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Duality between cost and density in optimal control

Rantzer, Anders LU orcid and Hedlund, Sven LU (2003) 2. p.1218-1221
Abstract
A theorem on duality between cost functions and density functions in optimal control is derived using the Hahn-Banach theorem. The result puts focus on convexity aspects in control synthesis and the theory of almost global stability. In particular, it gives a new proof that existence of a density function is both necessary and sufficient for almost global stability in a nonlinear system.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
duality, optimal control, Density function, stability
host publication
Proceedings. 42nd IEEE Conference on Decision and Control, 2003
volume
2
pages
1218 - 1221
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000189434100210
  • scopus:1542329037
ISSN
0191-2216
ISBN
0-7803-7924-1
DOI
10.1109/CDC.2003.1272774
language
English
LU publication?
yes
id
1327ae03-5ead-4910-aa6b-591571b2a379 (old id 536807)
date added to LUP
2016-04-01 17:07:11
date last changed
2025-10-14 09:02:04
@inproceedings{1327ae03-5ead-4910-aa6b-591571b2a379,
  abstract     = {{A theorem on duality between cost functions and density functions in optimal control is derived using the Hahn-Banach theorem. The result puts focus on convexity aspects in control synthesis and the theory of almost global stability. In particular, it gives a new proof that existence of a density function is both necessary and sufficient for almost global stability in a nonlinear system.}},
  author       = {{Rantzer, Anders and Hedlund, Sven}},
  booktitle    = {{Proceedings. 42nd IEEE Conference on Decision and Control, 2003}},
  isbn         = {{0-7803-7924-1}},
  issn         = {{0191-2216}},
  keywords     = {{duality; optimal control; Density function; stability}},
  language     = {{eng}},
  pages        = {{1218--1221}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Duality between cost and density in optimal control}},
  url          = {{https://lup.lub.lu.se/search/files/4880328/625647.pdf}},
  doi          = {{10.1109/CDC.2003.1272774}},
  volume       = {{2}},
  year         = {{2003}},
}