Geodesic
A numerical method for solving linear-quadratic control problems with constraints
Ural mathematical journal, Tome 2 (2016) no. 2, pp. 108-116

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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. 
@article{UMJ_2016_2_2_a8,
     author = {Mikhail I. Gusev and Igor V. Zykov},
     title = {A numerical method for solving linear-quadratic control problems with constraints},
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     pages = {108--116},
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     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2016_2_2_a8/}
}
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Mikhail I. Gusev; Igor V. Zykov. A numerical method for solving linear-quadratic control problems with constraints. Ural mathematical journal, Tome 2 (2016) no. 2, pp. 108-116. http://geodesic.mathdoc.fr/item/UMJ_2016_2_2_a8/