Stabilization for a semilinear heat equation with switching control

Wen Kang, Emilia Fridman, Chuan Xin Liu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This work discusses sampled-data stabilization by switching for 1-D nonlinear reaction-diffusion equation with spatially scheduled actuators. We suggest that the interval [0,1] is divided into N subdomains. We assume that N sensors are placed in each subdomain and measure the average value of the state in the discrete time. We stabilize the system by switching sampled-data static output-feedback. This switching control law can be implemented either by using one moving actuator that can move to the active subdomain in the negligible time or by N actuators placed in each subdomain. In the latter case switching control may reduce the energy that the system spends. Constructive conditions are derived to ensure that the resulting closed-loop system is exponentially stable by means of the Lyapunov approach. A numerical example shows the efficiency of the method.

Original languageEnglish
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages448-453
Number of pages6
ISBN (Electronic)9781665436595
DOIs
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: 13 Dec 202117 Dec 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2021-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States
CityAustin
Period13/12/2117/12/21

Funding

FundersFunder number
Beijing Science Foundation for the Excellent Youth Scholars2018000020124G067
Outstanding Chinese and Foreign Youth Exchange Program of China Association of Science and Technology, Israel Science Foundation673/19
National Natural Science Foundation of China61803026
Fundamental Research Funds for the Central UniversitiesFRF-TP-20-039A2Z, QNXM20210034

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