• RBF neural network based $\mathcal{H}_{\infty}$ synchronization for unknown chaotic systems

• # Keywords

$\mathcal{H}_{\infty}$ synchronization; radial basis function neural network (RBFNN); unknown chaotic systems; linear matrix inequality (LMI); learning law.

• # Abstract

In this paper, we propose a new $\mathcal{H}_{\infty}$ synchronization strategy, called a Radial Basis Function Neural Network $\mathcal{H}_{\infty}$ synchronization (RBFNNHS) strategy, for unknown chaotic systems in the presence of external disturbance. In the proposed framework, a radial basis function neural network (RBFNN) is constructed as an alternative to approximate the unknown nonlinear function of the chaotic system. Based on this neural network and linear matrix inequality (LMI) formulation, the RBFNNHS controller and the learning laws are presented to reduce the effect of disturbance to an $\mathcal{H}_{\infty}$ norm constraint. It is shown that ﬁnding the RBFNNHS controller and the learning laws can be transformed into the LMI problem and solved using the convex optimization method. A numerical example is presented to demonstrate the validity of the proposed RBFNNHS scheme.

• # Author Affiliations

1. Department of Automative Engineering, Seoul National University of Technology, 172 Gongneung 2-dong, Nowon-gu, Seoul 139–743