scholarly journals Modeling and Optimal Control on the Spread of Hantavirus Infection

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1192 ◽  
Author(s):  
Fauzi Mohamed Yusof ◽  
Farah Aini Abdullah ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control System ◽  
Maximum Principle ◽  
Optimal Control Theory ◽  
Necessary Condition ◽  
Hantavirus Infection ◽  
Kutta Method ◽  
Rodent Population ◽  
Runge Kutta Method

In this paper, optimal control theory is applied to a system of ordinary differential equations representing a hantavirus infection in rodent and alien populations. The effect of the optimal control in eliminating the rodent population that caused the hantavirus infection is investigated. In addition, Pontryagin’s maximum principle is used to obtain the necessary condition for the controls to be optimal. The Runge–Kutta method is then used to solve the proposed optimal control system. The findings from the optimal control problem suggest that the infection may be eradicated by implementing some controls for a certain period of time. This research concludes that the optimal control mathematical model is an effective method in reducing the number of infectious in a community and environment.

scholarly journals KONTROL PENGOBATAN OPTIMAL PADA MODEL PENYEBARAN TUBERKULOSIS TIPE SEIT

2017 ◽  
Vol 6 (2) ◽  
pp. 137
Author(s):  
JONNER NAINGGOLAN
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Infected Individual ◽  
Control Treatment ◽  
Kutta Method ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Tuberculosis Model ◽  
Runge Kutta Method ◽  
Number Of Individuals

A tuberculosis model of SEIT type which incorporates treatment of infectives is considered. The population is divided into four compartments, that is: S are individuals in the susceptible compartment, E are individuals in the exposed compartments, I are individuals in the infected compartment, and T are individuals in the treatment compartments. For this model, controls on treatment is incorporated to reduce the actively infected individual compartments, via application of the Pontryagins Maximum Principle of optimal control theory. Numerical calculations with the approach of the Runge-Kutta method of fourth order can be seen that, the influence of the control treatment to more effectively reduce the number of individuals in the infected compartment compared with no controls. The basic reproduction ratio with control less compared with no controls.

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

Heat Transfer Model in a Rotary Drum During the Fermentation Process

2020 ◽  
Vol 77 (1) ◽  
pp. 151-160
Author(s):  
Norazaliza Mohd Jamil ◽  
Aainaa Izyan Nafsun ◽  
Abdul Rahman Mohd Kasim
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Transfer Coefficient ◽  
Fermentation Process ◽  
Transfer Model ◽  
Kutta Method ◽  
Contact Heat ◽  
Contact Heat Transfer ◽  
Runge Kutta Method ◽  
Rotary Drum

A new mathematical model describing heat transfer during the fermentation process in a rotary drum is proposed. The model includes representations of the kinetic reactions, the temperature of the solid bed, and physical structures within the rotary drum. The model is developed using five ordinary differential equations and was then solved using the Runge-Kutta method embedded in MATLAB software. A reasonable behaviour for the temperature profile to the fermentation process is achieved. The results show that the mass of the solid bed, contact heat transfer coefficient, and the wall temperature has a significant effect on the fermentation process in a rotary drum.

scholarly journals Distributed-Order Non-Local Optimal Control

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 124
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Theory ◽  
Optimality Condition ◽  
Optimal Control Theory ◽  
Sufficient Optimality Condition ◽  
Weak Version ◽  
Fractional Optimal Control ◽  
Non Local ◽  
Distributed Order

Distributed-order fractional non-local operators were introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted integral of different orders of differentiation over a certain range. The subject of distributed-order non-local derivatives is currently under strong development due to its applications in modeling some complex real world phenomena. Fractional optimal control theory deals with the optimization of a performance index functional, subject to a fractional control system. One of the most important results in classical and fractional optimal control is the Pontryagin Maximum Principle, which gives a necessary optimality condition that every solution to the optimization problem must verify. In our work, we extend the fractional optimal control theory by considering dynamical system constraints depending on distributed-order fractional derivatives. Precisely, we prove a weak version of Pontryagin’s maximum principle and a sufficient optimality condition under appropriate convexity assumptions.

scholarly journals Adaptation of the control synthesized by the ACAR method to the control based on the implementation of the maximum principle

2018 ◽  
Vol 226 ◽  
pp. 02012 ◽  
Author(s):  
Viktor P. Lapshin ◽  
Ilya A. Turkin ◽  
Alexey A. Zakalyuzhnyy ◽  
Viktor F. Khlystunov ◽  
Gennadiy A. Kuzin
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Maximum Principle ◽  
Synthesis Method ◽  
The Maximum Principle ◽  
Analytical Construction ◽  
Optimal Linear ◽  
The Moment ◽  
Moment Of Resistance ◽  
Maximum Method

A special case of synthesizing the electromechanical control system by the maximum method and using the Analytical Construction method of Aggregate Regulators (ACAR) is considered in the article. For the basis the task of synthesizing the optimal for speed electromechanical positioning system was chosen, while the moment of resistance to movement linearly depended on the output coordinate of the system, that is, on the angle of the engine rotor rotation. Synthesis of the optimal system for speed makes it possible to increase the efficiency of the entire production process in many production tasks, and the synthesis of the optimal linear control system based on the maximum principle is a fairly well-formalized problem. Here it should be noted that the procedure for synergistic synthesis of the optimal control system has no such formalization. An approach that brings together the solutions obtained by these two methods, which makes it possible to increase the efficiency of the ACAR method by adding some features of the methodology for synthesizing optimal systems by introducing nonlinearity of the “saturation” type is proposed in the article. The results obtained made it possible to formulate the following basic scientific proposition: the synthesis of a control system based on the synergetic approach makes it possible to obtain a system close to optimal (quasi-optimal, but after the modification of the synergetic synthesis method itself.) Here we also formulate the hypothesis of a connection between the time constants, using the ACAR method, with the optimal control switching time determined in the maximum method.

Optimal Design of ADAS Damped MDOF Structures

1999 ◽  
Vol 15 (2) ◽  
pp. 317-330 ◽  
Author(s):  
Yuri Ribakov ◽  
Jacob Gluck
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Numerical Analysis ◽  
Optimal Control Theory ◽  
Passive Control ◽  
Design Method ◽  
Viscous Damping ◽  
Viscous Dampers ◽  
Structural Frame ◽  
Different Levels

Incorporated at various levels of a structural frame, ADAS devices may be used to improve the response of the structure during earthquakes. A design method of a passive control system for multistory structures using optimal Adding Damping And Stiffness (ADAS) dampers is presented. Optimal Control Theory (OCT) is commonly used to obtain the levels of viscous damping at each story. The optimization leads to different levels of damping at each story. Therefore, a solution with viscous dampers is inconvenient and can be expensive. The proposed method enables the use of relatively less expensive optimal ADAS devices dissipating energy which is equivalent to that of viscous dampers. The method is examined in a numerical analysis of a seven-story shear framed structure. Significant improvement was obtained in the behavior of the ADAS damped structure compared to the uncontrolled one.

Research of Optimal Control Model with Multiple Inputs and Multiple Outputs Based on Logic Algebra

2012 ◽  
Vol 214 ◽  
pp. 775-779
Author(s):  
Yi Chun Ling
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control System ◽  
Computer Control ◽  
Control Model ◽  
Computer Control System ◽  
Control Laws ◽  
Multiple Outputs ◽  
The Mathematical Model ◽  
Controlled Object

Through the study of computer control system, article puts forward a mathematical model in the computer control system which controlled object is digital, and describes the mathematical model through logic algebra to form a set of method solving optimal index control laws which has the characters of easy to understand and easy to operate.

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

scholarly journals Optimal Control Strategies in an Alcoholism Model

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Xun-Yang Wang ◽  
Hai-Feng Huo ◽  
Qing-Kai Kong ◽  
Wei-Xuan Shi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Control Strategies ◽  
Pontryagin’S Maximum Principle ◽  
Social Phenomenon ◽  
Pontryagin's Maximum Principle ◽  
Existence And Stability ◽  
Objective Functional

This paper presents a deterministic SATQ-type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results.

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