B.I. Anan’ev, P.A. Yurovskikh. Approximation of a guaranteed estimation problem with mixed constraints ... P. 48-63

Questions of finite-dimensional approximation for a guaranteed estimation problem are considered for linear nonstationary systems with disturbances subject to mixed integral and geometric constraints, where the geometric constraints are not assumed to be compact. The parameters of the system and the measurement equation are formed in such a way that the state vector of the system is not subject to geometric constraints. Under these assumptions, one can reduce the estimation problem to an optimal control problem without state constraints and use Pontryagin’s maximum principle. A discrete multistep system is proposed for which the information set converges in the Hausdorff metric to the corresponding information set of a continuous system as the partition step of the observation interval vanishes. Estimates characterizing the convergence rate are derived and an example is given.

Keywords: guaranteed estimation, filtering, variational inequalities, normal cone, maximum principle, information set

Received August 30, 2020

Revised October 19, 2020

Accepted October 26, 2020

Funding Agency: This study was supported by the Scientific Educational Center of the IMM UB RAS working under the Ural Mathematical Center.

Boris Ivanovich Ananyev, Dr. Phys.-Math. Sci., Leader Sci. Collaborator, 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

Polina Aleksandrovna Yurovskih, doctoral student, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: polina2104@list.ru


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Cite this article as: B.I. Anan’ev, P.A. Yurovskikh. Approximation of a guaranteed estimation problem with mixed constraints, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2020, vol. 26, no. 4, pp. 48–63.