引用本文:宋春跃,李 平.含扩散项不可靠生产系统最优生产控制的数值求解[J].控制理论与应用,2009,26(7):709~714.[点击复制]
SONG Chun-yue,LI Ping.Numerical solution for optimal production control of unreliable production systems with diffusion terms[J].Control Theory and Technology,2009,26(7):709~714.[点击复制]
含扩散项不可靠生产系统最优生产控制的数值求解
Numerical solution for optimal production control of unreliable production systems with diffusion terms
摘要点击 1576  全文点击 1617  投稿时间：2007-09-21  修订日期：2009-01-15
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DOI编号  10.7641/j.issn.1000-8152.2009.7.001
  2009,26(7):709-714
中文关键词  不可靠生产系统  生产控制  数值解  Markov决策过程
英文关键词  unreliable production systems  production control  numerical method  Markov decision process
基金项目  国家自然科学基金资助项目(60404018).
作者单位E-mail
宋春跃 浙江大学工业控制技术国家重点实验室工业控制研究所, 浙江 杭州 310027 cysong@iipc.zju.edu.cn 
李 平 浙江大学工业控制技术国家重点实验室工业控制研究所, 浙江 杭州 310027 pli@iipc.zju.edu.cn 
中文摘要
      针对含扩散项不可靠随机生产系统最优生产控制的优化命题, 采用数值解方法来求解该优化命题最优控制所满足的模态耦合的非线性偏微分HJB方程. 首先构造Markov链来近似生产系统状态演化, 并基于局部一致性原理, 把求解连续时间随机控制问题转化为求解离散时间的Markov决策过程问题, 然后采用数值迭代和策略迭代算法来实现最优控制数值求解过程. 文末仿真结果验证了该方法的正确性和有效性.
英文摘要
      The optimal production control for unreliable stochastic production system always involves in solving a mode-coupled nonlinear partial differential equation, i.e., HJB(Hamilton-Jacobi-Bellman) equation, which is the necessary and sufficient condition of optimal control. Numerical method for stochastic control problems in continuous time is adopted to solve the optimal production control problem involving diffusion terms by constructing Markov chains to approximate the evolution of the system states, and then, the associated HJB equation is transformed into a discrete time Markov decision process(MDP) under local consistence. Based on the MDP, an algorithm including numerical iteration and policy iteration is then proposed. Finally, some numerical examples of production system are presented to illustrate the usefulness of the numerical method.