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This article is cited in 3 scientific papers (total in 3 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
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.
DOI:
https://doi.org/10.7868/S004446691505004X
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:5, 749–765
Bibliographic databases:
UDC:
519.626
MSC: Primary 49M20; Secondary 49M05 Received: 07.08.2014 Revised: 16.11.2014
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
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http://mi.mathnet.ru/eng/zvmmf10200 http://mi.mathnet.ru/eng/zvmmf/v55/i5/p758
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