Gradual-Impulsive Control for Continuous-Time Markov Decision Processes with Total Undiscounted Costs and Constraints: Linear Programming Approach via a Reduction Method
Gradual-Impulsive Control for Continuous-Time Markov Decision Processes with Total Undiscounted Costs and Constraints: Linear Programming Approach via a Reduction Method
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DOI：
10.1137/21m1444060
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
A. Piunovskiy;Yi Zhang
中科院分区：
文献类型：
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作者：
A. Piunovskiy;Yi Zhang
我们考虑了渐进脉冲CTMDP模型的约束最优控制问题，其性能标准是期望总未贴现成本（来自运行成本和每次施加脉冲的成本）。打折的型号属于特殊情况。我们充分证明了一种约简方法，并关闭了先前文献中的一个开放问题。该约简方法导出了一个等价但更简单的标准CTMDP模型，并在此基础上，在较自然的条件下，有效地建立了求解相关约束最优控制问题的线性规划方法。
We consider the constrained optimal control problem for the gradual-impulsive CTMDP model with the performance criteria being the expected total undiscounted costs (from the running cost and the cost from each time an impulse being applied). The discounted model is covered as a special case. We justify fully a reduction method, and close an open issue in the previous literature. The reduction method induces an equivalent but simpler standard CTMDP model with gradual control only, based on which, we establish effectively, under rather natural conditions, a linear programming approach for solving the concerned constrained optimal control problem.