Optimal control of linear cost networks
(2024) In European Journal of Control 80.- Abstract
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the Bellman equation giving the optimal cost function and resulting sparse state feedback for these systems can be stated explicitly, with the solution given by a linear program. Our framework admits a range of network routing problems with underlying linear dynamics. These dynamics can be used to model traditional graph-theoretical problems like shortest path as a special case, but can also capture more complex behaviors. We provide an asynchronous and distributed value iteration algorithm for obtaining the optimal cost function and control law.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8b5564bb-c6f8-4e00-a162-8349c5b52f4c
- author
- Ohlin, David
LU
; Tegling, Emma LU and Rantzer, Anders LU
- organization
- publishing date
- 2024-11
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Linear systems, Networked systems, Optimal control, Positive systems
- in
- European Journal of Control
- volume
- 80
- article number
- 101068
- publisher
- Lavoisier
- external identifiers
-
- scopus:85197051063
- ISSN
- 0947-3580
- DOI
- 10.1016/j.ejcon.2024.101068
- language
- English
- LU publication?
- yes
- id
- 8b5564bb-c6f8-4e00-a162-8349c5b52f4c
- date added to LUP
- 2024-12-16 12:41:55
- date last changed
- 2025-04-04 14:53:01
@article{8b5564bb-c6f8-4e00-a162-8349c5b52f4c, abstract = {{<p>We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the Bellman equation giving the optimal cost function and resulting sparse state feedback for these systems can be stated explicitly, with the solution given by a linear program. Our framework admits a range of network routing problems with underlying linear dynamics. These dynamics can be used to model traditional graph-theoretical problems like shortest path as a special case, but can also capture more complex behaviors. We provide an asynchronous and distributed value iteration algorithm for obtaining the optimal cost function and control law.</p>}}, author = {{Ohlin, David and Tegling, Emma and Rantzer, Anders}}, issn = {{0947-3580}}, keywords = {{Linear systems; Networked systems; Optimal control; Positive systems}}, language = {{eng}}, publisher = {{Lavoisier}}, series = {{European Journal of Control}}, title = {{Optimal control of linear cost networks}}, url = {{http://dx.doi.org/10.1016/j.ejcon.2024.101068}}, doi = {{10.1016/j.ejcon.2024.101068}}, volume = {{80}}, year = {{2024}}, }