Mean square H∞ synchronization of coupled stochastic partial differential systems

Liming Wang; Kai Ning Wu; Ya Nan Zhu; Xiaohua Ding

doi:10.1016/j.amc.2015.11.075

Mean square H_∞ synchronization of coupled stochastic partial differential systems

Liming Wang
, Kai Ning Wu^*
, Ya Nan Zhu
, Xiaohua Ding

^*Corresponding author for this work

Harbin Institute of Technology Weihai
Shanghai Jiao Tong University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, the criterion and control are considered for the mean square H_∞ synchronization of coupled stochastic partial differential systems (SPDSs). Based on the integral Lyapunov-like functional and by virtue of completing squares technique, a sufficient criterion is provided to guarantee the mean square H_∞ synchronization. The effect of spatial domain on the mean square H_∞ synchronization is also embodied in this criterion. When the coupled SPDSs cannot achieve the mean square H_∞ synchronization, the adaptive controllers are adopted for the coupled SPDSs, and the effectiveness of the adaptive controllers is verified via a rigorous mathematical analysis. When the number of the nodes in the complex networks is large, pinning control is a natural choice. The adaptive pinning control strategy is also presented and a criterion is obtained which guarantees the mean square H_∞ synchronization of coupled SPDSs. Numerical experiments are also given to illustrate the correctness of our results.

Original language	English
Pages (from-to)	386-393
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	275
DOIs	https://doi.org/10.1016/j.amc.2015.11.075
State	Published - 15 Feb 2016
Externally published	Yes

Keywords

Adaptive
H synchronization
Partial differential systems
Pinning control
Stochastic

Access to Document

10.1016/j.amc.2015.11.075

Cite this

@article{53383268517b4343838db41335e77fbf,

title = "Mean square H∞ synchronization of coupled stochastic partial differential systems",

abstract = "In this paper, the criterion and control are considered for the mean square H∞ synchronization of coupled stochastic partial differential systems (SPDSs). Based on the integral Lyapunov-like functional and by virtue of completing squares technique, a sufficient criterion is provided to guarantee the mean square H∞ synchronization. The effect of spatial domain on the mean square H∞ synchronization is also embodied in this criterion. When the coupled SPDSs cannot achieve the mean square H∞ synchronization, the adaptive controllers are adopted for the coupled SPDSs, and the effectiveness of the adaptive controllers is verified via a rigorous mathematical analysis. When the number of the nodes in the complex networks is large, pinning control is a natural choice. The adaptive pinning control strategy is also presented and a criterion is obtained which guarantees the mean square H∞ synchronization of coupled SPDSs. Numerical experiments are also given to illustrate the correctness of our results.",

keywords = "Adaptive, H synchronization, Partial differential systems, Pinning control, Stochastic",

author = "Liming Wang and Wu, \{Kai Ning\} and Zhu, \{Ya Nan\} and Xiaohua Ding",

year = "2016",

month = feb,

day = "15",

doi = "10.1016/j.amc.2015.11.075",

language = "英语",

volume = "275",

pages = "386--393",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Mean square H∞ synchronization of coupled stochastic partial differential systems

AU - Wang, Liming

AU - Wu, Kai Ning

AU - Zhu, Ya Nan

AU - Ding, Xiaohua

PY - 2016/2/15

Y1 - 2016/2/15

N2 - In this paper, the criterion and control are considered for the mean square H∞ synchronization of coupled stochastic partial differential systems (SPDSs). Based on the integral Lyapunov-like functional and by virtue of completing squares technique, a sufficient criterion is provided to guarantee the mean square H∞ synchronization. The effect of spatial domain on the mean square H∞ synchronization is also embodied in this criterion. When the coupled SPDSs cannot achieve the mean square H∞ synchronization, the adaptive controllers are adopted for the coupled SPDSs, and the effectiveness of the adaptive controllers is verified via a rigorous mathematical analysis. When the number of the nodes in the complex networks is large, pinning control is a natural choice. The adaptive pinning control strategy is also presented and a criterion is obtained which guarantees the mean square H∞ synchronization of coupled SPDSs. Numerical experiments are also given to illustrate the correctness of our results.

AB - In this paper, the criterion and control are considered for the mean square H∞ synchronization of coupled stochastic partial differential systems (SPDSs). Based on the integral Lyapunov-like functional and by virtue of completing squares technique, a sufficient criterion is provided to guarantee the mean square H∞ synchronization. The effect of spatial domain on the mean square H∞ synchronization is also embodied in this criterion. When the coupled SPDSs cannot achieve the mean square H∞ synchronization, the adaptive controllers are adopted for the coupled SPDSs, and the effectiveness of the adaptive controllers is verified via a rigorous mathematical analysis. When the number of the nodes in the complex networks is large, pinning control is a natural choice. The adaptive pinning control strategy is also presented and a criterion is obtained which guarantees the mean square H∞ synchronization of coupled SPDSs. Numerical experiments are also given to illustrate the correctness of our results.

KW - Adaptive

KW - H synchronization

KW - Partial differential systems

KW - Pinning control

KW - Stochastic

UR - https://www.scopus.com/pages/publications/84951030137

U2 - 10.1016/j.amc.2015.11.075

DO - 10.1016/j.amc.2015.11.075

M3 - 文章

AN - SCOPUS:84951030137

SN - 0096-3003

VL - 275

SP - 386

EP - 393

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Mean square H_∞ synchronization of coupled stochastic partial differential systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this