Phase Portrait Modeling of a Nonlinear System with a Dynamic Fuzzy Network |
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Authors: | Email author" target="_blank">Yusuf?OysalEmail author Yasar?Becerikli A?Ferit?Konar |
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Affiliation: | (1) Computer Engineering Department, Anadolu University, Eskisehir, Turkey;(2) Computer Engineering Department, Kocaeli University, Kocaeli, Turkey;(3) Computer Engineering Department, Dogus University, Istanbul, Turkey |
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Abstract: | Fuzzy logic and neural networks are two important technologies for modeling and control of dynamical systems and have been
constrained by the non-dynamical nature of their some popular architectures. There exist problems such as large rule bases
(i.e., curse of dimensionality), long training times, the need to determine buffer lengths. This article proposes to overcome
these major problems in phase portrait modeling of a nonlinear system with a dynamic fuzzy network (DFN) with unconstrained
connectivity and with dynamic fuzzy processing units called “feurons”. Nonlinear physical system properties can be encapsulated
by DFN. As an example, DFN has been used as the modeler for some nonlinear physical system such as chaotic, limit cycle, oscillator.
The minimization of an integral quadratic performance index subject to dynamic equality constraints is considered for a phase
portrait modeling application. For gradient computation adjoint sensitivity method has been used. Its computational complexity
is significantly less than direct sensitivity method, but it requires a backward integration capability. We used first and
approximate second order gradient-based methods including Broyden–Fletcher–Golfarb–Shanno algorithm to update the parameters
of the dynamic fuzzy networks yielding faster rate of convergence |
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Keywords: | Dynamic fuzzy logic neural networks chaos limit cycle phase portrait mathematical foundations |
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