Second-order problems involving time-dependent subdifferential operators and application to control

Soumia Saïdi; Fatima Fennour

doi:10.3934/mcrf.2022019

Article Contents

2023, Volume 13, Issue 3: 873-894. Doi: 10.3934/mcrf.2022019

This issue Previous Article Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling Next Article Dynamical estimation of a noisy input in a system with a Caputo fractional derivative. The case of continuous measurements of a part of phase coordinates

Second-order problems involving time-dependent subdifferential operators and application to control

Soumia Saïdi^, and
Fatima Fennour

LMPA Laboratory, Department of Mathematics, Mohammed Seddik Ben Yahia University, Jijel, Algeria

^* Corresponding author: Soumia Saïdi
^* Corresponding author: Soumia Saïdi

Received: November 2021

Revised: March 2022

Early access: April 2022

Published: September 2023

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Abstract

The paper provides a new result concerning the existence of solutions for second-order evolution problems associated with time-dependent subdifferential operators involving both single-valued and mixed semi-continuous set-valued perturbations. Optimal control problems corresponding to such differential inclusions using relaxation theorems with Young measures are investigated. The existence of solutions for a coupled system governed by a second-order differential equation with an evolution problem is also addressed.

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Mathematics Subject Classification: Primary: 34A60, 34G25, 47H10; Secondary: 49J52, 49J53.

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