### Abstract

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 language | English |
---|---|

Pages (from-to) | 13-27 |

Number of pages | 15 |

Journal | Research Reports on Information Science and Electrical Engineering of Kyushu University |

Volume | 4 |

Issue number | 1 |

Publication status | Published - Mar 1999 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Hardware and Architecture
- Engineering (miscellaneous)
- Electrical and Electronic Engineering

### Cite this

*Research Reports on Information Science and Electrical Engineering of Kyushu University*,

*4*(1), 13-27.

**Chaos control using universal learning network.** / Hirasawa, Kotaro; Wang, Xiaofeng; Hu, Jinghi; Murata, Junichi.

Research output: Contribution to journal › Article

*Research Reports on Information Science and Electrical Engineering of Kyushu University*, vol. 4, no. 1, pp. 13-27.

}

TY - JOUR

T1 - Chaos control using universal learning network

AU - Hirasawa, Kotaro

AU - Wang, Xiaofeng

AU - Hu, Jinghi

AU - Murata, Junichi

PY - 1999/3

Y1 - 1999/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032626745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032626745&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032626745

VL - 4

SP - 13

EP - 27

JO - Research Reports on Information Science and Electrical Engineering of Kyushu University

JF - Research Reports on Information Science and Electrical Engineering of Kyushu University

SN - 1342-3819

IS - 1

ER -