Boundary Constrained Control of Delayed Nonlinear Schrödinger Equation

Wen Kang; Emilia Fridman

doi:https://doi.org/10.1109/TAC.2018.2800526

Boundary Constrained Control of Delayed Nonlinear Schrödinger Equation

Wen Kang, Emilia Fridman

School of Electrical Engineering

Tel Aviv University

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

Abstract

This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-to-state stability of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay's inequality. Estimates on the set of initial conditions are found starting from which the solutions are exponentially attracted to a bounded set. A numerical example demonstrates the efficiency of the results.

Original language	English
Article number	8276290
Pages (from-to)	3873-3880
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	63
Issue number	11
DOIs	https://doi.org/10.1109/TAC.2018.2800526
State	Published - Nov 2018

Keywords

Boundary control
constrained control law
distributed parameter systems
nonlinear systems
time delay

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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https://doi.org/10.1109/TAC.2018.2800526

Cite this

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title = "Boundary Constrained Control of Delayed Nonlinear Schr{\"o}dinger Equation",

abstract = "This paper studies regional boundary stabilization of nonlinear Schr{\"o}dinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-to-state stability of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay's inequality. Estimates on the set of initial conditions are found starting from which the solutions are exponentially attracted to a bounded set. A numerical example demonstrates the efficiency of the results.",

keywords = "Boundary control, constrained control law, distributed parameter systems, nonlinear systems, time delay",

author = "Wen Kang and Emilia Fridman",

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year = "2018",

month = nov,

doi = "https://doi.org/10.1109/TAC.2018.2800526",

language = "الإنجليزيّة",

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AU - Kang, Wen

AU - Fridman, Emilia

PY - 2018/11

Y1 - 2018/11

N2 - This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-to-state stability of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay's inequality. Estimates on the set of initial conditions are found starting from which the solutions are exponentially attracted to a bounded set. A numerical example demonstrates the efficiency of the results.

AB - This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-to-state stability of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay's inequality. Estimates on the set of initial conditions are found starting from which the solutions are exponentially attracted to a bounded set. A numerical example demonstrates the efficiency of the results.

KW - Boundary control

KW - constrained control law

KW - distributed parameter systems

KW - nonlinear systems

KW - time delay

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U2 - https://doi.org/10.1109/TAC.2018.2800526

DO - https://doi.org/10.1109/TAC.2018.2800526

M3 - مقالة

SN - 0018-9286

VL - 63

SP - 3873

EP - 3880

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 11

M1 - 8276290

ER -

Boundary Constrained Control of Delayed Nonlinear Schrödinger Equation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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