A new control method of nonlinear systems based on impulse responses of universal learning networks

Kotaro Hirasawa, Takayuki Furuzuki, Junichi Murata, ChunZhi Jin

Research output: Contribution to journalArticle

Abstract

A new control method of nonlinear dynamic systems is proposed based on impulse responses of Universal Learning Networks (ULNs). ULNs form a superset 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 order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. The algorithm can also be used in a unified manner for almost all kinds of learning networks. In this paper, not only the controlled object but also its controller are described by the ULNs and the controller is constructed by using the higher order derivatives of ULNs. The main feature of the proposed control method is to use impulse response defined by the higher order derivatives as a criterion function of the network. By using the impulse response, nonlinear dynamics with not only quick response but also quick damping can be more easily obtained than the conventional nonlinear control systems with quadratic form criterion functions of control variables.

Original languageEnglish
Pages (from-to)159-172
Number of pages14
JournalResearch Reports on Information Science and Electrical Engineering of Kyushu University
Volume3
Issue number2
Publication statusPublished - 1998 Sep
Externally publishedYes

Fingerprint

Impulse response
Nonlinear systems
Derivatives
Nonlinear control systems
Controllers
Learning algorithms
Time delay
Dynamical systems
Damping
Neural networks

Keywords

  • Control systems
  • Higher order derivatives
  • Large-scale complicated systems
  • Learning networks
  • Neural networks
  • Optimization
  • Quick damping
  • Quick response

ASJC Scopus subject areas

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

Cite this

A new control method of nonlinear systems based on impulse responses of universal learning networks. / Hirasawa, Kotaro; Furuzuki, Takayuki; Murata, Junichi; Jin, ChunZhi.

In: Research Reports on Information Science and Electrical Engineering of Kyushu University, Vol. 3, No. 2, 09.1998, p. 159-172.

Research output: Contribution to journalArticle

@article{b932e55f837d459daf16caff96f8e9ec,
title = "A new control method of nonlinear systems based on impulse responses of universal learning networks",
abstract = "A new control method of nonlinear dynamic systems is proposed based on impulse responses of Universal Learning Networks (ULNs). ULNs form a superset 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 order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. The algorithm can also be used in a unified manner for almost all kinds of learning networks. In this paper, not only the controlled object but also its controller are described by the ULNs and the controller is constructed by using the higher order derivatives of ULNs. The main feature of the proposed control method is to use impulse response defined by the higher order derivatives as a criterion function of the network. By using the impulse response, nonlinear dynamics with not only quick response but also quick damping can be more easily obtained than the conventional nonlinear control systems with quadratic form criterion functions of control variables.",
keywords = "Control systems, Higher order derivatives, Large-scale complicated systems, Learning networks, Neural networks, Optimization, Quick damping, Quick response",
author = "Kotaro Hirasawa and Takayuki Furuzuki and Junichi Murata and ChunZhi Jin",
year = "1998",
month = "9",
language = "English",
volume = "3",
pages = "159--172",
journal = "Research Reports on Information Science and Electrical Engineering of Kyushu University",
issn = "1342-3819",
publisher = "Kyushu University, Faculty of Science",
number = "2",

}

TY - JOUR

T1 - A new control method of nonlinear systems based on impulse responses of universal learning networks

AU - Hirasawa, Kotaro

AU - Furuzuki, Takayuki

AU - Murata, Junichi

AU - Jin, ChunZhi

PY - 1998/9

Y1 - 1998/9

N2 - A new control method of nonlinear dynamic systems is proposed based on impulse responses of Universal Learning Networks (ULNs). ULNs form a superset 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 order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. The algorithm can also be used in a unified manner for almost all kinds of learning networks. In this paper, not only the controlled object but also its controller are described by the ULNs and the controller is constructed by using the higher order derivatives of ULNs. The main feature of the proposed control method is to use impulse response defined by the higher order derivatives as a criterion function of the network. By using the impulse response, nonlinear dynamics with not only quick response but also quick damping can be more easily obtained than the conventional nonlinear control systems with quadratic form criterion functions of control variables.

AB - A new control method of nonlinear dynamic systems is proposed based on impulse responses of Universal Learning Networks (ULNs). ULNs form a superset 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 order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. The algorithm can also be used in a unified manner for almost all kinds of learning networks. In this paper, not only the controlled object but also its controller are described by the ULNs and the controller is constructed by using the higher order derivatives of ULNs. The main feature of the proposed control method is to use impulse response defined by the higher order derivatives as a criterion function of the network. By using the impulse response, nonlinear dynamics with not only quick response but also quick damping can be more easily obtained than the conventional nonlinear control systems with quadratic form criterion functions of control variables.

KW - Control systems

KW - Higher order derivatives

KW - Large-scale complicated systems

KW - Learning networks

KW - Neural networks

KW - Optimization

KW - Quick damping

KW - Quick response

UR - http://www.scopus.com/inward/record.url?scp=0032154383&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032154383&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032154383

VL - 3

SP - 159

EP - 172

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 - 2

ER -