Abstract
In the paper, an optimal control problem with weighted L 1-norm in the cost function is studied. The problem is considered as a parametric problem where L 1-norm weight ratio is treated as a parameter. We analyze the dependence of solution to the mentioned optimization problem on values of the parameter. A theorem that describes properties of the solution under small parameter perturbations is proved. Differential properties of the solution are investigated. Under assumption that a solution to unperturbed problem is known, rules for construction of solutions to perturbed optimization problems are given.
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Original Russian Text © O.I. Kostyukova, E.A. Kostina, N.M. Fedortsova, 2010, published in Avtomatika i Vychislitel’naya Tekhnika, 2010, No. 4, pp. 5–18.
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Kostyukova, O.I., Kostina, E.A. & Fedortsova, N.M. Parametric optimal control problems with weighted L 1-norm in the cost function. Aut. Conrol Comp. Sci. 44, 179–190 (2010). https://doi.org/10.3103/S0146411610040012
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DOI: https://doi.org/10.3103/S0146411610040012