Automatic Control and Computer Sciences

, Volume 44, Issue 4, pp 179–190

Parametric optimal control problems with weighted L1-norm in the cost function

  • O. I. Kostyukova
  • E. A. Kostina
  • N. M. Fedortsova
Article

Abstract

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 words

optimal control problems differentiability of solution with respect to parameter weight ratio 

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Copyright information

© Allerton Press, Inc. 2010

Authors and Affiliations

  • O. I. Kostyukova
    • 1
  • E. A. Kostina
    • 2
  • N. M. Fedortsova
    • 3
  1. 1.Institute of MathematicsBelarus Academy of SciencesMinskBelarus
  2. 2.Marburg University, GermanyMarburgGermany
  3. 3.Belarusian State University of Computer Science and RadioelectronicsMinskBelarus

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