scholarly journals Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Saeed Islam ◽  
Sher Afzal Khan ◽  
Ilyas Khan ◽  
Sharidan Shafie ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Human Population ◽  
Cost Effective ◽  
Farm Animals ◽  
Effective Control ◽  
Multiple Control ◽  
Control Variables ◽  
Control Functions

Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.

scholarly journals Prevention of Influenza Pandemic by Multiple Control Strategies

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Numerical Techniques ◽  
Multiple Control ◽  
Control Functions ◽  
Transmission Of Disease

We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method.

scholarly journals Multiple Control Strategies for Prevention of Avian Influenza Pandemic

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Avian Influenza ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Multiple Control ◽  
Control Functions ◽  
The Cost

We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.

Dynamical Behavior of a Malaria Model with Discrete Delay and Optimal Insecticide Control

2017 ◽  
Vol 12 (01) ◽  
pp. 19-38 ◽  
Author(s):  
Tuhin Kumar Kar ◽  
Soovoojeet Jana
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Control Variable ◽  
Discrete Delay ◽  
Insecticide Control

In this paper we have proposed and analyzed a simple three-dimensional mathematical model related to malaria disease. We consider three state variables associated with susceptible human population, infected human population and infected mosquitoes, respectively. A discrete delay parameter has been incorporated to take account of the time of incubation period with infected mosquitoes. We consider the effect of insecticide control, which is applied to the mosquitoes. Basic reproduction number is figured out for the proposed model and it is shown that when this threshold is less than unity then the system moves to the disease-free state whereas for higher values other than unity, the system would tend to an endemic state. On the other hand if we consider the system with delay, then there may exist some cases where the endemic equilibrium would be unstable although the numerical value of basic reproduction number may be greater than one. We formulate and solve the optimal control problem by considering insecticide as the control variable. Optimal control problem assures to obtain better result than the noncontrol situation. Numerical illustrations are provided in support of the theoretical results.

scholarly journals Robust Multi-Objective Singular Optimal Control Ofpenicillin Fermentation Process

2020 ◽  
pp. 23-30
Author(s):  
Gustavo B. Libotte ◽  
Fran S. Lobato ◽  
Gustavo M. Platt ◽  
Francisco D. Moura Neto
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fermentation Process ◽  
Singular Problem ◽  
Fed Batch ◽  
Control Variables ◽  
Singular Optimal Control ◽  
Multi Objective ◽  
Singular Optimal Control Problem

The determination of optimal feeding profile of fed-batch fermentation requires the solution of a singular optimal control problem. The complexity in obtaining the solution to this singular problem is due to the nonlinear dynamics of the system model, the presence of control variables in linear form and the existence of constraints in both the state and control variables. Traditionally, during the optimization process, uncertainties associated with design variables, control parameters and mathematical model are not considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of a singular optimal control problem is proposed. This approach consists of the Multi-objective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multi- objective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time.

Local generalization of transversality conditions for optimal control problem

2019 ◽  
Vol 14 (3) ◽  
pp. 310
Author(s):  
Beyza Billur İskender Eroglu ◽  
Dіlara Yapişkan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Hamiltonian Formalism ◽  
Variational Calculus ◽  
Control Problems ◽  
Conformable Derivative ◽  
Transversality Conditions ◽  
Control Functions

In this paper, we introduce the transversality conditions of optimal control problems formulated with the conformable derivative. Since the optimal control theory is based on variational calculus, the transversality conditions for variational calculus problems are first investigated and then supported by some illustrative examples. Utilizing from these formulations, the transversality conditions for optimal control problems are attained by using the Hamiltonian formalism and Lagrange multiplier technique. To illustrate the obtained results, the dynamical system on which optimal control problem constructed is taken as a diffusion process modeled in terms of the conformable derivative. The optimal control law is achieved by analytically solving the time dependent conformable differential equations occurring from the eigenfunction expansions of the state and the control functions. All figures are plotted using MATLAB.

scholarly journals Seeking Best-Balanced Patch-Injecting Strategies through Optimal Control Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Kaifan Huang ◽  
Pengdeng Li ◽  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Yuan Yan Tang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Negative Impact ◽  
Cost Effective ◽  
Control Approach ◽  
Novel Virus ◽  
Optimality Systems ◽  
Objective Functional ◽  
Optimal Control Approach

To restrain escalating computer viruses, new virus patches must be constantly injected into networks. In this scenario, the patch-developing cost should be balanced against the negative impact of virus. This article focuses on seeking best-balanced patch-injecting strategies. First, based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem, in which (a) each admissible control stands for a feasible patch-injecting strategy and (b) the objective functional measures the balance of a feasible patch-injecting strategy. Second, the solvability of the optimal control problem is proved, and the optimality system for solving the problem is derived. Next, a few best-balanced patch-injecting strategies are presented by solving the corresponding optimality systems. Finally, the effects of some factors on the best balance of a patch-injecting strategy are examined. Our results will be helpful in defending against virus attacks in a cost-effective way.

scholarly journals High-order homogenization in optimal control by the Bloch wave method

2021 ◽  
Author(s):  
Agnes Lamacz-Keymling ◽  
Irwin Yousept
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Periodic Coefficient ◽  
State Equation ◽  
Bloch Wave ◽  
High Order ◽  
Effective Control ◽  
Linear Quadratic

This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\eps$. The small parameter $\eps>0$ denotes the periodicity length. We propose a high-order effective control problem with constant coefficients that provides an approximation of the original one with error $O(\eps^M)$, where $M\in\N$ is as large as one likes. Our analysis relies on a Bloch wave expansion of the optimal solution and is performed in two steps. In the first step, we expand the lowest Bloch eigenvalue in a Taylor series to obtain a high-order effective optimal control problem. In the second step, the original and the effective problem are rewritten in terms of the Bloch and the Fourier transform, respectively. This allows for a direct comparison of the optimal control problems via the corresponding variational inequalities, leading to our main theoretical result on the high-oder approximation.

scholarly journals Numerical solution of an optimal control problem with variable time points in the objective function

2002 ◽  
Vol 43 (4) ◽  
pp. 463-478 ◽  
Author(s):  
K. L. Teo ◽  
Y. Liu ◽  
W. R. Lee ◽  
L. S. Jennings ◽  
S. Wang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Control Problems ◽  
Time Points ◽  
Variable Time ◽  
Control Functions

AbstractIn this paper, we consider the numerical solution of a class of optimal control problems involving variable time points in their cost functions. The control enhancing transform is first used to convert the optimal control problem with variable time points into an equivalent optimal control problem with fixed multiple characteristic time (MCT). Using the control parametrization technique, the time horizon is partitioned into several subintervals. Let the partition points also be taken as decision variables. The control functions are approximated by piecewise constant or piecewise linear functions in accordance with these variable partition points. We thus obtain a finite dimensional optimization problem. The control parametrization enhancing control transform (CPET) is again used to convert approximate optimal control problems with variable partition points into equivalent standard optimal control problems with MCT, where the control functions are piecewise constant or piecewise linear functions with pre-fixed partition points. The transformed problems are essentially optimal parameter selection problems with MCT. The gradient formulae for the objective function as well as the constraint functions with respect to relevant decision variables are obtained. Numerical examples are solved using the proposed method.

scholarly journals Optimal control problem for systems governed by nonlinear parabolic equations without initial conditions

2016 ◽  
Vol 8 (1) ◽  
pp. 21-37
Author(s):  
M.M. Bokalo ◽  
A.M. Tsebenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Parabolic Equations ◽  
Initial Conditions ◽  
Nonlinear Parabolic Equations ◽  
State Equations ◽  
Control Functions ◽  
Nonlinear Parabolic ◽  
Final Observation

An optimal control problem for systems described by Fourier problem for nonlinear parabolic equations is studied. Control functions occur in the coefficients of the state equations. The existence of the optimal control in the case of final observation is proved. 

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