Minimax Linear Optimal Control of Positive Systems
Gurpegui, Alba LU ; Tegling, Emma LU and Rantzer, Anders LU
(2023)
In IEEE Control Systems Letters
7.
p.3920-3925
- Abstract
We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the Bellman equation can be obtained, revealing that the optimal control policy (among all possible policies) is linear. This policy can in turn be computed through standard value iterations. Moreover, the feedback matrix of the optimal controller inherits the sparsity structure from the constraint matrix of the problem statement. This permits structural controller constraints in the problem design and simplifies the application to large-scale systems. We use a simple example of voltage control in an... (More)
We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the Bellman equation can be obtained, revealing that the optimal control policy (among all possible policies) is linear. This policy can in turn be computed through standard value iterations. Moreover, the feedback matrix of the optimal controller inherits the sparsity structure from the constraint matrix of the problem statement. This permits structural controller constraints in the problem design and simplifies the application to large-scale systems. We use a simple example of voltage control in an electric network to illustrate the problem setup.
(Less)
- author
- Gurpegui, Alba
LU
; Tegling, Emma
LU
and Rantzer, Anders
LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Dynamic Programming, Dynamic programming, Linear programming, Minimax, Optimal Control, Optimal control, Optimization, Positive Systems, Power system dynamics, Uncertainty, Voltage control
- in
- IEEE Control Systems Letters
- volume
- 7
- pages
- 6 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85179805128
- ISSN
- 2475-1456
- DOI
- 10.1109/LCSYS.2023.3341344
- language
- English
- LU publication?
- yes
- id
- 47c6ec23-04e0-4d57-8228-03207554751a
- date added to LUP
- 2024-01-10 09:42:22
- date last changed
- 2024-06-05 08:52:27
@article{47c6ec23-04e0-4d57-8228-03207554751a,
abstract = {{<p>We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the Bellman equation can be obtained, revealing that the optimal control policy (among all possible policies) is linear. This policy can in turn be computed through standard value iterations. Moreover, the feedback matrix of the optimal controller inherits the sparsity structure from the constraint matrix of the problem statement. This permits structural controller constraints in the problem design and simplifies the application to large-scale systems. We use a simple example of voltage control in an electric network to illustrate the problem setup.</p>}},
author = {{Gurpegui, Alba and Tegling, Emma and Rantzer, Anders}},
issn = {{2475-1456}},
keywords = {{Dynamic Programming; Dynamic programming; Linear programming; Minimax; Optimal Control; Optimal control; Optimization; Positive Systems; Power system dynamics; Uncertainty; Voltage control}},
language = {{eng}},
pages = {{3920--3925}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Control Systems Letters}},
title = {{Minimax Linear Optimal Control of Positive Systems}},
url = {{http://dx.doi.org/10.1109/LCSYS.2023.3341344}},
doi = {{10.1109/LCSYS.2023.3341344}},
volume = {{7}},
year = {{2023}},
}