ملف المستخدم
صورة الملف الشخصي

عبد الحق حفظ الله

إرسال رسالة

التخصص: رياضيات تطبيقية

الجامعة: جامعة العربي التبسي- الجزائر

النقاط:

38
معامل الإنتاج البحثي

الخبرات العلمية

  • Applied mathematics; control theory

الأبحاث المنشورة

On the optimal control of linear systems depending upon a parameter and with missing data

المجلة: Nonlinear Studies

سنة النشر: 2020

تاريخ النشر: 2020-05-27

The aim of this paper is to study general and abstract control systems with incomplete data. Actually, we introduce the notions of averaged no-regret control and its approximation, the averaged low-regret control to get a full characterization for the optimal control via an optimality system. As an example, we apply the described theory on an optimal control problem for an equation of vibrating thin plate depending on an uncertainty parameter and with missing initial conditions where optimality systems characterizing the averaged no-regret control and the averaged low-regret control are

Identification of diffusion coefficient in a semi-linear parabolic equation with incomplete initial condition: a no-regret control method

المجلة: Journal of Control and Decision

سنة النشر: 2023

تاريخ النشر: 2023-12-13

This paper addresses the problem of identifying the unknown diffusion coefficient in a semi-linear parabolic equation with incomplete initial condition. We propose an optimal control approach using the no-regret control method and the adapted low-regret control. Our approach provides a full characterisation of the unknown diffusion coefficient independent of the missing initial condition. We also present an optimality system that describes the adapted low-regret control and use it to find a full description of the no-regret control by taking the limit of the sequence of adapted low-regret controls.

Identification of the Potential Coefficient in the Schrödinger Equation with Incomplete Initial Conditions from a Boundary Observation

المجلة: Russian Journal of Mathematical Physics volume

سنة النشر: 2023

تاريخ النشر: 2023-06-18

This paper deals with an inverse problem of the Schrödinger equation, a fundamental equation in quantum mechanics. Specifically, we focus on incomplete data, where there are missing terms in the potential term and the initial condition. The potential term is a critical part of the equation, representing the potential energy of the system under investigation. Our objective is to obtain valuable information about this potential term without the need to determine the unknown initial condition. To achieve this, we employ the sentinel method, which is a functional that is sensitive to only one unknown and insensitive to others. Our research shows that the existence of this functional is connected to solving an optimal control problem, which we accomplish using the Hilbert Uniqueness Method. By using this approach, we are able to gain insights into the potential coefficient, which can provide significant benefits in a wide range of applications.

Sentinels of nth-Order Insensitivity for Identification Problems With High-Order Incomplete Data

المجلة: Boletim da Sociedade Paranaense de Matematica

سنة النشر: 2023

تاريخ النشر: 2023-04-22

This study generalizes the definition of the sentinel function, which was introduced by J.L. Lions to study identification problems, to a more insensitive kind of sentinel, which is applied to identify pollution terms of the polynomial form w. r. t. the real λ. The main idea is to reconstruct the sentinel function to be nth-order independent of the incomplete data. Contrary to the original definition, information about the pollution term with an error of order n + 1 is given by the sentinel of nth-order insensitivity

Identification of the Potential Coefficient in the Wave Equation with Incomplete Data: A Sentinel Method

المجلة: Russian Mathematics

سنة النشر: 2023

تاريخ النشر: 2023-03-17

In this paper, we consider a wave equation with incomplete data, where we do not know the potential coefficient and the initial conditions. From observing the system in the boundary, we want to get information on the potential coefficient independently of the initial conditions. This can be obtained using the sentinel method of Lions, which is a functional insensitive to certain parameters. Shows us through the adjoint system that the existence of the sentinel is equivalent to an optimal control problem. We solve this optimal control problem by using the Hilbert uniqueness method (HUM).

Identification of the bulk modulus coefficient in the acoustic equation from boundary observation: a sentinel method

المجلة: Boundary Value Problems

سنة النشر: 2023

تاريخ النشر: 2023-03-09

In this paper, we consider an acoustic equation with incomplete data, where the bulk modulus coefficient and initial conditions are partially known. Our goal is to get information about the bulk modulus coefficient independently of the initial conditions from boundary observations. To achieve this goal, we apply the sentinel method introduced by J.L. Lions, which is a functional that links the solution to the given problem with a control function and a state observation. We prove that the existence of the sentinel functional is equivalent to a boundary-null controllability problem with constraints on the control. We use the Hilbert uniqueness method to study this controllability problem to establish the control of minimal norm.

Identification problem of a fractional thermoelastic deformation system with incomplete data: A sentinel method

المجلة: Nonlinear Studies

سنة النشر: 2022

تاريخ النشر: 2022-05-28

In this work, the problem of the deformations for fractional coupled thermoelastic systems is formulated and solved by Riemann Liouville and Caputo fractional derivatives. In this work, the problem of the deformations for fractional coupled thermoelastic systems is formulated and solved by Riemann Liouville and Caputo fractional derivatives. The initial conditions and some boundary conditions are partially known, thus the problem studied here is an inverse problem with incomplete data. The initial conditions are understood here in the left Riemann-Liouville fractional integrals sense. Our purpose is to estimate unknown boundary conditions of the transverse displacement since the other missing terms in the initial conditions are of no interest to us. We base our estimates on the measured temperature in a small observatory domain. We look for the desired sentinel function which will obviously lead to study the null controllability problem. The right Caputo fractional derivative is more suitable to introduce the fractional coupled adjoint state systems. The identification problem with the Riemann Liouville and Caputo fractional derivatives senses suggested in this work is the generalization of classical identification problems in the no fractional case

Averaged No-Regret Control for an Electromagnetic Wave Equation Depending upon a Parameter with Incomplete Initial Conditions

المجلة: intechopen

سنة النشر: 2021

تاريخ النشر: 2021-03-11

This chapter concerns the optimal control problem for an electromagnetic wave equation with a potential term depending on a real parameter and with missing initial conditions. By using both the average control notion introduced recently by E. Zuazua to control parameter depending systems and the no-regret method introduced for the optimal control of systems with missing data. The relaxation of averaged no-regret control by the averaged low-regret control sequence transforms the problem into a standard optimal control problem. We prove that the problem of average optimal control admits a unique averaged no-regret control that we characterize by means of optimality systems

Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis

المجلة: Ural Mathematical Journal

سنة النشر: 2020

تاريخ النشر: 2020-07-28

In this paper, we investigate the problem of optimal control for an ill-posed wave equation without using the extra hypothesis of Slater i.e. the set of admissible controls has a non-empty interior. Firstly, by a controllability approach, we make the ill-posed wave equation a well-posed equation with some incomplete data initial condition. The missing data requires us to use the no-regret control notion introduced by Lions to control distributed systems with incomplete data. After approximating the no-regret control by a low-regret control sequence, we characterize the optimal control by a singular optimality system

Averaged null controllability for some hyperbolic equations depending on a parameter

المجلة: Journal of Mathematical Analysis and Applications

سنة النشر: 2020

تاريخ النشر: 2020-10-16

The aim of this paper is to prove the averaged null controllability property for a wave equation with an unknown velocity of propagation parameter and for parameter-dependent vibrating plate equation under the effect of a boundary control. The choice of the Hilbert uniqueness method seems to be the best-adapted method to our theory, where the key point to prove the desired result is an averaged inverse inequality (averaged observability inequality). Consequently, we'll prove the desired property for a large time enough and we'll design a single control chosen independently of the parameter value transferring the average of the state to the origin.

Predictive Modeling and Multi-response Optimization of Physical and Mechanical Properties of SCC Based on Sand’s Particle Size Distribution

المجلة: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING

سنة النشر: 2020

تاريخ النشر: 2020-07-17

This paper focuses on the modeling and optimization of the physical and mechanical properties of self-compacting concrete (SCC), prepared using the modified packing model design, taking into consideration sand’s particle size distribution (PSD) and fineness modulus (FM). The optimization is predicated using the response surface methodology. The analysis of variance is exploited to determine the statistical significance of the PSD on the studied properties of SCC. For that, we studied twenty-four SCC mixtures, using three kinds of sands with different FM and particle shapes: dune sand, river sand, and crushed sand. The results show that PSD properties of used sand, despite its shape, are good predictors for SCC fresh properties, but less predictive for compressive strength. The multi-response optimization allowed the estimation of sand’s PSD parameters that give the optimal physical and mechanical properties of SCC, with an overall desirability of 0.923

Regional averaged controllability for hyperbolic parameter dependent systems

المجلة: Control Theory and Technology

سنة النشر: 2020

تاريخ النشر: 2020-07-08

The purpose of this paper is to extend the notion of regional controllability for hyperbolic parameter dependent systems. The key idea is the characterization of the averaged regional control with minimal energy. This control steers the state average (with respect to such a parameter) towards the desired state only on a given part of the system evolution domain. In this paper, we give the precis definition and the properties of this new concept. Then, we use an approach based on an extension of the Hilbert uniqueness method devoted to the calculation of the control in two different cases: zone control and pointwise control

Optimal control of a thermoelastic body with missing initial conditions

المجلة: International Journal of Control

سنة النشر: 2019

تاريخ النشر: 2019-09-11

This paper aims to control the deformation and the temperature of a thermoelastic body by acting on him by an exterior force applied on a part of the body. In this case, all the initial data in the main model are missing values. The incomplete data in the considered model requires the use of the notion of no-regret control introduced by J. L. Lions for optimal control of distributed systems with missing data. An optimality system formed of coupled equations and adjoint coupled equations characterises the optimal pair (control state)

Optimal control of electromagnetic wave displacement with an unknown velocity of propagation

المجلة: International Journal of Control

سنة النشر: 2018

تاريخ النشر: 2018-04-16

The aim of this paper is to control an electromagnetic wave that penetrates in a medium with some missing information about its physical properties. The missing value of wave velocity of propagation leads us to use averaged control notion which is recently introduced by E. Zuazua, also the boundary Dirichlet condition is unknown which requires using the notion of no-regret control introduced by J. L. Lions. In this work, we combine these two techniques where we introduce the notion of averaged no-regret control to solve our optimal control problem with missing data. The averaged no-regret control will be characterised by an optimality system

No-regret optimal control characterization for an ill-posed wave equation

المجلة: International Journal of Mathematics Trends and Technology

سنة النشر: 2017

تاريخ النشر: 0017-12-11

In this paper, we give a characterization (optimality system) of a quadratic optimal control for an ill-posed wave equation without using the extra hypothesis of Slater (ie. 𝑼𝒂𝒅 set of admissible controls has a non-empty interior). By using a parabolic regularization we get a missing data problem where we associate a no-regret control to obtain a singular optimality system, then we pass to limit and by a corrector of order zero we complete the information

Optimal Control of a Partially Known Coupled System of BOD and DO

المجلة: International Journal of Analysis and Applications

سنة النشر: 2021

تاريخ النشر: 2021-11-25

The work presented in this paper is concerned with the organic pollution problem and water quality valuation. Biochemical oxygen demand has been used to evaluate the quality of water. If organic matter is present the dissolved oxygen is consumed. This article considers an optimal control problem of coupled system with missing initial conditions, which presents the relation between the biochemical oxygen demand and the dissolved oxygen. The main objective is to control the concentration of dissolved oxygen using the information given in the biochemical oxygen demand equation. The main tool used to characterize the optimal control of the investigate system under the Pareto control formulation