Stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic

Andújar, José Manuel; Bravo, José Manuel; Peregrín, Antonio

doi:10.1016/j.fss.2004.01.008

Cited by 30 publications

(23 citation statements)

References 28 publications

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“…One of the main reasons for the use of nonlinear models is based on the dynamics of linear systems, since conventional mathematical formulations are not rich enough to reproduce a series of phenomena that usually appear in the real life [2,16,17]. The dynamic behaviour of a linear system, without considering its order, is basically governed by the eigenvalues of the corresponding state matrix [8].…”

Section: Introductionmentioning

confidence: 99%

“…When the model of the system is completely unknown, this information could help to clarify how the system works, even to ease the design of an appropriate control. It should be noted that despite the existence of recent works that present formal analysis methodologies based on Fuzzy logic [17,20,21,32] the authors have not currently found any work focused from the NN point of view, under a general approach as presented in this proposal.…”

Section: Introductionmentioning

confidence: 99%

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About Extracting Dynamic Information of Unknown Complex Systems by Neural Networks

et al. 2018

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This work presents a straightforward methodology based on neural networks (NN) which allows to obtain relevant dynamic information of unknown nonlinear systems. It provides an approach for cases in which the complex task of analyzing the dynamic behaviour of nonlinear systems makes it excessively challenging to obtain an accurate mathematical model. After reviewing the suitability of multilayer perceptrons (MLPs) as universal approximators to replace a mathematical model, the first part of this work presents a system representation using a model formulated with state variables which can be exported to a NN structure. Considering the linearization of the NN model in a mesh of operating points, the second part of this work presents the study of equilibrium states in such points by calculating the Jacobian matrix of the system through the NN model. The results analyzed in three case studies provide representative examples of the strengths of the proposed method. Conclusively, it is feasible to study the system behaviour based on MLPs, which enables the analysis of the local stability of the equilibrium points, as well as the system dynamics in its environment, therefore obtaining valuable information of the system dynamic behaviour.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

About Extracting Dynamic Information of Unknown Complex Systems by Neural Networks

et al. 2018

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“…with time t ∈ R, state x(t) ∈ R n and input u(t) ∈ R. The vector field f : (3.35), the flat output y can be obtained from the feedback system, using current values of state variables x, control signal u and some of its derivatives u (1) , .., u (p) . On the other hand, the flat output can be constructed externally with polynomial functions.…”

Section: Differential Flatnessmentioning

confidence: 99%

“…For example the interval [2,5] corresponding to a proper modal interval X = ( [2,5] , ∃). The interval [2,1] is perfectly valid, and corresponds to an improper modal interval X = ( [1,2] , ∀). In particular, an interval as [3,3] is denominated point-interval.…”

Section: The Development and Theoretical Foundation Of The Interval Mmentioning

confidence: 99%

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Interval Robust Control for Nonlinear Flat Systems

Valencia¹,

César²

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SummaryThis thesis mainly focuses on the robust control of nonlinear flat systems. The main goal is to determine a family of robust controllers in order to assure the fulfillment of a desired specifications set under parametric uncertainty in the process. The family of robust controllers are determined with a new approach of robust possibilistic control together with the theory of flat systems. The specifications and parametric uncertainty are established through the intervals. Modal Interval Arithmetic and Analysis Quantified Sets Inversion Algorithms are applied to find solution sets. Different problems of robust control are solved such as: Solution sets referred to the attainable specifications by a family of controllers, as well as the determination of the maximum uncertainty admitted by a nominal controller.This thesis develops a new methodology of robustness analysis of controllers based on differential flatness, where the use of a feedforward is required. The methodology developed is applied to different processes, especially to fed-batch bioreactors given the importance of these high density stirred tank reactors for efficient industrial production of proteins and enzymes. ResumenEsta tesis se enfoca principalmente en el control robusto de sistemas no lineales planos. El objetivo principal es determinar una familia de controladores robustos con la finalidad de asegurar el cumplimiento de un conjunto de especificaciones deseadas bajo incertidumbre paramétrica en el proceso. La familia de controladores robustos se determina con un nuevo enfoque de control robusto posibilistico conjuntamente con la teoría de los sistemas planos. Las especificaciones e incertidumbre paramétrica se establecen mediante intervalos. Se aplican la Aritmética Intervalar Modal y el Análisis de Algoritmos de Inversión de Conjuntos Cuantificados para encontrar los conjuntos de soluciones. Se resuelven diferentes problemas de control robusto tales como: Conjuntos de soluciones referidos a las especificaciones alcanzables por una familia de controladores, así como la determinación de la incertidumbre máxima admitida por un controlador nominal. En esta tesis se desarrolla una nueva metodología de análisis de robustez de controladores basados en platitud diferencial, donde el uso de una pre alimentación es requerida. La metodología desarrollada es aplicada a diferentes procesos, específicamente a bioreactores fed-batch, dada la importancia de estos reactores de alta densidad de tanque agitado para la producción industrial eficiente de proteínas y enzimas. ResúmAquesta tesi es centra fonamentalment al control robust de sistemes no lineals plans. L'objectiu principalés determinar una família de controladors robustos amb la finalitat d'assegurar el compliment d'un conjunt d'especificacions desitjades baix incertesa paramètrica al procés. La família de controladors robustos es determina mitjançant un nou enfocament de control robust possibilistic, conjuntament amb l'ús de la teoria de sistemes plans. Les especificacions e incertesa paramètri...

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Contrast of evolution models for agricultural contaminants in ground waters by means of fuzzy logic and data mining

et al. 2005

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Stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic

Cited by 30 publications

References 28 publications

About Extracting Dynamic Information of Unknown Complex Systems by Neural Networks

About Extracting Dynamic Information of Unknown Complex Systems by Neural Networks

Interval Robust Control for Nonlinear Flat Systems

Contrast of evolution models for agricultural contaminants in ground waters by means of fuzzy logic and data mining

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