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Synthesis Theory in Optimal Control

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Abstract

In this entry we review the theory of optimal synthesis. We describe the steps necessary to solve an optimal control problem and the sufficient conditions for optimality given by the theory. We describe some relevant examples that have important applications in mechanics, in the theory of hypoelliptic operators, and for the study of models of geometry of vision. Finally, we discuss the problem of optimal stabilization and the difficulties encountered if one tries to give the solution to the problem in feedback form.

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Acknowledgements

The first author has been supported by the ANR projects SRGI ANR-15-CE40-0018 and Quaco ANR-17-CE40-0007-01.

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Authors and Affiliations

  1. CNRS, Sorbonne Université, Université de Paris, INRIA team CAGE, Laboratorie Jacques-Louis Lions, Paris, France

    Ugo Boscain

  2. Mathematical Sciences and Center for Computational and Integrative Biology, Rutgers University, Camden, NJ, USA

    Benedetto Piccoli

Authors
  1. Ugo Boscain
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  2. Benedetto Piccoli
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Corresponding author

Correspondence to Ugo Boscain .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Department of Mathematics, The University of Michigan, Ann Arbor, MI, USA

    Anthony Bloch

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Boscain, U., Piccoli, B. (2021). Synthesis Theory in Optimal Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_50-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_50-2

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Synthesis Theory in Optimal Control
    Published:
    09 November 2020

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_50-2

  2. Original

    Synthesis Theory in Optimal Control
    Published:
    06 October 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_50-1

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