Funnel Equations and Multivalued Integration Problems for Control Synthesis

  • A. B. Kurzhanski
  • O. I. Nikonov
Part of the Progress in Systems and Control Theory book series (PSCT, volume 2)


This paper deals with the problem of synthesizing a feedback control strategy for a linear controlled system subjected to unknown but bounded input disturbances and convex state constraints (see [1–7]). While seeking for the solution in the form of an “extremal strategy” as introduced by N.N. Krasovski, it is shown that the respective sets of solubility states that are crucial for the solution of the control problem could also be treated as cross-sections of trajectory tubes for some specially designed “funnel equations”. The set-valued solutions to these could be then presented in the form of specially derived multivalued integrals.


State Constraint Differential Game Differential Inclusion Multivalued Function Linear Control System 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • A. B. Kurzhanski
    • 1
    • 2
  • O. I. Nikonov
    • 1
    • 2
  1. 1.I.I.A.S.A.LaxenburgAustria
  2. 2.Institute of Mathematics & MechanicsSverdlovskUSSR

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