Problems of the guaranteed estimation of phase coordinates for multistep dynamic systems in the presence of inexact restrictions for disturbances, which, in particular, can be random, are considered. An approach involving inexact probabilities is applied, in which functions of coherent lower previsions with properties of positive uniformity and superadditivity are used instead of average values. Main attention is given to discrete-time systems. For these systems, the dynamic programming method when determining information sets is generalized. To ensure justice in the process, further constraints are imposed on the perturbations to maintain the compactness of the functions in the space of limited measurable functions. Information on partial orders and optimality criteria for compact sets of limited functions is included for reference. The condition for a dynamic programming method's justice in time-reversible systems is specified. We investigate examples.
Keywords: guaranteed estimation, information sets, dynamical programming, functions of coherent low prevision
Received February 4, 2025
Revised March 7, 2025
Accepted March 10, 2025
Boris Ivanovich Ananyev, Dr. Phys.-Math. Sci., leading researcher, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: abi@imm.uran.ru
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Cite this article as: B.I. Ananyev. On estimation of dynamical systems under inexact constraints on parameters. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 2, pp. 15–29.
