Optimal Control on Positive Cones
Pates, Richard LU and Rantzer, Anders LU
(2024)
63rd IEEE Conference on Decision and Control, CDC 2024
In Proceedings of the IEEE Conference on Decision and Control
p.992-997
- Abstract
An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A separate theorem relates the assumption on the cone to the existence of minimal elements in certain subsets of the dual cone. Three special cases are derived as examples. The first one, where the positive cone is the set of positive semi-definite matrices, reduces to standard linear quadratic control. The second one, where the positive cone is a polyhedron, reduces to a recent result on optimal control of positive systems. The third special case corresponds to linear quadratic control with additional... (More)
An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A separate theorem relates the assumption on the cone to the existence of minimal elements in certain subsets of the dual cone. Three special cases are derived as examples. The first one, where the positive cone is the set of positive semi-definite matrices, reduces to standard linear quadratic control. The second one, where the positive cone is a polyhedron, reduces to a recent result on optimal control of positive systems. The third special case corresponds to linear quadratic control with additional structure, such as spatial invariance.
(Less)
- author
- Pates, Richard
LU
and Rantzer, Anders
LU
- organization
- publishing date
- 2024
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the IEEE Conference on Decision and Control
- series title
- Proceedings of the IEEE Conference on Decision and Control
- pages
- 6 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 63rd IEEE Conference on Decision and Control, CDC 2024
- conference location
- Milan, Italy
- conference dates
- 2024-12-16 - 2024-12-19
- external identifiers
-
- scopus:86000614898
- ISSN
- 2576-2370
- 0743-1546
- ISBN
- 9798350316339
- DOI
- 10.1109/CDC56724.2024.10886638
- language
- English
- LU publication?
- yes
- id
- c2ed640f-477e-40e5-8d9f-98c42f20b4da
- date added to LUP
- 2025-06-03 09:27:00
- date last changed
- 2025-07-15 13:44:33
@inproceedings{c2ed640f-477e-40e5-8d9f-98c42f20b4da,
abstract = {{<p>An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A separate theorem relates the assumption on the cone to the existence of minimal elements in certain subsets of the dual cone. Three special cases are derived as examples. The first one, where the positive cone is the set of positive semi-definite matrices, reduces to standard linear quadratic control. The second one, where the positive cone is a polyhedron, reduces to a recent result on optimal control of positive systems. The third special case corresponds to linear quadratic control with additional structure, such as spatial invariance.</p>}},
author = {{Pates, Richard and Rantzer, Anders}},
booktitle = {{Proceedings of the IEEE Conference on Decision and Control}},
isbn = {{9798350316339}},
issn = {{2576-2370}},
language = {{eng}},
pages = {{992--997}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{Proceedings of the IEEE Conference on Decision and Control}},
title = {{Optimal Control on Positive Cones}},
url = {{http://dx.doi.org/10.1109/CDC56724.2024.10886638}},
doi = {{10.1109/CDC56724.2024.10886638}},
year = {{2024}},
}