局部信息约束下网络演化博弈的动力学与优化（英文）
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摘要
网络演化博弈的优化问题是混合值逻辑网络的一个自然推广.本文研究了一类网络演化博弈的优化控制问题,其中每个控制个体在极大化自己的收益时只能获取到邻域信息.首先,利用矩阵的半张量积,将局部信息约束下控制网络演化博弈的动力学转化为相应的代数形式.然后得到了局部信息约束下确定型网络演化博弈的最优控制序列.最后,基于动态规划的解,研究了局部信息约束下概率型网络演化博弈的优化控制问题,得到了最优控制序列的简单计算公式.两个数值例子验证了本文的理论结果.
The optimization of networked evolutionary games(NEGs) is a natural extension of optimization for mixvalued logical networks. This paper studies the optimization problem for a class of control NEGs, where each controller can only use the information of its neighbors so as to maximize its payoff over a finite or infinite number of time steps. First,the dynamics of control NEGs with local information is converted into an algebraic form by using the semi-tensor product of matrices. Then the optimal control sequences for deterministic NEGs with local information are obtained. Finally, based on the dynamic programming solutions, some easily computable formulas are provided for stochastic NEGs with local information. Two examples are presented to illustrate the theoretical results.
The optimization of networked evolutionary games(NEGs) is a natural extension of optimization for mixvalued logical networks. This paper studies the optimization problem for a class of control NEGs, where each controller can only use the information of its neighbors so as to maximize its payoff over a finite or infinite number of time steps. First,the dynamics of control NEGs with local information is converted into an algebraic form by using the semi-tensor product of matrices. Then the optimal control sequences for deterministic NEGs with local information are obtained. Finally, based on the dynamic programming solutions, some easily computable formulas are provided for stochastic NEGs with local information. Two examples are presented to illustrate the theoretical results.
引文
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[5] MOJICA-NAVA E, MACANA C A, QUIJANO N. Dynamic population games for optimal dispatch on hierarchical microgrid control. IEEE Transactions on Systems, Man, and Cybernetics:Systems,2014, 44(3):306–317.
[6] NOWAK M A, MAY R M. Evolutionary games and spatial chaos.Nature, 1992, 359:826–829.
[7] TANG C, WU B, WANG J, et al. Evolutionary origin of asymptotically stable consensus. Scientific Reports, 2014, Article number:4590.
[8] CHENG D, QI H, LI Z. Analysis and Control of Boolean Networks:A Semi-tensor Product Approach. London:Springer, 2011.
[9] CHENG D, QI H, ZHAO Y. An Introduction to Semi-tensor Product of Matrices and Its Applications. Singapore:World Scientific, 2012.
[10] LI F, SUN J. Stability and stabilization of Boolean networks with impulsive effects. Systems&Control Letters, 2012, 61(1):1–5.
[11] LI H, XIE L, WANG Y. On robust control invariance of Boolean control networks. Automatica, 2016, 68(C):392–396.
[12] MENG M, LIU L, FENG G. Stability and l1 gain analysis of Boolean networks with Markovian jump parameters. IEEE Transactions on Automatic Control, 2017, 62(8):4222–4228.
[13] LU J, ZHONG J, HUANG C, et al. On pinning controllability of Boolean control networks. IEEE Transactions on Automatic Control,2016, 61(6):1658–1663.
[14] LIU Z, WANG Y, LI H. Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks. Science China Information Sciences, 2014, 57(5):1–10.
[15] ZHAO G, FU S. Matrix approach to trajectory control of higher-order k-valued logical control networks. IET Control Theory and Applications, 2017, 11(13):2110–2115.
[16] CHENG D, ZHAO Y, XU T. Receding horizon based feedback optimization for mix-valued logical networks. IEEE Transactions on Automatic Control, 2015, 60(12):3362–3366.
[17] LI H, ZHAO G, MENG M, et al. A survey on applications of semitensor product method in engineering. Science China Information Sciences, 2018, 61(1):010202.
[18] WANG Y, LIU T, CHENG D. From weighted potential game to weighted harmonic game. IET Control Theory and Applications,2017, 11(13):2161–2169.
[19] WANG Y, CHENG D, LIU X. Matrix expression of Shapley value and its application to distributed resource allocation. Science China Information Sciences, 2018, DOI:10.1007/s11432-018-9414-5.
[20] GUO P, ZHANG H, ALSAADI F E, et al. Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games. IET Control Theory and Applications, 2017,11(13):2140–2145.
[21] CHENG D, QI H, HE F, et al. Semi-tensor product approach to networked evolutionary games. Control Theory and Technology, 2014,12(2):198–214.
[22] CHENG D, HE F, QI H, et al. Modeling, analysis and control of networked evolutionary games. IEEE Transactions on Automatic Control, 2015, 60(9):2402–2415.
[23] GUO P, WANG Y, LI H. Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor method. Automatica, 2013, 49(11):3384–3389.
[24] RASMUSEN E. Games and Information:An Introduction to Game Theory. Oxford, England:Blackwell, 2007.
[25] YOUNG H P. The evolution of conventions. Econometrica, 1993,61(1):57–84.
[26] GUO P, WANG Y. Matrix expression and vaccination control for epidemic dynamics over dynamic networks. Control Theory and Technology, 2016, 14(1):39–48.
[27] BERTSEKAS D P. Dynamic Programming and Stochastic Control.New York:Academic Press, 1976.