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Stabilization of Recurrent Fuzzy Systems via Sum of Squares-based Hybrid Control

Gering, Stefan ; Adamy, Jürgen (2023)
Stabilization of Recurrent Fuzzy Systems via Sum of Squares-based Hybrid Control.
In: IFAC Proceedings Volumes, 2014, 47 (3)
doi: 10.26083/tuprints-00023292
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Stabilization of Recurrent Fuzzy Systems via Sum of Squares-based Hybrid Control
Language: English
Date: 2023
Place of Publication: Darmstadt
Year of primary publication: 2014
Publisher: IFAC - International Federation of Automatic Control
Journal or Publication Title: IFAC Proceedings Volumes
Volume of the journal: 47
Issue Number: 3
DOI: 10.26083/tuprints-00023292
Corresponding Links:
Origin: Secondary publication service

This paper presents an approach for stabilization of equilibria in recurrent fuzzy systems. This type of dynamic fuzzy systems being defined via linguistic rules can be interpreted as interpolation between constant gradients, and therefore as hybrid dynamical system. It is shown that the latter viewpoint allows for a precise description of the system dynamics, but on the other hand lacks transparency. In order to render a given equilibrium of the recurrent fuzzy system globally asymptotically stable, local polynomial controllers are computed via sum of squares optimization to allow only for deterministic mode transitions on a micro level. In addition, the controlled recurrent fuzzy system can then be interpreted as finite deterministic automaton, thus allowing for analysis of system properties on a more abstract macro level. Relaxations are proposed in cases where recurrent fuzzy systems may not be rendered deterministic and the method is applied to two examples.

Uncontrolled Keywords: Recurrent Fuzzy Systems, Hybrid Systems, Automata, Polynomial Control, Sum of Squares
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-232922
Additional Information:

Zugl. Konferenzveröffentlichung: 19th IFAC World Congress (IFAC 2014), 24.-29.08.2014, Cape Town, South Africa

Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Methods and Intelligent Systems
Date Deposited: 01 Mar 2023 13:39
Last Modified: 26 May 2023 07:04
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23292
PPN: 507988841
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