Risk minimization under functional constraints on the dynamic disturbance
D. A. Serkovab
a 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
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.
full memory strategy, Savage criterion, functionally limited disturbance.
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MSC: 93C15, 49N30, 49N35
D. A. Serkov, “Risk minimization under functional constraints on the dynamic disturbance”, Izv. IMI UdGU, 2014, no. 2(44), 3–95
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\paper Risk minimization under functional constraints on the dynamic disturbance
\jour Izv. IMI UdGU
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