Sampled-data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements

Zi-Peng Wang; Han-Xiong Li; Huai-Ning Wu

doi:10.1016/j.fss.2019.01.011

Sampled-data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements

Zi-Peng Wang^*, Han-Xiong Li, Huai-Ning Wu^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

26 Citations (Scopus)

Abstract

In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method.

Original language	English
Pages (from-to)	60-81
Journal	Fuzzy Sets and Systems
Volume	374
Online published	22 Jan 2019
DOIs	https://doi.org/10.1016/j.fss.2019.01.011
Publication status	Published - 1 Nov 2019

Research Keywords

Distributed parameter systems
Exponential stability
Fuzzy control
Linear matrix inequality (LMI)
Sampled-data control

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10.1016/j.fss.2019.01.011

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@article{bf876061cb1b481c9a8a09ca25ad0323,

title = "Sampled-data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements",

abstract = "In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method.",

keywords = "Distributed parameter systems, Exponential stability, Fuzzy control, Linear matrix inequality (LMI), Sampled-data control",

author = "Zi-Peng Wang and Han-Xiong Li and Huai-Ning Wu",

year = "2019",

month = nov,

day = "1",

doi = "10.1016/j.fss.2019.01.011",

language = "English",

volume = "374",

pages = "60--81",

journal = "Fuzzy Sets and Systems",

issn = "0165-0114",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Sampled-data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements

AU - Wang, Zi-Peng

AU - Li, Han-Xiong

AU - Wu, Huai-Ning

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method.

AB - In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method.

KW - Distributed parameter systems

KW - Exponential stability

KW - Fuzzy control

KW - Linear matrix inequality (LMI)

KW - Sampled-data control

UR - http://www.scopus.com/inward/record.url?scp=85060642504&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85060642504&origin=recordpage

U2 - 10.1016/j.fss.2019.01.011

DO - 10.1016/j.fss.2019.01.011

M3 - RGC 21 - Publication in refereed journal

SN - 0165-0114

VL - 374

SP - 60

EP - 81

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

ER -

Sampled-data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements

Abstract

Research Keywords

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