The present thesis employs fuzzy-polynomial control techniques in order to
improve the stability analysis and control of nonlinear systems. Initially, it
reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems,
such as the more relevant results about polynomial and fuzzy polynomial
systems. The basic framework uses fuzzy polynomial models by Taylor series
and sum-of-squares techniques (semidefinite programming) in order to obtain
stability guarantees.
The contributions of the thesis are:
¿ Improved domain of attraction estimation of nonlinear systems for both
continuous-time and discrete-time cases. An iterative methodology based
on invariant-set results is presented for obtaining polynomial boundaries
of such domain of attraction.
¿ Extension of the above problem to the case with bounded persistent disturbances
acting. Different characterizations of inescapable sets with
polynomial boundaries are determined.
¿ State estimation: extension of the previous results in literature to the
case of fuzzy observers with polynomial gains, guaranteeing stability of
the estimation error and inescapability in a subset of the zone where the
model is valid.
¿ Proposal of a polynomial Lyapunov function with discrete delay in order
to improve some polynomial control designs from literature. Preliminary
extension to the fuzzy polynomial case.
Last chapters present a preliminary experimental work in order to check
and validate the theoretical results on real platforms in the future. / Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773
| Identifer | oai:union.ndltd.org:upv.es/oai:riunet.upv.es:10251/34773 |
| Date | 07 January 2014 |
| Creators | Pitarch Pérez, José Luis |
| Contributors | Sala Piqueras, Antonio, Universitat Politècnica de València. Departamento de Ingeniería de Sistemas y Automática - Departament d'Enginyeria de Sistemes i Automàtica |
| Publisher | Universitat Politècnica de València |
| Source Sets | Universitat Politècnica de València |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis, info:eu-repo/semantics/acceptedVersion |
| Source | Riunet |
| Rights | http://rightsstatements.org/vocab/InC/1.0/, info:eu-repo/semantics/openAccess |
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