Using contaminated tools fuels outbreaks of BananaXanthomonas wilt: An optimal control study within plantations using Runge–Kutta fourth-order algorithms

2015 ◽  
Vol 08 (05) ◽  
pp. 1550065 ◽  
Author(s):  
B. Nannyonga ◽  
L. S. Luboobi ◽  
P. Tushemerirwe ◽  
M. Jabłońska-Sabuka
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Control Theory ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Optimal Control Theory ◽  
Optimal Controls ◽  
Preventive Methods ◽  
Control Study ◽  
Banana Xanthomonas Wilt

Optimal control theory is applied to a system of ordinary differential equations modeling banana Xanthomonas wilt within plantations. The objective is to reduce the proportion of infected plants by use of controls representing two types of preventive methods: vector and contaminated tool prevention. The optimal controls are characterized in terms of the optimality system, which is solved analytically and numerically for several scenarios.

scholarly journals Numerical Optimal Control of HIV Transmission in Octave/MATLAB

2019 ◽  
Vol 25 (1) ◽  
pp. 1 ◽  
Author(s):  
Carlos Campos ◽  
Cristiana J. Silva ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Initial Value

We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70–75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge–Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge–Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article.

OPTIMAL CONTROL MEASURES FOR TUBERCULOSIS MATHEMATICAL MODELS INCLUDING IMMIGRATION AND ISOLATION OF INFECTIVE

2010 ◽  
Vol 18 (01) ◽  
pp. 17-54 ◽  
Author(s):  
D. OKUONGHAE ◽  
V. U. AIHIE
Keyword(s):  
Optimal Control ◽  
Population Dynamics ◽  
Iterative Method ◽  
Fourth Order ◽  
Optimal Control Theory ◽  
Control Measures ◽  
Optimal Controls ◽  
Medical Testing ◽  
Order Scheme ◽  
Parameter Values

Optimal control theory is applied to a system of ordinary differential equations modeling the population dynamics of tuberculosis with isolation and immigration of infective. Seeking to minimize the number of infectious individuals and reduce the transmission of the disease, we use controls to represent the screening/medical testing of infected immigrants into the population as well as isolation of infective in the population. The optimal controls are characterized in terms of the optimality system, which is solved numerically for several scenarios using an iterative method with Runge-Kutta fourth order scheme. Parameter values used are those reported for Nigeria.

scholarly journals Quenching Time Optimal Control for Some Ordinary Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Ping Lin
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Parabolic Equations ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Time Optimal ◽  
Differential Control ◽  
Quenching Time ◽  
The Pontryagin Maximum Principle

This paper concerns time optimal control problems of three different ordinary differential equations inℝ2. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations.

Maximizing Distance of the Golf Drive: An Optimal Control Study

1975 ◽  
Vol 97 (4) ◽  
pp. 362-367 ◽  
Author(s):  
M. A. Lampsa
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Variational Formulation ◽  
Necessary Conditions ◽  
Model Parameter ◽  
Steepest Ascent ◽  
Parameter Values ◽  
Control Study

Optimal control theory is used to search for the optimal control torques necessary to maximize distance of the golf drive. In the method, a mathematical model of a generalized golf swing is first developed. Film of the author’s swing serves to verify the model and to supply parameter values, constraints, and actual torques. The variational formulation of optimal control theory is utilized to establish necessary conditions for optimal control, in which constraint violations are discouraged by inclusion of penalty functions. Finally, the method of steepest ascent is used to compute optimal control torques. Also, comparison of optimal and actual torques is made, and the sensitivity of the results to small changes in model parameter values is investigated.

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