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

作　　者：符繁强 韦维 周荧 钱柳 

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳 [2]贵州大学数学与统计学院,贵州贵阳

出　　处：《应用数学进展》2018年第10期1308-1316,共9页Advances in Applied Mathematics

基　　金：国家自然科学基金(No.11761021),贵州民族大学科研基金资助项目(No.2017ZD017)。

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。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.

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 

分 类 号：F2[经济管理—国民经济]