M.S. Nikol’skii. On the maximal guaranteed payoff in some problems of conflict control of multistep processes ... P. 167-172

We consider multistep conflict-controlled processes with two controlling partners. The duration of the process is fixed, and there are no constraints on the right end of the discrete trajectory. The first player aims to maximize the terminal functional without information about the future behavior of the second player. We study the important notion of maximal guaranteed payoff of the first player using the ideas of Bellman’s dynamic programming method. Based on this method, a formula for the maximal guaranteed payoff is derived in Theorem 1 under broad assumptions on the conflict-controlled process. In Theorem 2, we obtain sufficient conditions under which the corresponding functions of Bellman type are Lipschitz. Two examples are considered.

Keywords: discrete controlled processes, conflict, dynamical programming

Received November 4, 2019

Revised February 5, 2020

Accepted February 10, 2020

Mikhail Sergeevich Nikolskii, Dr. Phys.-Math. Sci, Steklov Mathematical Institute of the Russian Academy of Science, Moscow, 119991 Russia, e-mail: mni@mi-ras.ru

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Cite this article as: M.S. Nikolskii. On the maximal guaranteed payoff in some problems of conflict control of multistep processes, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2020, vol. 26, no. 1, pp. 167–172.