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

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

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:1, 34–43

Bibliographic databases:

UDC: 519.626

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
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
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
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
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
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
7. Kurzhanskii A.B., “Hamiltonian Formalism in Team Control Problems”, Differ. Equ., 55:4 (2019), 532–540
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