Optimal control problems for a neutral integro-differential system with infinite delay

Hai Huang; Xianlong Fu

doi:10.3934/eect.2020107

Article Contents

2022, Volume 11, Issue 1: 177-197. Doi: 10.3934/eect.2020107

This issue Previous Article Some results on the behaviour of transfer functions at the right half plane Next Article Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems

Optimal control problems for a neutral integro-differential system with infinite delay

Hai Huang and
Xianlong Fu^,

School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, P. R. China

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

Received: April 30, 2020

Revised: August 31, 2020

Early access: December 2020

Published: February 2022

This work is supported by NSF of China (Nos. 11671142 and 11771075), Science and Technology Commission of Shanghai Municipality (STCSM) (grant No. 18dz2271000)

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Abstract

This work devotes to the study on problems of optimal control and time optimal control for a neutral integro-differential evolution system with infinite delay. The main technique is the theory of resolvent operators for linear neutral integro-differential evolution systems constructed recently in literature. We first establish the existence and uniqueness of mild solutions and discuss the compactness of the solution operator for the considered control system. Then, we investigate the existence of optimal controls for the both cases of bounded and unbounded admissible control sets under some assumptions. Meanwhile, the existence of time optimal control to a target set is also considered and obtained by limit arguments. An example is given at last to illustrate the applications of the obtained results.

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Mathematics Subject Classification: Primary: 34K30, 49J20; Secondary: 34K40, 45K05, 93C23.

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