scholarly journals Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System

2018 ◽  
Vol 23 (4) ◽  
pp. 52 ◽  
Author(s):  
Fadwa Kihal ◽  
Imane Abouelkheir ◽  
Mostafa Rachik ◽  
Ilias Elmouki
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Control Function ◽  
Isoperimetric Problem ◽  
Control Policy ◽  
Computational Method ◽  
Susceptible Population ◽  
Sirs Epidemic Model ◽  
Sufficient And Necessary Conditions ◽  
Isoperimetric Constraint

We consider a discrete-time susceptible-infected-removed-susceptible “again” (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem.

scholarly journals Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
I. Ameen ◽  
M. Hidan ◽  
Z. Mostefaoui ◽  
H.M. Ali
Keyword(s):  
Optimal Control ◽  
Heart Disease ◽  
Fish Consumption ◽  
Control Function ◽  
Real Data ◽  
World Health ◽  
Susceptible Population ◽  
Fractional Optimal Control ◽  
The World ◽  
The Impact

According to the World Health Organization (WHO), Chronic Heart Disease (CHD) is one of the greatest defies currently confronting humankind which is sweeping the whole globe, with an expanding trend in developing countries. In this paper, a mathematical model (MM) was proposed to study the connection between fish consumption and CHD mortality in Egypt, by considering a system of ordinary differential equations (ODEs) involving time-fractional derivative (FD). We considered here the study on Egypt for the ease of obtaining real data, but the method and approach adopted here is not limited to Egypt only and can be applied to any country in the world with the information of the real data related to the subject of the study. Additionally, the control function which represents the metabolic and the behavioural risk factors of CHD that help to reduce the number of mortality due to CHD is incorporated in the proposed MM. A fractional optimal control problem (FOCP) with a proposed control is formulated and studied theoretically using the Pontryagin maximum principle, to minimize the susceptible population and also to decrease the mortality rate of CHD. Moreover, firstly we discussed the positivity and boundedness of solutions; then, the model equilibria are determined and their local stability analysis was investigated; furthermore, we use the improved forward-backward sweep method (FBSM) based on the predictor-corrector method (PCM) in order to obtain the solution of proposed FOCP. In addition, some numerical simulations were performed to show the effect of the proposed optimal control (OC) besides the impact of fish consumption on the mortality of CHD.

Dynamics analysis and optimal control strategy for a SIRS epidemic model with two discrete time delays

2020 ◽  
Vol 95 (3) ◽  
pp. 035213
Author(s):  
Linhe Zhu ◽  
Xuewei Wang ◽  
Huihui Zhang ◽  
Shuling Shen ◽  
Yimin Li ◽  
...  
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Control Strategy ◽  
Epidemic Model ◽  
Time Delays ◽  
Dynamics Analysis ◽  
Optimal Control Strategy ◽  
Sirs Epidemic Model

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.

scholarly journals Implementation of an FPGA-Based Current Control and SVPWM ASIC with Asymmetric Five-Segment Switching Scheme for AC Motor Drives

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1462
Author(s):  
Ming-Fa Tsai ◽  
Chung-Shi Tseng ◽  
Po-Jen Cheng
Keyword(s):  
Discrete Time ◽  
Control Function ◽  
Current Control ◽  
Motor Drives ◽  
Modulation Scheme ◽  
Time Interval ◽  
Switching Scheme ◽  
Two Phase ◽  
Ac Motor ◽  
Ac Motor Drives

This paper presents the design and implementation of an application-specific integrated circuit (ASIC) for a discrete-time current control and space-vector pulse-width modulation (SVPWM) with asymmetric five-segment switching scheme for AC motor drives. As compared to a conventional three-phase symmetric seven-segment switching SVPWM scheme, the proposed method involves five-segment two-phase switching in each switching period, so the inverter switching times and power loss can be reduced by 33%. In addition, the produced PWM signal is asymmetric with respect to the center-symmetric triangular carrier wave, and the voltage command signal from the discrete-time current control output can be given in each half period of the PWM switching time interval, hence increasing the system bandwidth and allowing the motor drive system with better dynamic response. For the verification of the proposed SVPWM modulation scheme, the current control function in the stationary reference frame is also included in the design of the ASIC. The design is firstly verified by using PSIM simulation tool. Then, a DE0-nano field programmable gate array (FPGA) control board is employed to drive a 300W permanent-magnet synchronous motor (PMSM) for the experimental verification of the ASIC.

Sign in / Sign up

Export Citation Format

Share Document