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

Xianlong Fu

doi:10.3934/eect.2017026

Article Contents

2017, Volume 6, Issue 4: 517-534. Doi: 10.3934/eect.2017026

This issue Previous Article Exact and approximate controllability of coupled one-dimensional hyperbolic equations Next Article Finite determining parameters feedback control for distributed nonlinear dissipative systems -a computational study

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

Xianlong Fu^,

Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China

* Corresponding author: Xianlong Fu
* Corresponding author: Xianlong Fu

Received: November 30, 2016

Revised: June 30, 2017

Published: November 2017

This work is supported by NSF of China (Nos. 11671142 and 11371087), STCSM (No. 13dz2260400) and Shanghai Leading Academic Discipline Project (No. B407).

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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 $C_0-$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.

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Mathematics Subject Classification: Primary: 34K30, 93B05; Secondary: 34K35, 35R10, 49K24.

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