Understanding Probabilistic Uncertainty Using ν-Gap
(2024)Department of Automatic Control
- Abstract
- System uncertainty constitutes a fundamental restriction on control performance. System models are never perfect and the differences between system and model can be difficult to contend with. Applying a model based controller to the true system with uncertain dynamics can yield unpredictable results which led researchers to produce methods of robust control design. Existing theory on the ν-gap metric provides control performance guarantees given bounds on the metric. However, it does not utilize any further information than the bounds, essentially restricting the set of possible systems into an uncertainty set for which the guarantees apply.
This thesis aims to investigate how additional information about the uncertain system can be... (More) - System uncertainty constitutes a fundamental restriction on control performance. System models are never perfect and the differences between system and model can be difficult to contend with. Applying a model based controller to the true system with uncertain dynamics can yield unpredictable results which led researchers to produce methods of robust control design. Existing theory on the ν-gap metric provides control performance guarantees given bounds on the metric. However, it does not utilize any further information than the bounds, essentially restricting the set of possible systems into an uncertainty set for which the guarantees apply.
This thesis aims to investigate how additional information about the uncertain system can be leveraged to provide sharper results; specifically, by additionally considering a probability distribution function (PDF) on the uncertainty set. Considering the uncertain system as a random quantity with a known distribution models it as more than simply belonging to some uncertainty set. It also incorporates further knowledge as to where in the set it is more likely to be. As such, this thesis opens up an entirely new perspective on the field of probabilistic uncertainty in control systems using the lens of the ν-gap.
Using the additional information, this thesis provides insight into how the difference between a known model and the uncertain system is characterized as well as the potential effect on control performance. Two expressions for the cumulative distribution function (CDF) of one such difference metric called the chordal distance is derived. With knowledge of this distribution, probabilistic guarantee results of a performance measure called the point-wise generalized stability margin are also produced. Some intermediate results which further illuminate the concepts and their relation to each other are also found. Lastly, a thorough discussion is given on how this field of research could be explored to expand the work started in this thesis. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9172310
- author
- Nyström, Anton
- supervisor
- organization
- year
- 2024
- type
- H3 - Professional qualifications (4 Years - )
- subject
- report number
- TFRT-6230
- other publication id
- 0280-5316
- language
- English
- id
- 9172310
- date added to LUP
- 2024-08-22 14:20:22
- date last changed
- 2024-08-27 09:27:53
@misc{9172310,
abstract = {{System uncertainty constitutes a fundamental restriction on control performance. System models are never perfect and the differences between system and model can be difficult to contend with. Applying a model based controller to the true system with uncertain dynamics can yield unpredictable results which led researchers to produce methods of robust control design. Existing theory on the ν-gap metric provides control performance guarantees given bounds on the metric. However, it does not utilize any further information than the bounds, essentially restricting the set of possible systems into an uncertainty set for which the guarantees apply.
This thesis aims to investigate how additional information about the uncertain system can be leveraged to provide sharper results; specifically, by additionally considering a probability distribution function (PDF) on the uncertainty set. Considering the uncertain system as a random quantity with a known distribution models it as more than simply belonging to some uncertainty set. It also incorporates further knowledge as to where in the set it is more likely to be. As such, this thesis opens up an entirely new perspective on the field of probabilistic uncertainty in control systems using the lens of the ν-gap.
Using the additional information, this thesis provides insight into how the difference between a known model and the uncertain system is characterized as well as the potential effect on control performance. Two expressions for the cumulative distribution function (CDF) of one such difference metric called the chordal distance is derived. With knowledge of this distribution, probabilistic guarantee results of a performance measure called the point-wise generalized stability margin are also produced. Some intermediate results which further illuminate the concepts and their relation to each other are also found. Lastly, a thorough discussion is given on how this field of research could be explored to expand the work started in this thesis.}},
author = {{Nyström, Anton}},
language = {{eng}},
note = {{Student Paper}},
title = {{Understanding Probabilistic Uncertainty Using ν-Gap}},
year = {{2024}},
}