Risk minimization under functional constraints on the dynamic disturbance

D. A. Serkov<sup>ab

a</sup> Institute of Mathematics and Mechanics named after N. N. Krasovskii, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
^b Ural Federal University named after the first President of Russia B. N. Yeltsin, ul. Mira, 19, Yekaterinburg, 620002, Russia

Abstract: In this review the application of the Niehans–Savage criterion to control problems under dynamic disturbances is discussed: motivation and formulation of the risk minimizing problem are given; direct relations for the results in different classes of disturbance constraints and solving strategies are provided; the examples of solving process for various problems with this control criteria are given; the results obtained by using the Niehans–Savage criterion are compared with the results based on the classic minimax criterion; the conditions of unimprovability of the strategies with full memory are studied; the optimal risk function as a limit of iterative program construct for the functional of regret is presented; the regularity condition for this functional is given; some additional conditions on the control system to ensure the possibility of numerical implementation of the risk-optimal strategy are considered.

Keywords: full memory strategy, Savage criterion, functionally limited disturbance.

UDC: 517.977

MSC: 93C15, 49N30, 49N35

Received: 31.08.2014

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