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Towards the optimal control of Markov chains with constraints |
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| Authors: | Boris Miller [Author Vitae] Gregory Miller [Author Vitae] |
| Affiliation: | a Monash University, School of Mathematical Sciences, Clayton, Victoria, 3800, Australia b Institute for Information Transmission Problems, 19, B. Karetny Per., 127994 Moscow, Russia c Institute of Informatics Problems, RAS, 44/2, Vavilova str., 119333 Moscow, Russia d Probability Theory Department, Moscow Aviation Institute, 4, Volokolamskoye shosse, 125993 Moscow, Russia |
| Abstract: | An optimal control problem with constraints is considered on a finite interval for a non-stationary Markov chain with a finite state space. The constraints are given as a set of inequalities. The optimal solution existence is proved under a natural assumption that the set of admissible controls is non-empty. The stochastic control problem is reduced to a deterministic one and it is shown that the optimal solution satisfies the maximum principle, moreover it can be chosen within a class of Markov controls. On the basis of this result an approach to the numerical solution is proposed and its implementation is illustrated by examples. |
| Keywords: | Markov chains Constraints Optimal control Maximum principle |
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