Topological Derivatives for Optimal Control Problems

  • Antonio André NovotnyEmail author
  • Jan Sokołowski
  • Antoni Żochowski
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 188)


In this chapter, the topological derivative is obtained for the optimal value of the cost functional for a class of optimal control problems. We obtain the closed form of the topological derivative. Such an approach would allow to consider simultaneous structure design and control modifications. In order to introduce the topological derivative of the shape functional \(\varOmega \rightarrow J(\varOmega )\) we usually consider the mapping \(\varOmega \rightarrow y\) for the boundary value problem which gives the function y. In the case of optimal control problems the couple (uy) of the control u and the state y is given by the optimality system.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Antonio André Novotny
    • 1
  • Jan Sokołowski
    • 2
    • 3
    • 4
  • Antoni Żochowski
    • 3
  1. 1.Coordenação de Métodos Matemáticos e ComputacionaisLaboratório Nacional de Computação Científica LNCC/MCTICPetrópolisBrazil
  2. 2.Institut Élie Cartan de Nancy, UMR 7502Université de Lorraine, CNRSVandœuvre-Lès-NancyFrance
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  4. 4.Universidade Federal da Paraiba, Centro de informaticaJoão PessoaBrazil

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