Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states

Tzu Sung Wu, Mansour Karkoub, Chien Ting Chen, Wen Shyong Yu, Ming Guo Her, Jui Yiao Su

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

Original languageEnglish
Pages (from-to)1300-1313
Number of pages14
JournalInternational Journal of Control, Automation and Systems
Volume11
Issue number6
DOIs
Publication statusPublished - Dec 2013

Fingerprint

Fuzzy control
Nonlinear systems
Fuzzy systems
Pendulums
Uncertainty
Drag
Friction

Keywords

  • H control
  • indirect adaptive fuzzy control
  • MIMO nonlinear systems
  • Riccati-like equation
  • time delayed uncertainty
  • two inverted pendulums on carts system
  • two-degree-of-freedom mass-spring-damper system
  • variable structure scheme

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

Cite this

Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states. / Wu, Tzu Sung; Karkoub, Mansour; Chen, Chien Ting; Yu, Wen Shyong; Her, Ming Guo; Su, Jui Yiao.

In: International Journal of Control, Automation and Systems, Vol. 11, No. 6, 12.2013, p. 1300-1313.

Research output: Contribution to journalArticle

Wu, Tzu Sung ; Karkoub, Mansour ; Chen, Chien Ting ; Yu, Wen Shyong ; Her, Ming Guo ; Su, Jui Yiao. / Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states. In: International Journal of Control, Automation and Systems. 2013 ; Vol. 11, No. 6. pp. 1300-1313.
@article{bbc9561559cd4fe68e13a88a77b13561,
title = "Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states",
abstract = "It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H ∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.",
keywords = "H control, indirect adaptive fuzzy control, MIMO nonlinear systems, Riccati-like equation, time delayed uncertainty, two inverted pendulums on carts system, two-degree-of-freedom mass-spring-damper system, variable structure scheme",
author = "Wu, {Tzu Sung} and Mansour Karkoub and Chen, {Chien Ting} and Yu, {Wen Shyong} and Her, {Ming Guo} and Su, {Jui Yiao}",
year = "2013",
month = "12",
doi = "10.1007/s12555-012-0543-x",
language = "English",
volume = "11",
pages = "1300--1313",
journal = "International Journal of Control, Automation and Systems",
issn = "1598-6446",
publisher = "Institute of Control, Robotics and Systems",
number = "6",

}

TY - JOUR

T1 - Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states

AU - Wu, Tzu Sung

AU - Karkoub, Mansour

AU - Chen, Chien Ting

AU - Yu, Wen Shyong

AU - Her, Ming Guo

AU - Su, Jui Yiao

PY - 2013/12

Y1 - 2013/12

N2 - It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H ∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

AB - It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H ∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

KW - H control

KW - indirect adaptive fuzzy control

KW - MIMO nonlinear systems

KW - Riccati-like equation

KW - time delayed uncertainty

KW - two inverted pendulums on carts system

KW - two-degree-of-freedom mass-spring-damper system

KW - variable structure scheme

UR - http://www.scopus.com/inward/record.url?scp=84890583937&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890583937&partnerID=8YFLogxK

U2 - 10.1007/s12555-012-0543-x

DO - 10.1007/s12555-012-0543-x

M3 - Article

AN - SCOPUS:84890583937

VL - 11

SP - 1300

EP - 1313

JO - International Journal of Control, Automation and Systems

JF - International Journal of Control, Automation and Systems

SN - 1598-6446

IS - 6

ER -