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Optimal control of linear cost networks

Ohlin, David LU orcid ; Tegling, Emma LU and Rantzer, Anders LU orcid (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.

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author
; and
organization
publishing date
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}},
}