Geodesic
Parametric regularization of the functional in a linear-quadratic optimal control problem
The Bulletin of Irkutsk State University. Series Mathematics, Tome 49 (2024), pp. 32-44

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A linear-quadratic optimal control problem with parameters and arbitrary matrices in the quadratic cost functional is considered on the set of stepwise control functions. As a quality criterion of the admissible set of parameters it is proposed to choose a condition number of the final matrix, which is expressed through the boundaries of its spectrum. As a result, parameter optimization problems are constructed which provide a strong convexity of the objective function on control variables together with relatively good conditionality of the corresponding quadratic programming problem. A similar approach is realized for the minimax problem. In this case, the objective function acquires a convex-concave structure and the choice of parameters is based on minimization of some convolution of two condition numbers.
Keywords: linear-quadratic optimal control problem, cost functional with parameters, parameter optimization, minimization of the condition number. 
@article{IIGUM_2024_49_a2,
     author = {V. A. Srochko and A. V. Arguchintsev},
     title = {Parametric regularization of the functional in a linear-quadratic optimal control problem},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {32--44},
     publisher = {mathdoc},
     volume = {49},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2024_49_a2/}
}
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V. A. Srochko; A. V. Arguchintsev. Parametric regularization of the functional in a linear-quadratic optimal control problem. The Bulletin of Irkutsk State University. Series Mathematics, Tome 49 (2024), pp. 32-44. http://geodesic.mathdoc.fr/item/IIGUM_2024_49_a2/