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.

MODELING AND OPTIMAL CONTROL FOR ANTIRETROVIRAL THERAPY

2014 ◽  
Vol 22 (02) ◽  
pp. 199-217 ◽  
Author(s):  
ELLINA V. GRIGORIEVA ◽  
EVGENII N. KHAILOV ◽  
NATALIA V. BONDARENKO ◽  
ANDREI KOROBEINIKOV
Keyword(s):  
Optimal Control ◽  
Control Function ◽  
Optimal Solution ◽  
Target Cells ◽  
Model Parameters ◽  
Time Interval ◽  
Intake Rate ◽  
Bounded Control ◽  
Infection Level ◽  
Hiv Model

We consider a three-dimensional nonlinear control model based on the Wodarz HIV model. The model phase variables are populations of the uninfected and infected target cells and the concentration of an antiretroviral drug. The drug intake rate is assumed to be a bounded control function. An optimal control problem of minimizing the cumulative infection level (the infected cells population) on a given time interval is stated and solved, and the types of the optimal control for different model parameters are found by analytical methods. We thereby reduce the two-point boundary value problem (TPBVP) for the Pontryagin maximum principle to a problem of the finite-dimensional optimization. Numerical results are presented to illustrate the optimal solution.

Maximum Principle for the Optimal Control of a Hyperbolic Equation in Two Space Dimensions

1996 ◽  
Vol 2 (1) ◽  
pp. 3-15 ◽  
Author(s):  
I.S. Sadek ◽  
J.M. Sloss ◽  
S. Adali ◽  
J.C. Bruch
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Hyperbolic Equation ◽  
Vibration Suppression ◽  
Control Function ◽  
Time Derivative ◽  
The State ◽  
Control Force ◽  
The Maximum Principle ◽  
Two Space Dimensions

A maximum principle is developed for a class of problems involving the optimal control of a damped parameter system governed by a not-necessarily separable linear hyperbolic equation in two space dimensions. An index of performance is formulated, which consists of functions of the state variable, its first and second order space derivatives and first order time derivative, and a penalty function involving the open-loop control force. The solution of the optimal control problem is shown to be unique using convexity arguments. The maximum principle given involves a Hamiltonian, which contains an adjoint variable as well as an admissible control function. The state and adjoint variables are linked by terminal conditions leading to a boundary/initial/terminal value problem. The maximum principle can be used to compute the optimal control function and is particularly suitable for problems involving the active control of two-dimensional structural elements for vibration suppression.

scholarly journals Optimal Control of a Multilayer Electroelastic Engine with a Longitudinal Piezoeffect for Nanomechatronics Systems

2020 ◽  
Vol 3 (4) ◽  
pp. 53
Author(s):  
Sergey M. Afonin
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Control System ◽  
Maximum Principle ◽  
Order Differential Equation ◽  
Control Function ◽  
Control Time ◽  
Switching Line ◽  
Laser Systems ◽  
The Pontryagin Maximum Principle

A electroelastic engine with a longitudinal piezoeffect is widely used in nanotechnology for nanomanipulators, laser systems, nanopumps, and scanning microscopy. For these nanomechatronics systems, the transition between individual positions of the systems in the shortest possible time is relevant. It is relevant to solve the problem of optimizing the nanopositioning control system with a minimum control time. This work determines the optimal control of a multilayer electroelastic engine with a longitudinal piezoeffect and minimal control time for an optimal nanomechatronics system. The expressions of the control function and switching line are obtained with using the Pontryagin maximum principle for the optimal control system of the multilayer electroelastic engine at a longitudinal piezoeffect with an ordinary second-order differential equation of system. In this optimal nanomechatronics system, the control function takes only two values and changes once.

scholarly journals Modeling and Research of the Controllability of Wheeled Tractors

2019 ◽  
Vol 9 (1) ◽  
pp. 2344-2351
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
External Disturbances ◽  
The Maximum Principle ◽  
Moving Direction ◽  
The Stability ◽  
Optimal Control Methods ◽  
The Pontryagin Maximum Principle

In this paper we considered the issues of controllability and stability of wheeled tractors on the slopes with the help of mathematical modeling and optimal control. The well-known methods of modeling and research for improving the stability of the tractor do not allow solving the problem of stable motion of the tractor on the slopes, as they do not provide sufficient correction of the moving direction, which depends on the character of external disturbances. The application of modern optimal control methods allows to investigate this problem at the design phase of the machine with using mathematical models. To solve the problem, we created the equations of motion of a wheeled tractor using the Lagrange equations of the second kind. On the basis of the equations of motion we developed models and algorithms for optimal control of a wheeled tractor. The necessary conditions for optimal control of the motion using the Pontryagin maximum principle were investigated. With the help of auxiliary functions of Hamilton-Pontryagin, we have determined the coefficients of stiffness and viscous resistance of wheel tractor tires. The boundary value problem of the maximum principle to determine the transient process motion of the tractor is formulated and on its basis the equations of horizontal and vertical oscillations of the tractor were solved at an uneven distribution of mass between the front and rear driven wheels and the coefficient of adhesion of the wheels and the lateral slip of the tractor in turning were calculated.

Dynamics Response Control of a Mindlin-Type Beam

2017 ◽  
Vol 17 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Kenan Yildirim ◽  
Seda G. Korpeoglu ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Maximum Principle ◽  
Control Problem ◽  
Control Function ◽  
Initial Boundary ◽  
Response Control ◽  
Adjoint Variables ◽  
Dynamics Response ◽  
Optimal Control Function

Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

Optimal Control of a General Environmental Space

1986 ◽  
Vol 108 (4) ◽  
pp. 330-339 ◽  
Author(s):  
M. A. Townsend ◽  
D. B. Cherchas ◽  
A. Abdelmessih
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Moisture Content ◽  
Control Strategies ◽  
Switching Control ◽  
The Maximum Principle ◽  
Environmental Space ◽  
And Performance

This study considers the optimal control of dry bulb temperature and moisture content in a single zone, to be accomplished in such a way as to be implementable in any zone of a multi-zone system. Optimality is determined in terms of appropriate cost and performance functions and subject to practical limits using the maximum principle. Several candidate optimal control strategies are investigated. It is shown that a bang-bang switching control which is theoretically periodic is a least cost practical control. In addition, specific attributes of this class of problem are explored.

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