scholarly journals Optimal control of COVID-19

2021 ◽  
Vol 11 (1) ◽  
pp. 114-122
Author(s):  
Nacima Moussouni ◽  
Mohamed Aliane
Keyword(s):  
Infectious Disease ◽  
Optimal Control ◽  
Maximum Principle ◽  
Indirect Method ◽  
Shooting Method ◽  
Discretization Method ◽  
Seir Model ◽  
The World ◽  
Respiratory Droplets ◽  
The Pontryagin Maximum Principle

Coronavirus disease of 2019 or COVID-19 (acronym for coronavirus disease 2019) is an emerging infectious disease caused by a strain of coronavirus called SARS-CoV-22, contagious with human-to-human transmission via respiratory droplets or by touching contaminated surfaces then touching them face. Faced with what the world lives, to define this problem, we have modeled it as an optimal control problem based on the models of William Ogilvy Kermack et Anderson Gray McKendrick, called SEIR model, modified by adding compartments suitable for our study. Our objective in this work is to maximize the number of recovered people while minimizing the number of infected. We solved the problem theoretically using the Pontryagin maximum principle, numerically we used and compared results of two methods namely the indirect method (shooting method) and the Euler discretization method, implemented in MATLAB.

scholarly journals Optimization of cereal output in presence of locusts

2016 ◽  
Vol 6 (1) ◽  
pp. 53-61 ◽  
Author(s):  
Nacima Moussouni ◽  
Mohamed Aidene
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pontryagin Maximum Principle ◽  
Shooting Method ◽  
The Pontryagin Maximum Principle

In this paper, we study a modelization of the evolution of cereal output production, controlled by adding fertilizers and in presence of locusts, then by adding insecticides. The aim is to maximize the cereal output and meanwhile minimize pollution caused by adding fertilizers and insecticides.The optimal control problem obtained is solved theoretically by using the Pontryagin Maximum Principle, and then numerically with shooting method.

scholarly journals Optimal control of a rectilinear motion of a rocket

2020 ◽  
Vol 8 (1) ◽  
pp. 281-295
Author(s):  
Mohamed Aliane ◽  
Nacima Moussouni ◽  
Mohand Bentobache
Keyword(s):  
Optimal Control ◽  
Approximate Solution ◽  
Maximum Principle ◽  
Analytical Solution ◽  
Shooting Method ◽  
Rectilinear Motion ◽  
Euler Formula ◽  
Simulation Results ◽  
The One ◽  
The Pontryagin Maximum Principle

In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.

WHY REGULARIZATION OF LAGRANGE PRINCIPLE AND PONTRYAGIN MAXIMUM PRINCIPLE IS NEEDED AND WHAT IT GIVES

2018 ◽  
pp. 757-775
Author(s):  
Mikhail Iosifovich Sumin
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Mathematical Programming ◽  
Optimality Conditions ◽  
Pontryagin Maximum Principle ◽  
Lagrange Principle ◽  
Convex Problems ◽  
The Pontryagin Maximum Principle

We consider the regularization of the classical Lagrange principle and the Pontryagin maximum principle in convex problems of mathematical programming and optimal control. On example of the “simplest” problems of constrained infinitedimensional optimization, two main questions are discussed: why is regularization of the classical optimality conditions necessary and what does it give?

scholarly journals Regularized classical optimality conditions in iterative form for convex optimization problems for distributed Volterra-type systems

2021 ◽  
Vol 31 (2) ◽  
pp. 265-284
Author(s):  
V.I. Sumin ◽  
M.I. Sumin
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Pontryagin Maximum Principle ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Lagrange Principle ◽  
The Pontryagin Maximum Principle

We consider the regularization of the classical optimality conditions (COCs) — the Lagrange principle and the Pontryagin maximum principle — in a convex optimal control problem with functional constraints of equality and inequality type. The system to be controlled is given by a general linear functional-operator equation of the second kind in the space $L^m_2$, the main operator of the right-hand side of the equation is assumed to be quasinilpotent. The objective functional of the problem is strongly convex. Obtaining regularized COCs in iterative form is based on the use of the iterative dual regularization method. The main purpose of the regularized Lagrange principle and the Pontryagin maximum principle obtained in the work in iterative form is stable generation of minimizing approximate solutions in the sense of J. Warga. Regularized COCs in iterative form are formulated as existence theorems in the original problem of minimizing approximate solutions. They “overcome” the ill-posedness properties of the COCs and are regularizing algorithms for solving optimization problems. As an illustrative example, we consider an optimal control problem associated with a hyperbolic system of first-order differential equations.

scholarly journals OPTIMIZING THE QUARANTINE COST FOR SUPPRESSION OF THE COVID-19 EPIDEMIC IN MEXICO

2020 ◽  
Vol 28 (1) ◽  
pp. 55-78
Author(s):  
ABDON E. CHOQUE RIVERO ◽  
EVGENII N. KHAILOV ◽  
ELLINA V. GRIGORIEVA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Function ◽  
Optimal Solution ◽  
Weighted Sum ◽  
Bounded Control ◽  
Infection Level ◽  
Total Cost ◽  
The Maximum Principle ◽  
The Pontryagin Maximum Principle

This paper is one of the few attempts to use the optimal control theory to find optimal quarantine strategies for eradication of the spread of the COVID-19 infection in the Mexican human population. This is achieved by introducing into the SEIR model a bounded control function of time that reflects these quarantine measures. The objective function to be minimized is the weighted sum of the total infection level in the population and the total cost of the quarantine. An optimal control problem reflecting the search for an effective quarantine strategy is stated and solved analytically and numerically. The properties of the corresponding optimal control are established analytically by applying the Pontryagin maximum principle. The optimal solution is obtained numerically by solving the two-point boundary value problem for the maximum principle using MATLAB software. A detailed discussion of the results and the corresponding practical conclusions are presented.

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