Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

On PI-control in Capacity-Limited Networks

Agner, Felix LU and Rantzer, Anders LU orcid (2024) In Automatica
Abstract
This paper concerns control of a class of systems where multiple dynamically stable agents share a nonlinear and bounded control-interconnection. The agents are subject to a disturbance which is too large to reject with the available control action, making it impossible to stabilize all agents in their desired states. In this nonlinear setting, we consider two different anti-windup equipped proportional-integral control strategies and analyze their properties. We show that a fully decentralized strategy will globally, asymptotically stabilize a unique equilibrium. This equilibrium also minimizes a weighted sum of the tracking errors. We also consider a light addition to the fully decentralized strategy, where rank-1 coordination between... (More)
This paper concerns control of a class of systems where multiple dynamically stable agents share a nonlinear and bounded control-interconnection. The agents are subject to a disturbance which is too large to reject with the available control action, making it impossible to stabilize all agents in their desired states. In this nonlinear setting, we consider two different anti-windup equipped proportional-integral control strategies and analyze their properties. We show that a fully decentralized strategy will globally, asymptotically stabilize a unique equilibrium. This equilibrium also minimizes a weighted sum of the tracking errors. We also consider a light addition to the fully decentralized strategy, where rank-1 coordination between the agents is introduced via the anti-windup action. We show that any equilibrium to this closed-loop system minimizes the maximum tracking error for any agent. A remarkable property of these results is that they rely on extremely few assumptions on the interconnection between the agents. Finally we illustrate how the considered model can be applied in a district heating setting, and demonstrate the two considered controllers in a simulation. (Less)
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
submitted
subject
in
Automatica
publisher
Elsevier
ISSN
0005-1098
DOI
10.48550/arXiv.2411.14077
project
Scalable Control for Increased Flexibility in District Heating Networks
Scalable Control of Interconnected Systems
language
English
LU publication?
yes
id
7a574b33-a89c-4b1c-9f54-45838b0ee8ec
date added to LUP
2024-11-22 08:20:56
date last changed
2025-04-04 14:28:08
@article{7a574b33-a89c-4b1c-9f54-45838b0ee8ec,
  abstract     = {{This paper concerns control of a class of systems where multiple dynamically stable agents share a nonlinear and bounded control-interconnection. The agents are subject to a disturbance which is too large to reject with the available control action, making it impossible to stabilize all agents in their desired states. In this nonlinear setting, we consider two different anti-windup equipped proportional-integral control strategies and analyze their properties. We show that a fully decentralized strategy will globally, asymptotically stabilize a unique equilibrium. This equilibrium also minimizes a weighted sum of the tracking errors. We also consider a light addition to the fully decentralized strategy, where rank-1 coordination between the agents is introduced via the anti-windup action. We show that any equilibrium to this closed-loop system minimizes the maximum tracking error for any agent. A remarkable property of these results is that they rely on extremely few assumptions on the interconnection between the agents. Finally we illustrate how the considered model can be applied in a district heating setting, and demonstrate the two considered controllers in a simulation.}},
  author       = {{Agner, Felix and Rantzer, Anders}},
  issn         = {{0005-1098}},
  language     = {{eng}},
  month        = {{11}},
  publisher    = {{Elsevier}},
  series       = {{Automatica}},
  title        = {{On PI-control in Capacity-Limited Networks}},
  url          = {{http://dx.doi.org/10.48550/arXiv.2411.14077}},
  doi          = {{10.48550/arXiv.2411.14077}},
  year         = {{2024}},
}