scholarly journals Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse

2021 ◽  
Vol 17 (3) ◽  
pp. 339-348
Author(s):  
Nita Anggriani ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Drug Abuse ◽  
Mathematical Models ◽  
Minimum Principle ◽  
Self Psychology ◽  
Sweep Method ◽  
Pontryagin Minimum Principle ◽  
Counseling Needs ◽  
Forward Backward Sweep Method

This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.

scholarly journals Optimal Control of a Mathematical Model of Smoking with Temporary Quitters and Permanent Quitters

2021 ◽  
Vol 18 (1) ◽  
pp. 42-54
Author(s):  
Andi Utari Samsir ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Numerical Simulations ◽  
Minimum Principle ◽  
Sweep Method ◽  
Pontryagin Minimum Principle ◽  
Education Campaigns ◽  
Research Period ◽  
Forward Backward Sweep Method

Abstract This article discusses the optimal control of a mathematical model on smoking. This model consists of six population classes, namely potential to become smoker  snuffing class  irregular smokers regular smokers  temporary quitters  and permanent quitters  The completion of this research uses the Pontryagin minimum principle and numerically using the forward-backward Sweep method. Numerical simulations of the optimal problem show that with the implementation of education campaigns and anti-nicotine medicine, the smokers can be decreased more quickly and the smoking population who quit permanently can be increased. The implementation of both through large amounts needs to be done from the beginning. The use of control in the form of education campaigns is of great value until the end of the research period means that it needs to be done continuously to reduce the number of smokers in the population.  

scholarly journals Application and benchmarking of a direct method to optimize the fuel consumption of a diesel electric locomotive

2018 ◽  
Vol 232 (9) ◽  
pp. 2272-2289 ◽  
Author(s):  
V Macian ◽  
C Guardiola ◽  
B Pla ◽  
A Reig
Keyword(s):  
Optimal Control ◽  
Direct Method ◽  
Minimum Principle ◽  
Optimization Technique ◽  
Direct Methods ◽  
Optimization Methods ◽  
Computational Time ◽  
Electric Locomotive ◽  
Pontryagin Minimum Principle ◽  
A Direct Method

This paper addresses the optimal control of a long-haul passenger train to deliver minimum-fuel operations. Contrary to the common Pontryagin minimum principle approach in railroad-related literature, this work addresses this optimal control problem with a direct method of optimization, the use of which is still marginal in this field. The implementation of a particular direct method based on the Euler collocation scheme and its transcription into a nonlinear problem are described in detail. In this paper, this optimization technique is benchmarked with well-known optimization methods in the literature, namely dynamic programming and the Pontryagin minimum principle, by simulating a real route. The results showed that the direct methods are on the same level of optimality compared with other algorithms while requiring reduced computational time and memory and being able to handle very complex dynamic systems. The performance of the direct method is also compared to the real trajectory followed by the train operator and exhibits up to 20% of fuel saving in the example route.

scholarly journals Implementation and acceleration of optimal control for systems biology

2021 ◽  
Vol 18 (181) ◽  
pp. 20210241
Author(s):  
Jesse A. Sharp ◽  
Kevin Burrage ◽  
Matthew J. Simpson
Keyword(s):  
Optimal Control ◽  
Systems Biology ◽  
Iteration Process ◽  
System Size ◽  
Sweep Method ◽  
Acceleration Techniques ◽  
Fixed Point Iteration Process ◽  
Allocation Decisions ◽  
Insight Into ◽  
Forward Backward Sweep Method

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021 .

scholarly journals Optimal Control of an HIV Model with Gene Therapy and Latency Reversing Agents

2021 ◽  
Vol 26 (4) ◽  
pp. 77
Author(s):  
Zachary Abernathy ◽  
Kristen Abernathy ◽  
Andrew Grant ◽  
Paul Hazelton
Keyword(s):  
Gene Therapy ◽  
Optimal Control ◽  
Combination Treatment ◽  
Latent Reservoir ◽  
Sweep Method ◽  
Hiv Model ◽  
Future Work ◽  
Disease Free ◽  
Forward Backward Sweep Method ◽  
Reversing Agents

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of R0. We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work.

scholarly journals Analisis Kontrol Optimal Pada Model Matematika Penyebaran Pengguna Narkoba Dengan Faktor Edukasi

2020 ◽  
Vol 17 (2) ◽  
pp. 238-248
Author(s):  
Resmawan ◽  
M Eka ◽  
Nurwan ◽  
N Achmad
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Optimal Control ◽  
Drug Users ◽  
Minimum Principle ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Model Drug ◽  
And Control ◽  
The Mathematical Model

ABSTRACT This paper discusses the mathematical model of drug users with education. Optimal control theory was used on this model with education as a control to achieve the goal of minimizing the number of drug users. The optimal control problem was analyzed using Pontryagin’s minimum principle and performed numerical simulation by using a 4th-order Runge-Kutta method. Based on the numerical simulation, there was a change in the number in each population which caused the population with education to increase, and control with education resulted in the reduced number of drug users. Keywords: Optimal control; mathematical model; drug users; education   ABSTRAK Artikel ini membahas tentang model matematika penyebaran pengguna narkoba dengan faktor edukasi. Teori kontrol optimal diterapkan pada model ini dengan pemberian kontrol berupa edukasi dengan tujuan untuk meminimumkan jumlah pengguna narkoba. Kontrol optimal dianalisis menggunakan Prinsip Minimum Pontryagin dan dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde 4. Berdasarkan simulasi diperoleh bahwa terjadi perubahan jumlah di tiap populasi dan mengakibatkan jumlah populasi dengan edukasi bertambah, serta pemberian kontrol dengan edukasi mengakibatkan jumlah pengguna narkoba berkurang. Kata kunci       : Kontrol optimal; model matematika; pengguna narkoba; edukasi

scholarly journals Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

2021 ◽  
Author(s):  
Etienne Bertin ◽  
Elliot Brendel ◽  
Bruno Hérissé ◽  
Julien Alexandre dit Sandretto ◽  
Alexandre Chapoutot
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Minimum Principle ◽  
Open Loop ◽  
Pontryagin Minimum Principle ◽  
Interval Method ◽  
Bounded Uncertainties ◽  
The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

scholarly journals Application of Optimal Control to Influenza Pneumonia Coinfection with Antiviral Resistance

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Caroline W. Kanyiri ◽  
Livingstone Luboobi ◽  
Mark Kimathi
Keyword(s):  
Optimal Control ◽  
Optimal Strategies ◽  
Antiviral Resistance ◽  
System Control ◽  
High Morbidity ◽  
Prevention Measures ◽  
Sweep Method ◽  
Influenza Pneumonia ◽  
Major Impediment ◽  
Forward Backward Sweep Method

Influenza and pneumonia independently lead to high morbidity and mortality annually among the human population globally; however, a glaring fact is that influenza pneumonia coinfection is more vicious and it is a threat to public health. Emergence of antiviral resistance is a major impediment in the control of the coinfection. In this paper, a deterministic mathematical model illustrating the transmission dynamics of influenza pneumonia coinfection is formulated having incorporated antiviral resistance. Optimal control theory is then applied to investigate optimal strategies for controlling the coinfection using prevalence reduction and treatment as the system control variables. Pontryagin’s maximum principle is used to characterize the optimal control. The derived optimality system is solved numerically using the Runge–Kutta-based forward-backward sweep method. Simulation results reveal that implementation of prevention measures is sufficient to eradicate influenza pneumonia coinfection from a given population. The prevention measures could be social distancing, vaccination, curbing mutation and reassortment, and curbing interspecies movement of the influenza virus.

An Optimal Control Problem of Knowledge Dissemination

2020 ◽  
pp. 461-482
Author(s):  
Pantry Elastic ◽  
Toni Bakhtiar ◽  
Jaharuddin
Keyword(s):  
Optimal Control ◽  
Information Dissemination ◽  
Control Strategies ◽  
Minimum Principle ◽  
Control Model ◽  
Technical Training ◽  
Knowledge Dissemination ◽  
Transfer System ◽  
Pontryagin Minimum Principle

In this chapter, the authors develop an optimal control model of knowledge dissemination among people in the society. The knowledge transfer system is formulated in term of compartmental model, where the society members are categorized into four classes based on knowledge acquisition and their willingness to disseminate. The model is equipped with a set of control variables for process intervening, namely technical training for ignorant-immigrants, information dissemination through social media for solitariants and enthusiants, and technical training for solitariants. Optimality conditions in terms of differential equations system was derived by using Pontryagin minimum principle leading to the characterization of optimal control strategies that minimizing the number of solitariants, enthusiants, and ignorants simultaneously with the control efforts. The sweep method and the fourth order Runge-Kutta algorithm was implemented to numerically solve the equation systems. The effectiveness of the control strategies toward a set of control scenarios was evaluated through examples.

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