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Synthesis Theory in Optimal Control

Encyclopedia of Systems and Control

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 hypo-elliptic 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 European Research Council, ERC StG 2009 “GeCoMethods”, contract number 239748.

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Authors and Affiliations

  1. CNRS CMAP, École Polytechnique, Palaiseau, France

    Ugo Boscain

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  1. Ugo Boscain
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  2. Benedetto Piccoli
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Correspondence to Ugo Boscain .

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Editors and Affiliations

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

    John Baillieul

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

    Tariq Samad

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Boscain, U., Piccoli, B. (2014). 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_50-1

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

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  • 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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