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

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. 16–11–10146.

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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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
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
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