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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2019, Volume 12, Issue 4, Pages 41–51
DOI: https://doi.org/10.14529/mmp190403
(Mi vyuru516)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Modelling

Computational algorithm for optimal control of an object with distributed parameters in a nonsmooth area of final states

M. Yu. Livshits, A. V. Nenashev, Yu. E. Pleshivtseva

Samara State Technical University, Russian Federation
Full-text PDF (235 kB) Citations (1)
References:
Abstract: We propose the effective computational algorithm for solving boundary-value problems of time-optimal and maximum accuracy control with a minimax estimation of the deviation of the final trajectory from a given state. The problem is reduced to a nonconvex nonlinear programming problem. The proposed algorithm takes into account the non-convex nature of the problem of nonlinear programming, provides a search in the "ravines" zone, performs a search quite efficiently under conditions of increased dimension of the definition domain of the optimized functional, and provides the required accuracy of the solution. Due to the transformation of the multidimensional non-convex nonlinear programming problem to the problem of minimizing a smooth monotonically decreasing function of one variable, the algorithm significantly reduces the computational complexity of solving boundary-value problems of optimal speed and maximum accuracy with a minimax estimate of the deviation of the final trajectory from a given state. We give an example of the solution of the test optimal control problem for induction heating of a cylindrical billet.
Keywords: distributed parameters, boundary-value problem, optimality criterion, search procedure, local minimum, global minimum.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 10.3260.2017/4.6
Received: 09.09.2019
Document Type: Article
UDC: 661.935+519.633.2
MSC: 65P99
Language: Russian
Citation: M. Yu. Livshits, A. V. Nenashev, Yu. E. Pleshivtseva, “Computational algorithm for optimal control of an object with distributed parameters in a nonsmooth area of final states”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:4 (2019), 41–51
Citation in format AMSBIB
\Bibitem{LivNenPle19}
\by M.~Yu.~Livshits, A.~V.~Nenashev, Yu.~E.~Pleshivtseva
\paper Computational algorithm for optimal control of an object with distributed parameters in a nonsmooth area of final states
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2019
\vol 12
\issue 4
\pages 41--51
\mathnet{http://mi.mathnet.ru/vyuru516}
\crossref{https://doi.org/10.14529/mmp190403}
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  • https://www.mathnet.ru/eng/vyuru/v12/i4/p41
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :38
    References:26
     
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