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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 1, Pages 47–57 (Mi zvmmf9792)  

This article is cited in 6 scientific papers (total in 7 papers)

Parallel algorithm for calculating the invariant sets of high-dimensional linear systems under uncertainty

A. N. Daryin, A. B. Kurzhanski

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: The development of efficient computational methods for synthesizing controls of high-dimensional linear systems is an important problem in theoretical mathematics and its applications. This is especially true for systems with geometrical constraints imposed on the controls and uncertain disturbances. It is well known that the synthesis of target controls under the indicated conditions is based on the construction of weakly invariant sets (reverse reachable sets) generated by the solving equations of the process under study. Methods for constructing such equations and corresponding invariant sets are described, and the computational features for high-dimensional systems are discussed. The approaches proposed are based on the previously developed theory and methods of ellipsoidal approximations of multivalued functions.

Key words: dynamic programming, ellipsoidal approximation, parallel computations, algorithm for computing invariant sets of linear systems.

DOI: https://doi.org/10.7868/S0044466913010031

Full text: PDF file (542 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:1, 34–43

Bibliographic databases:

UDC: 519.626
Received: 06.07.2012

Citation: A. N. Daryin, A. B. Kurzhanski, “Parallel algorithm for calculating the invariant sets of high-dimensional linear systems under uncertainty”, Zh. Vychisl. Mat. Mat. Fiz., 53:1 (2013), 47–57; Comput. Math. Math. Phys., 53:1 (2013), 34–43

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. “Alexander Borisovich Kurzhanski. On the occasion of his 75th birthday”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 1–13  mathnet  crossref  mathscinet  isi
    2. E. K. Kostousova, “On the polyhedral method of solving problems of control strategy synthesis”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 140–155  mathnet  crossref  mathscinet  isi  elib
    3. Korda M., Henrion D., Jones C.N., “Convex Computation of the Maximum Controlled Invariant Set For Polynomial Control Systems”, SIAM J. Control Optim., 52:5 (2014), 2944–2969  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. B. Kurzhanskii, “Problem of collision avoidance for a group motion with obstacles”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 120–136  mathnet  crossref  mathscinet  isi  elib
    5. Sinyakov V.V., “Method For Computing Exterior and Interior Approximations To the Reachability Sets of Bilinear Differential Systems”, Differ. Equ., 51:8 (2015), 1097–1111  crossref  mathscinet  zmath  isi  elib  scopus
    6. E. K. Kostousova, “On polyhedral control synthesis for dynamical discrete-time systems under uncertainties and state constraints”, Discret. Contin. Dyn. Syst., 38:12, SI (2018), 6149–6162  crossref  isi  scopus
    7. Kurzhanskii A.B., “Hamiltonian Formalism in Team Control Problems”, Differ. Equ., 55:4 (2019), 532–540  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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