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Minimax Linear Regulator Problems for Positive Systems

Gurpegui Ramón, Alba LU orcid ; Jeeninga, Mark LU orcid ; Tegling, Emma LU orcid and Rantzer, Anders LU orcid (2026) In IEEE Transactions on Automatic Control p.1-1
Abstract
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a frame work to address adversarial conditions and uncertainty. This work considers a multi-disturbance minimax Linear Regulator (LR) framework for positive linear time-invariant systems in continuous time, which, analogous to the Linear-Quadratic Regulator (LQR) problem, can be utilized for the stabilization of positive systems. The problem is studied for nonnegative and state-bounded disturbances. Dynamic programming theory is leveraged to derive explicit solutions to the minimax LR problem for both finite and infinite time horizons. In addition, a fixed-point method is proposed... (More)
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a frame work to address adversarial conditions and uncertainty. This work considers a multi-disturbance minimax Linear Regulator (LR) framework for positive linear time-invariant systems in continuous time, which, analogous to the Linear-Quadratic Regulator (LQR) problem, can be utilized for the stabilization of positive systems. The problem is studied for nonnegative and state-bounded disturbances. Dynamic programming theory is leveraged to derive explicit solutions to the minimax LR problem for both finite and infinite time horizons. In addition, a fixed-point method is proposed that computes the solution for the infinite horizon case, and the minimum L1-induced gain of the system is studied. We motivate the prospective scalability properties of our framework with a large-scale water management network. (Less)
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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Automatic Control
article number
14
pages
14 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:105032765671
ISSN
1558-2523
DOI
10.1109/TAC.2026.3673160
project
eSSENCE@LU 12:4 - N-body society: Turning political science into mathematics and computational models
language
English
LU publication?
yes
id
6a96521d-575d-4c7c-8f13-a458d89ac02f
alternative location
https://ieeexplore.ieee.org/document/11430578
date added to LUP
2026-04-09 15:19:23
date last changed
2026-05-12 13:53:13
@article{6a96521d-575d-4c7c-8f13-a458d89ac02f,
  abstract     = {{Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a frame work to address adversarial conditions and uncertainty. This work considers a multi-disturbance minimax Linear Regulator (LR) framework for positive linear time-invariant systems in continuous time, which, analogous to the Linear-Quadratic Regulator (LQR) problem, can be utilized for the stabilization of positive systems. The problem is studied for nonnegative and state-bounded disturbances. Dynamic programming theory is leveraged to derive explicit solutions to the minimax LR problem for both finite and infinite time horizons. In addition, a fixed-point method is proposed that computes the solution for the infinite horizon case, and the minimum L1-induced gain of the system is studied. We motivate the prospective scalability properties of our framework with a large-scale water management network.}},
  author       = {{Gurpegui Ramón, Alba and Jeeninga, Mark and Tegling, Emma and Rantzer, Anders}},
  issn         = {{1558-2523}},
  language     = {{eng}},
  month        = {{03}},
  pages        = {{1--1}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{Minimax Linear Regulator Problems for Positive Systems}},
  url          = {{http://dx.doi.org/10.1109/TAC.2026.3673160}},
  doi          = {{10.1109/TAC.2026.3673160}},
  year         = {{2026}},
}