Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach

The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an i...

Full description

Saved in:
Bibliographic Details
Published in:Journal of optimization theory and applications 2010-08, Vol.146 (2), p.321-346
Main Authors: Cristiani, E., Martinon, P.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied sciences
Approximation
Calculus of variations and optimal control
Calculus of Variations and Optimal Control
Optimization
Control
Engineering
Exact sciences and technology
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Methods
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Optimization and Control
Partial differential equations
Sciences and techniques of general use
Studies
Theory of Computation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9649-6