
This article is cited in 2 scientific papers (total in 2 papers)
A numerical method for solving linearquadratic control problems with constraints
Mikhail I. Gusev^{}, Igor V. Zykov^{} ^{} N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
Abstract:
The paper is devoted to the optimal control problem for a linear system with integrally constrained control function. We study the problem of minimization of a linear terminal cost with terminal constraints given by a set of linear inequalities. For the solution of this problem we propose twostage numerical algorithm, which is based on construction of the reachable set of the system. At the first stage we find a solution to finitedimensional optimization problem with a linear objective function and linear and quadratic constraints. At the second stage we solve a standard linearquadratic control problem, which admits a simple and effective solution.
Keywords:
Optimal control, Reachable set, Integral constraints, Convex programming, Semiinfinite linear programming.
Funding Agency 
Grant Number 
Russian Science Foundation 
161110146 
The research is supported by Russian Science Foundation, project no. 16–11–10146. 
DOI:
https://doi.org/10.15826/umj.2016.2.009
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Mikhail I. Gusev, Igor V. Zykov, “A numerical method for solving linearquadratic control problems with constraints”, Ural Math. J., 2:2 (2016), 108–116
Citation in format AMSBIB
\Bibitem{GusZyk16}
\by Mikhail~I.~Gusev, Igor~V.~Zykov
\paper A numerical method for solving linearquadratic control problems with constraints
\jour Ural Math. J.
\yr 2016
\vol 2
\issue 2
\pages 108116
\mathnet{http://mi.mathnet.ru/umj24}
\crossref{https://doi.org/10.15826/umj.2016.2.009}
\zmath{https://zbmath.org/?q=an:1413.49043}
\elib{http://elibrary.ru/item.asp?id=27447889}
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This publication is cited in the following articles:

M. I. Gusev, I. V. Zykov, “On extremal properties of the boundary points of reachable sets for control systems with integral constraints”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 114–125

M. I. Gusev, I. V. Zykov, “On the geometry of reachable sets for control systems with isoperimetric constraints”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S76–S87

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