控—半张量积方法

发布时间：2018-05-11 09:58

本文选题：网络演化博弈 + 切换拓扑结构　；参考：《山东大学》2017年博士论文

【摘要】：最近几年,因为在生物系统,经济系统和社会系统中的广泛应用,图上的演化博弈理论(网络演化博弈理论)受到了越来越多学者的关注,并且已经变成了一个极具吸引力的研究领域.在此之中,在演化过程中分析博弈演化中玩家的行为是一个非常重要的问题.然而,现有的大部分关于网络演化博弈理论的成果,主要利用数据仿真方法,缺少一个合理的理论框架去分析和调控参与博弈过程的玩家的行为.本文利用矩阵的半张量积方法给出网络演化博弈一个合适的理论框架,并利用这个理论结果去分析和调控博弈过程中玩家的行为,来满足合适的控制目标.主要研究内容如下:1.对于给定的切换网络拓扑结构的网络演化博弈,建立其等价的代数表达式,并给出算法.基于这个代数表达式,分析相应的演化博弈中玩家的行为.然后,在合适的假设条件下,证明给定博弈的不动点的存在性,并设计自由控制序列使得博弈的最优局势全局可达.2.对于给定的具有有限记忆的网络演化博弈,建立其等价的代数表达式,并给出算法.基于这个代数表达式,分析相应的演化博弈中玩家的行为.然后,给出保证博弈纳什平衡点存在的条件,并设计自由可控制序列使得给定的具有有限记忆的网络演化博弈能演化到纳什平衡点.3.将具有随机进入特征的演化博弈看作一类特殊的切换网络拓扑结构的网络演化博弈,根据这种观点,将其表示为一种马尔科夫过程进行分析.利用滚动时域控制方法,将大玩家考虑成为控制输入,设计状态反馈控制器,解决具有随机进入特征的演化博弈的优化问题.4.将高阶k值逻辑控制网络看作从输入轨迹空间到输出轨迹空间一种映射,然后利用符号动力学的方法,分析这种映射的连续性,单射性和满射性.定义高阶k值逻辑控制网络的可逆性,给出判断其可逆性的等价判据,并用矩阵半张量积方法设计可逆的高阶k值逻辑控制网络的逆系统.定义高阶k值逻辑控制网络轨迹控制的概念,利用高阶k值逻辑控制网络可逆性,给出一个判定其轨迹可控的充分条件.5.针对一种一般的演化博弈系统,针对其具有折扣因子的优化目标,找到此系统的最优轨迹,利用此最优轨迹,设计状态反馈最优控制器。
[Abstract]:In recent years, because of its wide application in biological system, economic system and social system, the evolutionary game theory (network evolutionary game theory) has attracted more and more scholars' attention. And has become an attractive area of research. In the process of evolution, it is very important to analyze players' behavior in game evolution. However, most of the existing achievements of network evolutionary game theory mainly use the data simulation method, and lack a reasonable theoretical framework to analyze and regulate the behavior of players involved in the game process. In this paper, the semi-tensor product method of matrix is used to give an appropriate theoretical framework of network evolutionary game, and the theoretical results are used to analyze and regulate the player's behavior in the game process to meet the appropriate control objectives. The main research contents are as follows: 1. For a given network evolution game with a switching network topology, an equivalent algebraic expression is established and an algorithm is given. Based on this algebraic expression, the behavior of players in the corresponding evolutionary game is analyzed. Then, under suitable assumptions, the existence of fixed points of given game is proved, and a free control sequence is designed so that the optimal situation of the game can reach to .2. For a given network evolutionary game with finite memory, an equivalent algebraic expression is established and an algorithm is given. Based on this algebraic expression, the behavior of players in the corresponding evolutionary game is analyzed. Then, the conditions to guarantee the existence of Nash equilibrium point are given, and the free controllable sequence is designed so that the given network evolution game with finite memory can evolve to Nash equilibrium point. 3. The evolutionary game with random entry characteristics is regarded as a class of network evolution games with special topology structure of switched networks. According to this viewpoint, it is expressed as a Markov process to be analyzed. By using the rolling time domain control method, the large players are considered as control input, and the state feedback controller is designed to solve the optimization problem of evolutionary game with random entry characteristics. The high-order k-valued logic control network is regarded as a mapping from the input locus space to the output locus space, and then the continuity, singularity and surjectivity of the mapping are analyzed by the symbolic dynamics method. The reversibility of high order k valued logic control network is defined, and the equivalent criterion to judge its reversibility is given. The inverse system of reversible high order k valued logic control network is designed by matrix semi tensor product method. The concept of high-order k-valued logic control network trajectory control is defined. By using high-order k-valued logic control network reversibility, a sufficient condition. For a general evolutionary game system, the optimal trajectory of the system is found for its optimization objective with discount factor, and the optimal controller with state feedback is designed by using the optimal trajectory.
【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O225;O231

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