Parametric optimal control problems with weighted L1-norm in the cost function
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In the paper, an optimal control problem with weighted L1-norm in the cost function is studied. The problem is considered as a parametric problem where L1-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.
Key wordsoptimal control problems differentiability of solution with respect to parameter weight ratio
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