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Encyclopedia of Systems and Control pp 1–10Cite as

Numerical Methods for Nonlinear Optimal Control Problems

Abstract

In this article we describe the three most common approaches for numerically solving nonlinear optimal control problems governed by ordinary differential equations. For computing approximations to optimal value functions and optimal feedback laws, we present the Hamilton-Jacobi-Bellman approach. For computing approximately optimal open-loop control functions and trajectories for a single initial value, we outline the indirect approach based on Pontryagin’s maximum principle and the approach via direct discretization.

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of Bayreuth, 95440, Bayreuth, Germany

    Prof. Dr.Lars Grüne

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  1. Prof. Dr.Lars Grüne
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Correspondence to Prof. Dr.Lars Grüne .

Editor information

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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© 2014 Springer-Verlag London

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Grüne, P. (2014). Numerical Methods for Nonlinear Optimal Control Problems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_208-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_208-2

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Numerical Methods for Nonlinear Optimal Control Problems
    Published:
    02 November 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_208-3

  2. Numerical Methods for Nonlinear Optimal Control Problems
    Published:
    08 December 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_208-2

  3. Original

    Numerical Methods for Nonlinear Optimal Control Problems
    Published:
    13 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_208-1

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