Chaos control using universal learning network

Kotaro Hirasawa, Xiaofeng Wang, Jinghi Hu, Junichi Murata

Research output: Contribution to journalArticlepeer-review


Universal Learning Network (ULN) is proposed and its application to chaos control are discussed. ULNs form a super-set of neural networks. They consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary (positive, zero, or even negative) time delays. A generalized learning algorithm is derived for the ULNs, in which both the first ordered derivatives (gradients) and the higher ordered derivatives are incorporated. The derivatives are calculated by using forward or backward propagation scheme. The algorithm can also be used in a unified manner for almost all kinds of learning networks. As an application of ULNs, a chaos control method using maximum Lyapunov number of ULNs is proposed. The maximum Lyapunov number of ULNs can be formulated by using higher ordered derivatives of ULNs and parameters of ULNs can be adjusted for the maximum Lyapunov number to approach the target value. From simulation results, it has been shown that a fully connected ULN with three nodes is able to display chaotic behaviors.

Original languageEnglish
Pages (from-to)13-27
Number of pages15
JournalResearch Reports on Information Science and Electrical Engineering of Kyushu University
Issue number1
Publication statusPublished - Mar 1999

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • Electrical and Electronic Engineering


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