Morse Theory and Optimal Control Problems

  • A. A. Agrachev
  • S. A. Vakhrameev
Part of the Progress in Systems and Control Theory book series (PSCT, volume 9)


It is well known that Morse Theory is a very flexible tool for dealing with nonlinear problems of analysis and topological problems. The main purpose of the present paper is to describe a modification of this theory which can be used for the study of optimal control problems. The necessity of such a modification is related to the fact that for these problems the inequality constraints are typical (for example, control constraints, phase constraints, etc.) The inequalities destroy the smooth structure and hence the necessity to construct the theory for spaces with singularities. We encounter this situation in the case of optimal control problems.


Optimal Control Problem Homotopic Type Tangent Cone Morse Theory Morse Function 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • A. A. Agrachev
    • 1
  • S. A. Vakhrameev
    • 1
  1. 1.All Union Institute of Scientific and Technical InformationVINITIMoscowUSSR

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