A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS

Mikhail I. Gusev     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia, Russian Federation)
Igor V. Zykov     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia, Russian Federation)

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.

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References


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DOI: http://dx.doi.org/10.15826/umj.2016.2.009

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