论文标题
解决一组概率度量及其在半马多夫过程的最佳控制理论中的衬里分数积分功能的无条件极值问题的解决方案
Solution of the unconditional extremum problem for a liner-fractional integral functional on a set of probability measures and its application in the theory of optimal control of semi-Markov processes
论文作者
论文摘要
在本文中，考虑了一种新方法，用于解决具有有限多种状态的半马尔可夫过程的最佳控制问题。在一组概率措施上给出的衬里裂缝积分功能的极值上的主张的一种新形式被制定并证明。该形式是半马科过程的最佳控制策略定理的基础。事实证明，对于有限许多状态的半马多夫过程的最佳控制问题解决方案完全取决于Liner-Fractional积分函数的所谓测试功能，该功能是控制质量指数。同时，根据半马尔可夫模型的初始概率特征，获得了该测试功能的明确分析表示。
In this paper, a new method for solving the problem of optimal control of semi-Markov processes with finitely many states is considered. A new form of the assertion on an extremum of a liner-fractional integral functional given on a set of probability measures is formulated and proved. This form underlies the theorem of optimal control strategy for semi-Markov processes. It is proved that the solution of the optimal control problem for a semi-Markov process with finitely many states is completely determined by the extremum properties of the so-called test function of the liner-fractional integral functional which is the control quality index. At the same time, an explicit analytic representation was obtained for this test function in terms of the initial probability characteristics of the semi-Markov model.
