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Ural Math. J., 2016, Volume 2, Issue 2, Pages 108–116 (Mi umj24)  

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

A numerical method for solving linear-quadratic 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 two-stage numerical algorithm, which is based on construction of the reachable set of the system. At the first stage we find a solution to finite-dimensional optimization problem with a linear objective function and linear and quadratic constraints. At the second stage we solve a standard linear-quadratic control problem, which admits a simple and effective solution.

Keywords: Optimal control, Reachable set, Integral constraints, Convex programming, Semi-infinite linear programming.

Funding Agency Grant Number
Russian Science Foundation 16-11-10146
The research is supported by Russian Science Foundation, project no. 161110146.


DOI: https://doi.org/10.15826/umj.2016.2.009

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Citation: Mikhail I. Gusev, Igor V. Zykov, “A numerical method for solving linear-quadratic 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 linear-quadratic control problems with constraints
\jour Ural Math. J.
\yr 2016
\vol 2
\issue 2
\pages 108--116
\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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  isi  elib
    2. 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  mathnet  crossref  crossref  isi  elib
  • Ural Mathematical Journal
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