Closed-Loop Impulse Control

  • Alexander B. KurzhanskiEmail author
  • Alexander N. Daryin
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 468)


In this chapter, we study closed-loop impulse controls. The key to solving such feedback control problems is the Principle of Optimality for the related value functions. This move allows to derive related Dynamic Programming Equations. The infinitesimal form of such equations allows to calculate related value functions and the closed-loop controls. Next, it is necessary to explain how one should interpret the solution of the impulsive closed-loop system under such control. Here, we present several possible approaches complemented by examples for one- and two-dimensional systems. Finally, we discuss two problems related to feedback control, namely, the construction of reachability sets and the problem of stabilization by impulses, [1, 2, 3, 4, 5, 7].


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© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  • Alexander B. Kurzhanski
    • 1
    Email author
  • Alexander N. Daryin
    • 2
  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Google ResearchZürichSwitzerland

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