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Bilevel Programming for Analysis of Low-Complexity Control of Linear Systems with Constraints
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Norwegian University of Science and Technology, Norway.
Norwegian University of Science and Technology, Norway.
ETH Zürich, Schweiz.
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2009 (English)In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009, 946-951 p.Conference paper (Refereed)
Abstract [en]

In this paper we use bilevel programming to find the maximum difference between a reference controller and a low-complexity controller in terms of the infinity-norm difference of their control laws. A nominal MPC for linear systems with constraints, and a robust MPC for linear systems with bounded additive noise are considered as reference controllers. For possible low-complexity controllers we discuss partial enumeration (PE), Voronoi/closest point, triangulation, linear controller with saturation, and others. A small difference in the norm between a low-complexity controller and a robust MPC may be used to guarantee closed-loop stability of the low-complexity controller and indicate that the behaviour or performance of the low-complexity controller will be similar to that of the reference one. We further discuss how bilevel programming may be used for closed-loop analysis of model reduction.

Place, publisher, year, edition, pages
2009. 946-951 p.
Keyword [en]
Bilevel programming, Closed-loop analysis, Optimal control
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-89078DOI: 10.1109/CDC.2009.5400868ISBN: 978-1-4244-3872-3ISBN: 978-1-4244-3871-6OAI: diva2:606607
48th IEEE Conference on Decision and Control, Shanghai, China, December 2009
Available from: 2013-02-19 Created: 2013-02-19 Last updated: 2013-02-20

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Löfberg, Johan
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Automatic ControlThe Institute of Technology
Control Engineering

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ReferencesLink to record
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