<  Back to the Polytechnique Montréal portal

A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances

Jun Zheng, Guchuan Zhu

Article (2019)

Open Access document in PolyPublie
[img]
Preview
Open Access to the full text of this document
Accepted Version
Terms of Use: All rights reserved
Download (179kB)
Show abstract
Hide abstract

Abstract

This note addresses input-to-state stability (ISS) propertieswith respect to (w.r.t.) boundary and in-domain disturbances for Burgers'equation. The developed approach is a combination of the methodof De Giorgi iteration and the technique of Lyapunov functionals byadequately splitting the original problem into two subsystems. The ISSproperties in L2-norm for Burgers' equation have been established usingthis method. Moreover, as an application of De Giorgi iteration, ISS inL1-norm w.r.t. in-domain disturbances and actuation errors in boundaryfeedback control for a 1-D linear unstable reaction-diffusion equationhave also been established. It is the first time that the method of De Giorgiiteration is introduced in the ISS theory for infinite dimensional systems,and the developed method can be generalized for tackling some problemson multidimensional spatial domains and to a wider class of nonlinearpartial differential equations (PDEs).

Uncontrolled Keywords

De Giorgi iteration, boundary disturbance, indomain disturbance, Burgers’ equation, unstable reaction-diffusion equation.

Subjects: 2500 Electrical and electronic engineering > 2500 Electrical and electronic engineering
Department: Department of Electrical Engineering
Funders: CRSNG / NSERC
Grant number: RGPIN-2018-04571
PolyPublie URL: https://publications.polymtl.ca/3747/
Journal Title: IEEE Transactions on Automatic Control (vol. 64, no. 8)
Publisher: IEEE
DOI: 10.1109/tac.2018.2880160
Official URL: https://doi.org/10.1109/tac.2018.2880160
Date Deposited: 15 Jan 2019 12:09
Last Modified: 20 Nov 2022 03:50
Cite in APA 7: Zheng, J., & Zhu, G. (2019). A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances. IEEE Transactions on Automatic Control, 64(8). https://doi.org/10.1109/tac.2018.2880160

Statistics

Total downloads

Downloads per month in the last year

Origin of downloads

Dimensions

Repository Staff Only

View Item View Item