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Impulsive Control Problems Under Borel Measurability

  • Aram Arutyunov
  • Dmitry KaramzinEmail author
  • Fernando Lobo Pereira
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 477)

Abstract

In this chapter, the complexity of the dynamical control system in the optimal control problem under extension increases. Herein, it is not linear w.r.t. x and u but is still linear w.r.t. the impulsive control variable. Moreover, the matrix-multiplier for the impulsive control depends on the conventional control \(u(\cdot )\) given by Borel functions. The right-hand side of the dynamical system is assumed to be Borel w.r.t. u. The results of the first chapter are derived for this more general formulation. The concept of extension itself does not change so far, as the space of Borel measures yet suffices to describe all feasible trajectories. The chapter ends with seven exercises.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Aram Arutyunov
    • 1
    • 2
    • 3
  • Dmitry Karamzin
    • 4
    Email author
  • Fernando Lobo Pereira
    • 5
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Institute of Control Sciences of the Russian Academy of SciencesMoscowRussia
  3. 3.RUDN UniversityMoscowRussia
  4. 4.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia
  5. 5.FEUP/DEECPorto UniversityPortoPortugal

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