A Matrix Expression of Infinite Horizon Optimal Control Problem for Stochastic Logical Dynamical Systems
A Matrix Expression of Infinite Horizon Optimal Control Problem for Stochastic Logical Dynamical Systems
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DOI：
10.3182/20140824-6-za-1003.01152
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Yuhu Wu;T. Shen
中科院分区：
文献类型：
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作者：
Yuhu Wu;T. Shen
摘要 考虑有限状态的随机逻辑控制动力系统。在给出随机逻辑动力系统的两个等价描述：离散时间演化方程和马尔可夫过程的基础上，以代数形式给出了无限时域优化问题。基于矩阵的半张量乘积和增维技术，我们建立了最优控制问题的动态规划和贝尔曼方程的简洁矩阵表达式。
Abstract The stochastic logical control dynamical system with finite state is considered. After giving two equivalent descriptions of stochastic logical dynamical system: in term of discrete-time evolution equation and in term of Markov process, the infinite horizon optimization problem is presented in an algebraic form. Based on semi-tensor product of matrix and the increasing dimensional technique, we establish a succinct matrix expression of dynamic programming and Bellman's equation for the optimal control problem.