Geodesic
Risk minimization under functional constraints on the dynamic disturbance
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 44 (2014) no. 2, pp. 3-95

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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. 
@article{IIMI_2014_44_2_a0,
     author = {D. A. Serkov},
     title = {Risk minimization under functional constraints on the dynamic disturbance},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {3--95},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2014_44_2_a0/}
}
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D. A. Serkov. Risk minimization under functional constraints on the dynamic disturbance. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 44 (2014) no. 2, pp. 3-95. http://geodesic.mathdoc.fr/item/IIMI_2014_44_2_a0/