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Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations

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Abstract

Consideration was given to the problems of variational calculus and optimal control admitting impulsive controls and, correspondingly, discontinuous solutions. The evolution of the notion of singular space-time transformation beginning from the problem of classical variational calculus and ending with the problems of optimal control at the phase of impact was shown.

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Authors and Affiliations

  1. Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia

    B. M. Miller

  2. School of Mathematical Sciences, Monash University, Victoria, Australia

    B. M. Miller

  3. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    E. Ya. Rubinovich

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  1. B. M. Miller
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  2. E. Ya. Rubinovich
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Original Russian Text © B.M. Miller, E.Ya. Rubinovich, 2013, published in Avtomatika i Telemekhanika, 2013, No. 12, pp. 56–103.

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Miller, B.M., Rubinovich, E.Y. Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations. Autom Remote Control 74, 1969–2006 (2013). https://doi.org/10.1134/S0005117913120047

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