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

In this paper, an intelligent approach based on Radial Basis Function Neural Networks (RBFNNs) is used forsynchronization problem between two chaotic systems.In this scheme, parallel systems have been firstapplied by converting thesynchronization problem between two chaotic systems to synchronization problembetween their parallel systems.By employing an active control strategy, an Infinite Horizon Optimal Control Problem (IHOCP) is constructed related to theobtained 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 problemare examined in the form of two-point boundary value problems (TPBVPs).A fuzzy neural network approachthat utilizes Radial Basis Functions (RBFs) as its activation functions for one of the hidden layers is established toapproximate 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. Theobtainedalgebraic nonlinear equations system is then reduced into an error function minimization problem.A learningscheme via center points of RBFsas training dataset and based onthe Levenberg-Marquardt algorithm is employed as the optimizerto derive the adjustable parameters of trial solutions.Some various chaotic systems are synchronized based onnumerical simulations to guarantee the capability of theproposed plan.

کلیدواژه ها:

chaos synchronization ، parallel synchronization ، Optimal control ، Fuzzy System ، RBFNN ، Levenberg-Marquardt algorithm