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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 5, Pages 758–775
DOI: https://doi.org/10.7868/S004446691505004X (Mi zvmmf10200) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Optimal control of linear systems with interval constraints

V. M. Aleksandrov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.7868/S004446691505004X
Abstract: For linear systems with interval constraints, a method for computing a time-optimal control is proposed. The method is based on transforming a quasi-optimal control. The properties and features of the quasi-optimal control are examined. A technique is described for dividing the domain of initial conditions into reachable sets over different times and for approximating each set by a family of hyperplanes. An iterative method for computing an optimal control with interval constraints is developed. The convergence of the method is proved, and a sufficient condition for the convergence of the computational process is obtained. The radius of local quadratic convergence is found. Numerical results are presented.
Key words: optimal control, quasi-optimal control, interval constraints, time-optimal control, reachable set, adjoint system, convergence, iterative process.
Received: 07.08.2014
Revised: 16.11.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 5, Pages 749–765
DOI: https://doi.org/10.1134/S0965542515050048
Bibliographic databases:
Document Type: Article
UDC: 519.626
MSC: Primary 49M20; Secondary 49M05
Language: Russian
Citation: V. M. Aleksandrov, “Optimal control of linear systems with interval constraints”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015), 758–775; Comput. Math. Math. Phys., 55:5 (2015), 749–765
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
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