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 Trudy Inst. Mat. i Mekh. UrO RAN, 2019, Volume 25, Number 1, Pages 150–165 (Mi timm1607)

Calculation of elements of a guiding program package for singular clusters of the set of initial states in the package guidance problem

S. M. Orlovab, N. V. Strelkovskiiba

a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b International Institute for Applied Systems Analysis, Laxenburg

Abstract: A fixed-time package guidance problem is considered for a linear controlled dynamical system with a finite set of initial states. The control set is convex and compact and the target set is convex and closed. The paper focuses on the case where the set of initial states has singular clusters for which the existing algorithm for estimating the elements of a guiding program package is not applicable. It is suggested to consider a perturbed problem of augmented program guidance with a smoothed control set. It is proved that the motions of the original and perturbed problems are close to each other at the terminal time; the corresponding estimates are provided. In the case of an augmented target set with nonempty interior, it is also shown that a solution of the augmented program guidance problem that is precisely guiding to the target set can be obtained by applying the existing algorithm for the perturbed problem with compressed target set. The suggested theoretical constructions are illustrated with a model example.

Keywords: incomplete information, linear dynamical system, guidance problem, program package, singular cluster, smooth approximation.

 Funding Agency Grant Number Russian Science Foundation 14-11-00539 This work was supported by the Russian Science Foundation (project no. 14-11-00539).

DOI: https://doi.org/10.21538/0134-4889-2019-25-1-150-165

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Document Type: Article
UDC: 517.977
MSC: 49M05, 65D10, 93C41
Revised: 27.12.2018
Accepted:14.01.2019

Citation: S. M. Orlov, N. V. Strelkovskii, “Calculation of elements of a guiding program package for singular clusters of the set of initial states in the package guidance problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 1, 2019, 150–165

Citation in format AMSBIB
\Bibitem{OrlStr19} \by S.~M.~Orlov, N.~V.~Strelkovskii \paper Calculation of elements of a guiding program package for singular clusters of the set of initial states in the package guidance problem \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2019 \vol 25 \issue 1 \pages 150--165 \mathnet{http://mi.mathnet.ru/timm1607} \crossref{https://doi.org/10.21538/0134-4889-2019-25-1-150-165} \elib{http://elibrary.ru/item.asp?id=37051100}