Publications (21)
ARTICLE
ON OPTIMAL CONTROL OF AN EPIDEMIOLOGICAL SYSTEM STRUCTURED BY AGE
Georges Kologo , Cedric Kpèbbèwèrè Some, Somdouda Sawadogo
In this paper, we study optimal control problems for a system structured according to the age a and position x of an epidemic of the sveicrs type. We focus on solid biological knowledge about the modes of transmission of the SARS-CoV-2 virus via airborne transmission. First, we show the conditions for the existence of solutions and the princip(...)
Stochastic Optimal Control, Optimal Value, Epidemiological System, Stochastic Stability
ARTICLE
GNSS Analysis of the Ionospheric Response to the Extreme Geomagnetic Storm of May 11, 2024: Latitudinal Dependence of VTEC
Karim Guibula, Abidina Diabate, Moumouni Diallo
This study examines the ionospheric response to the extreme geomagnetic storm of May 11, 2024, (Dst ≈ −400 nT) using GNSS derived vertical total electron content (VTEC) from four stations distributed from northern mid-latitudes to southern low latitude. Disturbances are quantified using the relative deviation parameter (ΔVTEC) and interpreted(...)
ionosphere; extreme geomagnetic storm; VTEC; ΔVTEC; GNSS; latitudinal dependence
ARTICLE
SIMULTANEOUS SENTINELS WITH A GIVEN SENSITIVITY IN A POPULATION DYNAMICS PROBLEM WITH MISSING DATA
Kpèbbèwèrè Cédric SOME, Georges KOLOGO, Somdouda SAWADOGO
In this paper, we determine pollution parameters in a population dynamics model with missing data by using simultaneous sentinels with given sensitivity. First, we construct suitable functionals in order to introduce the notion of simultaneous sentinels. Next, we show that the existence of such sentinels is equivalent to the simultaneous null-(...)
simultaneous sentinels, null-controllability, Carleman inequalities, observability inequality, constraint control
ARTICLE
ASYMPTOTIC STABILITY AND OPTIMAL CONTROL OF A NONLINEAR TIME-VARYING SYSTEM WITH JOINT CONSTRAINTS AND EPIDEMIC ILLUSTRATIVE EXAMPLE
Kpèbbèwèrè Cédric Somé, Georges KOLOGO, Somdouda SAWADOGO
We study the optimal value of a functional cost for a control problem whose control function is piecewise continuous in a bounded closed space. We then use the convexity of the Hamiltonian function to prove the necessary and sufficient conditions for optimality. The optimal values of the control problem are determined by the optimality princip(...)
Nonlinear system, Joint (building), Stability (learning theory), Exponential stability, Control theory (sociology), Optimal control, Mathematics, Control (management), Computer science, Mathematical optimization, Applied mathematics, Engineering, Physics, Artificial intelligence, Structural engineering
ARTICLE
Control of Singular Distributed Systems by Controllability : The Ill-Posed Backwards Heat Equation
Bylli André Guel, Sadou Tao, Elie Ouedraogo
To deal with the ill-posed backwards heat equation, we propose the controllability method. The point of view adopted consists in interpreting the state equation as an inverse problem that allows us to obtain a decoupled and strong singular optimality system for the optimal control-state pair. This further permits to propose an existence criter(...)
singular distributed systems, optimal control, ill-posed backwards heat equation, controllability, inverse problem
ARTICLE
Optimal Control of a Nonlinear System with White Noise
Georges KOLOGO, Kpèbbèwèrè Cédric Somé, Somdouda Sawadogo
In this paper, we propose a control problem for nonlinear stochastic differential equations with noise. The system proposed for the control problem is a nonlinear system perturbed by standard Brownian motion. We write this problem in a coupled form where the control <i>u(t)</i> has a value in a convex space. Here, we propose suffic(...)
Control theory (sociology), White noise, Nonlinear system, Noise (video), Control (management), Computer science, Mathematics, Statistics, Physics, Artificial intelligence
ARTICLE
Response of the Magnetospheric Convection Electric Field (MCEF) to Geomagnetic Storms During the Solar Cycle 24 Maximum Phase
Bazié Nongobsom, Kaboré Salfo, Guibula Karim, Ouattara Frédéric
The present work focuses on the variability of the magnetospheric convection electric field (MCEF) during geomagnetic storms generated by coronal mass ejections (CMEs). The aim of the study was to analyze the response of the MCEF to geoeffective CMEs occurring during the maximum phase of Solar Cycle 24. A total of eight storms were selected on(...)
Coronal mass ejections; interplanetary magnetic field; magnetic storm; magnetospheric convection electric field
ARTICLE
LOCAL STABILITY AND OPTIMAL CONTROL STRATEGY FOR A SARS-CoV-2 EPIDEMIC
Georges Kologo , Cédric K. SOME, Somdouda SAWADOGO
This article assesses the effect of vaccination on the control of an infectious disease using a new mathematical model in which immunity is not acquired permanently. In this model, the number of elementary reproductions \mathcal{R}_0 is a major indicator of the extinction or propagation of the infection in a population. In this document, the c(...)
optimal value, epidemic model, loss of immunity, homogeneous environment.
ARTICLE
A METHOD FOR PARAMETERS IDENTIFICATION IN POPULATION DYNAMICS PROBLEM
Mifiamba SOMA, Cedric K SOME 2, Mamadou OUEDRAOGO 3, Somdouda SAWADOGO
The problems of pollution in population dynamics generally involve missing source terms, as well as missing initial or boundary conditions. This paper is concerned with identifying
the pollution terms arising in the state equation of a population dynamics system with incomplete initial conditions. To this end, the so-called sentinel method is(...)
Population dynamics, Carleman inequality, incomplete data, Controllability
PRéPUBLICATION
Control of Singular Distributed Systems by Controllability: The Ill-Posed Backwards Heat Equation
Bylli André Guel, Sadou Tao, Elie Ouedraogo
This paper deals with the ill-posed backwards heat equation. To do this, we propose the controllability method. The point of view adopted, which consists in interpreting the state equation as an inverse problem, allows us to obtain a decoupled and strong singular optimality system for the optimal control-state pair, but also to propose an exis(...)
Singular distributed systems, Optimal control, Ill-posed backwards heat equation, Controllability, Inverse problem
ARTICLE
Control of the Cauchy System for an Elliptic Operator : The Controllability Method
Bylli André B. Guel
In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. This is a follow-up to a previous paper on the same subject. Indeed, in an earlier publication, we introduced a regularization method, called the controllability method, which allowed us to propose, on the one hand, a characterization of the existence of(...)
Singular distributed system, optimal control, singular optimality system, the ill-posed Cauchy problem, controllability method, inverse problem
ARTICLE
Control of the Hyperbolic Ill-posed Cauchy Problem by Controllability
Bylli André Guel, Sadou Tao, Somdouda Sawadogo
The main purpose of this paper is the control of the hyperbolic ill-posed Cauchy problem. To do this, we adapt to the present case the controllability method previously introduced in the stationary case (Bylli 2023). So we interpret the problem as an inverse problem, and therefore a controllability problem. This point of view induces a regular(...)
Controllability, Mathematics, Cauchy problem, Well-posed problem, Inverse problem, Regularization (linguistics), Applied mathematics, Optimal control, Cauchy distribution, Control (management), Hyperbolic partial differential equation, Initial value problem, Mathematical optimization, Mathematical analysis, Partial differential equation, Computer science
PRéPUBLICATION
Control of the Cauchy System for an Elliptic Operator
Bylli André B. Guel
In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. A follow-up to a previous paper on the same subject (cf. [4]). Indeed, in [4], we introduced a regularization method, called the controllability method, which allowed us to know how to characterize, on the one hand, the existence of a regular solution to(...)
Singular distributed system, Optimal control, The ill-posed Cauchy Problem, Controllability, Inverse Problem
PRéPUBLICATION
Hierarchical Control for the parabolic ill-posed Cauchy problem
Bylli André Guel
This paper deals with the control problem of the parabolic ill-posed Cauchy system. To do this, we use a notion of hierarchical control inspired by the control of Stackelberg. This approach makes it possible to characterize the optimal control-state pair via a singular optimality system. And this, without using any additional assumptions, such(...)
Partial differential equations, Singular distributed systems, Ill-posed Cauchy problem, Optimal control, Hierarchical control, Singular optimality system
ARTICLE
The ill-posed Cauchy problem by Controllability the elliptic case
Bylli André Guel, Ousseynou Nakoulima
In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. To do this, we interpret the problem as an inverse problem, and therefore a controllability problem. This point of view induces a regularization method that makes it possible, on the one hand, to characterize the existence of a regular solution to the pro(...)
Singular distributed system, optimal control, singular optimality system, The ill-posed Cauchy problem, Controllability, Inverse problem