Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Numerical Methods for Nonlinear Optimal Control Problems

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


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.


Optimal control Ordinary differential equations Hamilton-Jacobi-Bellman equations Pontryagin’s maximum principle Direct discretization 
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© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of BayreuthBayreuthGermany