State-Constrained Control Under Higher Impulses

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


In these sections, we deal with additional constraints on the solutions to equations of Sects.  7.1 and  7.4, related to control under generalized (higher) impulses . These restrictions are an analogy of state constraints for systems controlled by ordinary impulses of Chap.  5 (see also [1, 7]). Discussing the problem of optimal control under higher impulses and state constraints we describe it first in terms of the theory of distributions [12, 13]. indicating conditions for its solvability. Then, in order to formulate conditions of optimality, we use a reduction of the system to the first-order form under vector measures, as shown in Sect.  7.3.


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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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