Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Numerical Methods for Nonlinear Optimal Control Problems

  • Lars GrüneEmail author
Living reference work entry

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


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.


Direct discretization Hamilton-Jacobi-Bellman equations Optimal control Ordinary differential equations Pontryagin’s maximum principle 
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© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of BayreuthBayreuthGermany

Section editors and affiliations

  • Michael Cantoni
    • 1
  1. 1.Department of Electrical & Electronic EngineeringThe University of MelbourneParkvilleAustralia