Parallel synchronization and a RBF neuro-fuzzy system to synchronization of chaotic systems

Document Type : Research Paper

Authors

1 Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Tel-Fax No:+98-23-32300235, Shahrood, Iran.

2 Shahrood University of Technology

Abstract

In this paper, an intelligent approach based on Radial Basis Function Neural Networks (RBFNNs) is used for
synchronization problem between two chaotic systems.
In this scheme, parallel systems have been first
applied by converting the
synchronization problem between two chaotic systems to synchronization problem
between their parallel systems.
By employing an active control strategy, an Infinite Horizon Optimal Control Problem (IHOCP) is constructed related to the
obtained paralleled dynamical models.
Using a suitable transformation, the IHOCP is then transformed into an equivalent finite-horizon one.
According to Pontryagin Maximum Principle (PMP),
the necessary optimality conditions for the finite horizon problem
are examined in the form of two-point boundary value problems (TPBVPs).
A fuzzy neural network approach
that utilizes Radial Basis Functions (RBFs) as its activation functions for one of the hidden layers is established to
approximate the solution of the TPBVP.
By relying on the ability of RBFNN as function approximator,
the trial solutions of variables are substituted in the TPBVP. The
obtained
algebraic nonlinear equations system is then reduced into an error function minimization problem.
A learning
scheme via center points of RBFs
as training dataset and based on
the Levenberg-Marquardt algorithm is employed as the optimizer
to derive the adjustable parameters of trial solutions.
Some various chaotic systems are synchronized based on
numerical simulations to guarantee the capability of the
proposed plan.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 6
November and December 2024
Pages 101-126

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