Improved H∞ sampled-data control for semilinear parabolic PDE systems

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

doi:10.1002/rnc.4464

Improved H_∞ sampled-data control for semilinear parabolic PDE systems

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

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

In this paper, an H_∞ sampled-data control problem is addressed for semilinear parabolic partial differential equation (PDE) systems. By using a time-dependent Lyapunov functional and vector Poincare's inequality, a sampled-data controller under spatially averaged measurements is developed to stabilize exponentially the PDE system with an H_∞ control performance. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of the diffusion equation and the FitzHugh-Nagumo equation are given to illustrate the effectiveness of the proposed design method.

Original language	English
Pages (from-to)	1872-1892
Journal	International Journal of Robust and Nonlinear Control
Volume	29
Issue number	6
Online published	16 Jan 2019
DOIs	https://doi.org/10.1002/rnc.4464
Publication status	Published - 1 Apr 2019

Funding

National Natural Science Foundation for Distinguished Young Scholars of China, Grant/Award Number: 61625302; National Natural Science Foundation of China, Grant/Award Number: 61473011, 61721091, and 61803177; Shandong Provincial Natural Science Foundation, Grant/Award Number: ZR2018BF015 This work was supported in part by the National Natural Science Foundation for Distinguished Young Scholars of China under grant 61625302; the National Natural Science Foundation of China under grants 61473011, 61721091, and 61803177; and by Shandong Provincial Natural Science Foundation under grant ZR2018BF015. The authors gratefully acknowledge the helpful comments and suggestions of the associate editor and anonymous reviewers, which have improved the presentation of this paper.

Research Keywords

distributed parameter systems
H∞ control
linear matrix inequality (LMI)
sampled-data control

Access Output

10.1002/rnc.4464

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{a048e55d9f084c2cb3dc1ebfa2d8983e,

title = "Improved H∞ sampled-data control for semilinear parabolic PDE systems",

abstract = "In this paper, an H∞ sampled-data control problem is addressed for semilinear parabolic partial differential equation (PDE) systems. By using a time-dependent Lyapunov functional and vector Poincare's inequality, a sampled-data controller under spatially averaged measurements is developed to stabilize exponentially the PDE system with an H∞ control performance. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of the diffusion equation and the FitzHugh-Nagumo equation are given to illustrate the effectiveness of the proposed design method.",

keywords = "distributed parameter systems, H∞ control, linear matrix inequality (LMI), sampled-data control",

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

year = "2019",

month = apr,

day = "1",

doi = "10.1002/rnc.4464",

language = "English",

volume = "29",

pages = "1872--1892",

journal = "International Journal of Robust and Nonlinear Control",

issn = "1049-8923",

publisher = "John Wiley \& Sons",

number = "6",

}

TY - JOUR

T1 - Improved H∞ sampled-data control for semilinear parabolic PDE systems

AU - Wu, Huai-Ning

AU - Wang, Zi-Peng

AU - Li, Han-Xiong

PY - 2019/4/1

Y1 - 2019/4/1

N2 - In this paper, an H∞ sampled-data control problem is addressed for semilinear parabolic partial differential equation (PDE) systems. By using a time-dependent Lyapunov functional and vector Poincare's inequality, a sampled-data controller under spatially averaged measurements is developed to stabilize exponentially the PDE system with an H∞ control performance. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of the diffusion equation and the FitzHugh-Nagumo equation are given to illustrate the effectiveness of the proposed design method.

AB - In this paper, an H∞ sampled-data control problem is addressed for semilinear parabolic partial differential equation (PDE) systems. By using a time-dependent Lyapunov functional and vector Poincare's inequality, a sampled-data controller under spatially averaged measurements is developed to stabilize exponentially the PDE system with an H∞ control performance. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of the diffusion equation and the FitzHugh-Nagumo equation are given to illustrate the effectiveness of the proposed design method.

KW - distributed parameter systems

KW - H∞ control

KW - linear matrix inequality (LMI)

KW - sampled-data control

UR - https://www.scopus.com/pages/publications/85060146850

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85060146850&origin=recordpage

U2 - 10.1002/rnc.4464

DO - 10.1002/rnc.4464

M3 - RGC 21 - Publication in refereed journal

SN - 1049-8923

VL - 29

SP - 1872

EP - 1892

JO - International Journal of Robust and Nonlinear Control

JF - International Journal of Robust and Nonlinear Control

IS - 6

ER -