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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 45

Guaranteed Estimation Problem for Multi-Step Systems

Author(s)
Boris I. Ananyev1, Polina A. Yurovskikh1

1Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russian Federation

Abstract
Questions of the guaranteed estimation of nonlinear multistep systems are considered, for which part of coordinates is not observable. For disturbances we set a priori restrictions with non-negative semi-continuous functions that includes geometrical restrictions as well. As the general formulas for creation of information sets and their specification in special cases are provided. Two-dimensional logistics systems and the equations of Lotka-Volterra are considered as examples. The case of the linear equations where basic functions of convex sets are used is separately considered. Under geometrical restrictions on disturbances the rough procedure of estimation with possible use of functions of distance to the set is given.
About the Authors

Boris I. Ananyev, Dr. Sci. (Phys.-Math.), Leading Researcher, Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, 620108, Russian Federation, abi@imm.uran.ru

Polina A. Yurovskikh, Mathematician, Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, 620108, Russian Federation, polina2104@list.ru

For citation
Ananyev B. I., Yurovskikh P. A. Guaranteed Estimation Problem for Multi-Step Systems. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 45, pp. 37–53. (in Russian) https://doi.org/10.26516/1997-7670.2023.45.37
Keywords
guaranteed estimation, multistep systems, information set, set of attainability
UDC
517.977
MSC
34G25, 93E10
DOI
https://doi.org/10.26516/1997-7670.2023.45.37
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