Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Numerical Methods for Nonlinear Optimal Control Problems

Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_208

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.

Keywords

Direct discretization Hamilton-Jacobi-Bellman equations Optimal control Ordinary differential equations Pontryagin’s maximum principle 
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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of BayreuthBayreuthGermany