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Formal methodology for analyzing the dynamic behavior of nonlinear systems using fuzzy logic.
Metodología formal de análisis del comportamiento dinámico de sistemas no lineales mediante lógica borrosa

AuthorsBarragán, Antonio Javier; Al-Hadithi, Basil Mohammed ; Andújar, José Manuel; Jiménez, Agustín
KeywordsModelado borroso
Metodología de Poincaré
Estado de equilibrio
Análisis dinámico
Takagi-Sugeno (TS) model
Poincaré’s methodology
Fuzzy modeling
Fuzzy control
Equilibrium state
Dynamic systems
Dynamic analysis
Sistemas dinámicos
Issue Date2015
PublisherElsevier España
CitationRIAI - Revista Iberoamericana de Automatica e Informatica Industrial 12: 434- 445 (2015)
AbstractCopyright © 2015 CEA. Publicado por Elsevier España, S.L. Todos los derechos reservados. Having the ability to analyze a system from a dynamic point of view can be very useful in many circumstances (industrial systems, biological, economical, . . . ). The dynamic analysis of a system allows to understand its behavior and response to different inputs, open loop stability, both locally and globally, or if it is affected by nonlinear phenomena, such as limit cycles, or bifurcations, among others. If the system is unknown or its dynamic is complex enough to obtain its mathematical model, in principle it would not be possible to make a formal dynamic analysis of the system. In these cases, fuzzy logic, and more specifically fuzzy TS models is presented as a powerful tool for analysis and design. The TS fuzzy models are universal approximators both of a function and its derivative, so it allows modeling highly nonlinear systems based on input/output data. Since a fuzzy model is a mathematical model formally speaking, it is possible to study the dynamic aspects of the real system that it models such as in the theory of nonlinear control. This article describes a methodology for obtaining the equilibrium states of a generic nonlinear system, the exact linearization of a completely general fuzzy model, and the use of the Poincaré's methodology for the study of periodic orbits in fuzzy models. From this information it is possible to study the local stability of the equilibrium states, the dynamics of the system in its environment, and the presence of oscillations, yielding valuable information on the dynamic behavior of the system.
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