Numerical methods for nonlinear optimal control problems

Titelangaben

Grüne, Lars:
Numerical methods for nonlinear optimal control problems.
In: Samad, Tariq ; Baillieul, John (Hrsg.): Encyclopedia of Systems and Control. - London : Springer , 2014
ISBN 978-1-447-15057-2
DOI: https://doi.org/10.1007/978-1-4471-5102-9_208-2

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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 Principles and the approach via direct discretization.