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Impulsive Control Problems with State Constraints

  • 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, in the context of the impulsive extension of the optimal control problem, the state constraints are studied. That is, it is assumed that a certain closed subset of the state space is given while feasible arcs are not permitted to take values outside of it. This set is defined functionally in our considerations. It should be noted that the state constraints are in great demand in various engineering applications. For example, an iRobot cleaning a house should be able to avoid obstacles or objects that arise in its path. These obstacles are nothing but state constraints, while the task of avoiding the obstacle represents an important class of problems with state constraints. Evidently, there is a host of other engineering problems, in which the state constraints play an important role. The chapter deals with the same problem formulation as in the previous chapter; however, the state constraints of the above type are added. For this impulsive control problem, the Gamkrelidze-like maximum principle is obtained. Conditions for nondegeneracy of the maximum principle are presented. The chapter ends with eight 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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