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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2011, Volume 8, Pages 72–104 (Mi semr314)  

This article is cited in 2 scientific papers (total in 2 papers)

Approximation of attainability sets and calculation of time-optimal control in real time

V. M. Aleksandrov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (351 kB) Citations (2)
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Abstract: A new approach to realization of time-optimal control in real time for linear systems under control with constraint is proposed. It is based on subdividing the computational costs on those made in advance of the control process and those carried as it proceeds. The preliminary computations do nit depend on actual initial condition and rely on approximation of attainability sets in different periods of time by complex of hyperplane. Methods of constructing them are given with a way to single out the support hyperplane. Methods of approximate finding and following correction for normalized vector of adjoint system initial conditions, switching times of time-optimal control, and the control completion time are suggested. Estimation of computational working time is given. Reduction of unspecified form systems to their canonical form is considered. Quantitative measure of total controllability is deter-mined. Results of modeling and numerical calculations are presented.
Keywords: optimal control, speed, attainability sets, hyperplane, real time, adjoint system, initial condition, edge point, first approximation, approximating construction, computational costs.
Received March 17, 2011, published May 11, 2011
Document Type: Article
UDC: 519.626.1
MSC: 49N05
Language: Russian
Citation: V. M. Aleksandrov, “Approximation of attainability sets and calculation of time-optimal control in real time”, Sib. Èlektron. Mat. Izv., 8 (2011), 72–104
Citation in format AMSBIB
\Bibitem{Ale11}
\by V.~M.~Aleksandrov
\paper Approximation of attainability sets and calculation of time-optimal control in real time
\jour Sib. \`Elektron. Mat. Izv.
\yr 2011
\vol 8
\pages 72--104
\mathnet{http://mi.mathnet.ru/semr314}
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  • This publication is cited in the following 2 articles:
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