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Minimax Linear Optimal Control of Positive Systems

Gurpegui, Alba LU ; Tegling, Emma LU and Rantzer, Anders LU orcid (2023) In IEEE Control Systems Letters
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.

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author
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publishing date
type
Contribution to journal
publication status
epub
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
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
2024-01-10 09:44:25
@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}},
  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}},
  year         = {{2023}},
}