一类多值控制网络最优决策的半张量积求解法研究
Research on Semi-Tensor Product Solution Method for Optimal Decision of a Class of Multi-Valued Control Networks
DOI: 10.12677/AAM.2018.710152, PDF,    国家自然科学基金支持
作者: 符繁强, 韦维, 钱柳：贵州民族大学，数据科学与信息工程学院，贵州 贵阳；周荧：贵州大学，数学与统计学院，贵州 贵阳
关键词: 矩阵半张量积；多值逻辑控制网络；最优控制；离散型动态规划方法；Semi-Tensor Product； Multi-Valued Logic Control Network； Optimal Control； Discrete Dynamic Programming
摘要: 有限动态博弈过程在部分玩家的策略给定情形下，可以转化为多值逻辑控制网络的最优控制问题。本文研究这一类单输入输出的有限动态博弈问题，论文利用矩阵半张量积的方法，推导出多值逻辑动态系统的代数表达式和收益目标泛函的半张量积的表达形式，并证明此收益最大化问题新的表达方式与原问题的等价性；进而，给出了求解半张量积系统最优控制问题的动态规划法和算法；最后，应用此算法求解一个实例。
Abstract: The finite dynamic game process can be transformed into the optimal control problem of multi-valued logic control networks given the strategy of some players. In this paper, we study the finite dynamic game problem of single input and output. The paper uses the method of matrix half tensor product to derive the algebraic expression of multi-valued logic dynamic system and the expression of the semi-tensor product of the income objective functional, and proves the equivalence between the new expression of this income maximization problem and the problem. Furthermore, the dynamic programming method and algorithm for solving the optimal control problem of semi-tensor product system are given. Finally, an algorithm is used to solve an example.
文章引用：符繁强, 韦维, 周荧, 钱柳. 一类多值控制网络最优决策的半张量积求解法研究[J]. 应用数学进展, 2018, 7(10): 1308-1316. https://doi.org/10.12677/AAM.2018.710152

参考文献

[1] Kauffman, S.A. (1992) The Origins of Order: Self-Organization and Selection in Evolution. Journal of Evolutionary Biology, 13, 133-144.
[2] Kurten, K.E. (1999) Correspondence between Neural Threshold Networks and Kauffman Boolean Cellular Automata. Journal of Physics A General Physics, 21, L615.
[3] Davidson, E.H., Rast, J.P., Oliveri, P., et al. (2002) A Genomic Regulatory Network for Development. Science, 295, 1669. [Google Scholar] [CrossRef] [PubMed]
[4] Harris, S.E., Sawhill, B.K., Wuensche, A., et al. (2002) A Model of Transcriptional Regulatory Networks Based on Biases in the Observed Regulation Rules. Complexity, 7, 23-40. [Google Scholar] [CrossRef] 
[5] Kauffman, S.A. (1969) Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets. Journal of Theoretical Biology, 22, 437-467. [Google Scholar] [CrossRef] [PubMed]
[6] Smith, J.M. and Price, G.R. (1973) The Logic of Animal Conflict. Nature, 246, 15-18. [Google Scholar] [CrossRef] 
[7] Smith, J.M. (1982) Evolution and the Theory of Games. Evolution and the Theory of Games. Cambridge University Press, Cambridge, 41-45. [Google Scholar] [CrossRef] 
[8] Nowak, M.A. and May, R.M. (1992) Evolutionary Games and Spatial Chaos. Nature, 359, 826-829. [Google Scholar] [CrossRef] 
[9] 程代展, 齐洪胜. 矩阵的半张量积理论与应用[M]. 北京: 科学出版社, 2007.
[10] Cheng, D., Qi, H. and Zhao, Y. (2012) An Introduction to Semi-Tensor Product of Matrices and Its Applications. World Scientific, Singapore. [Google Scholar] [CrossRef] 
[11] Cheng, D., Qi, H. and Li, Z. (2010) Analysis and Control of Boolean Networks. In: Communications & Control Engineering, Vol. 13, Springer, Berlin.
[12] 程代展, 赵寅, 徐听听. 演化博弈与逻辑动态系统的优化控制[J]. 系统科学与数学, 2012, 32(10): 1226-1238.
[13] Zhao, Y., Li, Z. and Cheng, D. (2011) Optimal Control of Logical Control Networks. IEEE Transactions on Automatic Control, 56, 1766-1776. [Google Scholar] [CrossRef] 
[14] Mu, Y. and Guo, L. (2009) Optimization and Identification in a Non-Equilibrium Dynamic Game. Proceedings of the 48th IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, Shanghai, 15-18 December 2009, 5750-5755. [Google Scholar] [CrossRef] 
[15] 钱柳, 韦维, 符繁强, 周荧. 布尔控制网络最小能耗问题的半张量方法[J]. 应用数学进展, 2018, 7(1): 95-103.
[16] 程代展, 夏元清, 马宏宾, 等. 矩阵代数、控制与博弈[M]. 北京: 北京理工大学出版社, 2016.

为你推荐