Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay

Xianlong Fu

doi:10.3934/eect.2017026

Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay

Xianlong Fu^*

^*Corresponding author for this work

School of Mathematical Sciences

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

35 Scopus citations

Abstract

The controllability of non-autonomous evolution systems is an important and difficult topic in control theory. In this paper, we study the approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay. The theory of linear evolution operators is used instead of C₀-semigroup to discuss the problem. Some sufficient conditions of approximate controllability are formulated and proved here by using the resolvent operator condition. Finally, two examples are provided to illustrate the applications of the obtained results.

Original language	English
Pages (from-to)	517-534
Number of pages	18
Journal	Evolution Equations and Control Theory
Volume	6
Issue number	4
DOIs	https://doi.org/10.3934/eect.2017026
State	Published - Dec 2017

Keywords

Approximate controllability
Fractional power operator
Linear evolution system
Non-autonomous evolution equation
State-dependent delay

Access to Document

10.3934/eect.2017026

Cite this

@article{0d70bf6f6a7c407780c3a645fe5ce01d,

title = "Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay",

abstract = "The controllability of non-autonomous evolution systems is an important and difficult topic in control theory. In this paper, we study the approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay. The theory of linear evolution operators is used instead of C0-semigroup to discuss the problem. Some sufficient conditions of approximate controllability are formulated and proved here by using the resolvent operator condition. Finally, two examples are provided to illustrate the applications of the obtained results.",

keywords = "Approximate controllability, Fractional power operator, Linear evolution system, Non-autonomous evolution equation, State-dependent delay",

author = "Xianlong Fu",

year = "2017",

month = dec,

doi = "10.3934/eect.2017026",

language = "英语",

volume = "6",

pages = "517--534",

journal = "Evolution Equations and Control Theory",

issn = "2163-2472",

publisher = "American Institute of Mathematical Sciences",

number = "4",

}

TY - JOUR

T1 - Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay

AU - Fu, Xianlong

PY - 2017/12

Y1 - 2017/12

N2 - The controllability of non-autonomous evolution systems is an important and difficult topic in control theory. In this paper, we study the approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay. The theory of linear evolution operators is used instead of C0-semigroup to discuss the problem. Some sufficient conditions of approximate controllability are formulated and proved here by using the resolvent operator condition. Finally, two examples are provided to illustrate the applications of the obtained results.

AB - The controllability of non-autonomous evolution systems is an important and difficult topic in control theory. In this paper, we study the approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay. The theory of linear evolution operators is used instead of C0-semigroup to discuss the problem. Some sufficient conditions of approximate controllability are formulated and proved here by using the resolvent operator condition. Finally, two examples are provided to illustrate the applications of the obtained results.

KW - Approximate controllability

KW - Fractional power operator

KW - Linear evolution system

KW - Non-autonomous evolution equation

KW - State-dependent delay

UR - https://www.scopus.com/pages/publications/85029395531

U2 - 10.3934/eect.2017026

DO - 10.3934/eect.2017026

M3 - 文章

AN - SCOPUS:85029395531

SN - 2163-2472

VL - 6

SP - 517

EP - 534

JO - Evolution Equations and Control Theory

JF - Evolution Equations and Control Theory

IS - 4

ER -

Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this