Minimax dual control with finite-dimensional information state
Kjellqvist, Olle LU
(2024)
242.
p.299-311
- Abstract
- This article considers output-feedback control of systems where the function mapping states to measurements has a set-valued inverse. We show that if the set has a bounded number of elements, then minimax dual control of such systems admits finite-dimensional information states. We specialize our results to a discrete-time integrator with magnitude measurements and derive a surprisingly simple sub-optimal control policy that ensures finite gain of the closed loop. The sub-optimal policy is a proportional controller where the magnitude of the gain is computed offline, but the sign is learned, forgotten, and relearned online.
The discrete-time integrator with magnitude measurements captures real-world applications such as antenna... (More) - This article considers output-feedback control of systems where the function mapping states to measurements has a set-valued inverse. We show that if the set has a bounded number of elements, then minimax dual control of such systems admits finite-dimensional information states. We specialize our results to a discrete-time integrator with magnitude measurements and derive a surprisingly simple sub-optimal control policy that ensures finite gain of the closed loop. The sub-optimal policy is a proportional controller where the magnitude of the gain is computed offline, but the sign is learned, forgotten, and relearned online.
The discrete-time integrator with magnitude measurements captures real-world applications such as antenna alignment, and despite its simplicity, it defies established control-design methods. For example, whether a stabilizing linear time-invariant controller exists for this system is unknown, and we conjecture that none exists.
(Less) - Abstract (Swedish)
- Artikeln behandlar utsignalåterkoppling av system där funktionen som avbildar tillstånden på mätsignarlerna har en mängdvärd invers.
Vi visar att om mängden har begränsad kardinalitet, så går det att komprimera historiken till en ändlig vektor som beräknas rekursivt.
Resultatet exemplifieras på diskrettidsintegratorn där mätsignalen är absolutbeloppet av tillståndet och får fram en förvånandsvärt enkelt suboptimal regulator. Exemplet är givande därför att trots enkelheten så går det inte att applicera etablerade syntesmetoder. Vi förmodar att exemplet inte går att lösa med en linjär tidsinvariant regulator.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f95faee0-e716-4b50-a79c-17b5533d28d8
- author
- Kjellqvist, Olle
LU
- organization
- alternative title
- Minimax dual reglering med ändligdimensionella informationstillstånd
- publishing date
- 2024-07-15
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the 6th Annual Learning for Dynamics & Control Conference
- volume
- 242
- pages
- 12 pages
- publisher
- PMLR
- project
- Scalable Control using Learning and Adaptation
- language
- English
- LU publication?
- yes
- id
- f95faee0-e716-4b50-a79c-17b5533d28d8
- alternative location
- https://arxiv.org/abs/2312.05156
- https://proceedings.mlr.press/v242/kjellqvist24a.html
- date added to LUP
- 2024-08-28 09:50:18
- date last changed
- 2024-09-13 09:41:11
@inproceedings{f95faee0-e716-4b50-a79c-17b5533d28d8,
abstract = {{This article considers output-feedback control of systems where the function mapping states to measurements has a set-valued inverse. We show that if the set has a bounded number of elements, then minimax dual control of such systems admits finite-dimensional information states. We specialize our results to a discrete-time integrator with magnitude measurements and derive a surprisingly simple sub-optimal control policy that ensures finite gain of the closed loop. The sub-optimal policy is a proportional controller where the magnitude of the gain is computed offline, but the sign is learned, forgotten, and relearned online.<br/> The discrete-time integrator with magnitude measurements captures real-world applications such as antenna alignment, and despite its simplicity, it defies established control-design methods. For example, whether a stabilizing linear time-invariant controller exists for this system is unknown, and we conjecture that none exists.<br/>}},
author = {{Kjellqvist, Olle}},
booktitle = {{Proceedings of the 6th Annual Learning for Dynamics & Control Conference}},
language = {{eng}},
month = {{07}},
pages = {{299--311}},
publisher = {{PMLR}},
title = {{Minimax dual control with finite-dimensional information state}},
url = {{https://arxiv.org/abs/2312.05156}},
volume = {{242}},
year = {{2024}},
}