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 Model. Anal. Inform. Sist., 2013, Volume 20, Number 3, Pages 130–152 (Mi mais317)

Transformations of Optimal Control Problems

A. Tsirlin

Program Systems Institute of RAS, Petra I st., 2, s. Ves’kovo, Pereslavskii raion, Yaroslavskaya obl., 152021, Russia

Abstract: The paper considers such transformations of variational and optimal control problems (by a change of phase variables) that help to get the solution. Among these techniques are methods of the dimensionality reduction by a transition from an original argument to a new one, by a detection of a variable staying unchanged through equations of the system (invariant), by extension of the original problem and a transition from it to a simpler problem that gives an estimate solution of the original one. In some cases we can get a solution that is simplified by a transition from a set of conditions in the form of differential equations to the only integral condition. This relates to equations with a retarded argument. The paper gives examples of application of these techniques to real engineering problems such as an optimal control of biosynthesis, cooling of crystal systems by a laser radiation, etc.

Keywords: optimum control, transformation, variable condition, decision.

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Citation: A. Tsirlin, “Transformations of Optimal Control Problems”, Model. Anal. Inform. Sist., 20:3 (2013), 130–152

Citation in format AMSBIB
\Bibitem{Tsi13} \by A.~Tsirlin \paper Transformations of Optimal Control Problems \jour Model. Anal. Inform. Sist. \yr 2013 \vol 20 \issue 3 \pages 130--152 \mathnet{http://mi.mathnet.ru/mais317} 

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This publication is cited in the following articles:
1. V. I. Gurman, I. V. Rasina, I. S. Guseva, O. V. Fesko, “Metody priblizhennogo resheniya zadach optimalnogo upravleniya”, Programmnye sistemy: teoriya i prilozheniya, 6:4 (2015), 113–137
2. V. I. Gurman, I. V. Rasina, O. V. Fes'ko, I. S. Guseva, “On certain approaches to optimization of control processes. I”, Autom. Remote Control, 77:8 (2016), 1370–1385
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