Optimal Control Model of Two Dimensional Missile Using Forward Backward Sweep Method (FBSM)

2021 ◽  
Author(s):  
Teguh Herlambang ◽  
Dinita Rahmalia ◽  
Denis Fidita Karya ◽  
Fajar Annas Susanto ◽  
Firman Yudianto ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control Model ◽  
Two Dimensional ◽  
Sweep Method ◽  
Forward Backward Sweep Method

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 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.

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 On Characterization of Optimal Control Model of Whooping Cough

2021 ◽  
pp. 175-188
Author(s):  
A. S. Ismail ◽  
Y. O. Aderinto
Keyword(s):  
Optimal Control ◽  
Whooping Cough ◽  
Equilibrium Points ◽  
Public Health Problem ◽  
Sweep Method ◽  
Optimal Control Strategy ◽  
Runge Kutta Method ◽  
Disease Free ◽  
Forward Backward Sweep Method

Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.

scholarly journals A Multiregion Discrete-Time Epidemic Model of Mycobacterium tuberculosis Infections: An Optimal Control Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Rachid Bouajaji ◽  
Hassan Laarabi ◽  
Mostafa Rachik ◽  
Abdelhadi Abta
Keyword(s):  
Optimal Control ◽  
Epidemic Model ◽  
Discrete Systems ◽  
Sweep Method ◽  
Treatment Control ◽  
Control Approach ◽  
Multipoint Boundary Value Problems ◽  
Optimal Control Approach ◽  
Forward Backward Sweep Method ◽  
Temporal Spread

The main goal of this article is to devise the spatial-temporal spread of TB, in multiple neighboring domains, taking into account the epidemiological diversity of their populations. However, since both the environment and any population are spatially heterogeneous, it is obviously desirable to include spatial structure into an epidemic model. Individuals with tuberculosis can spread the disease by moving from one area to another. In addition, people travel by air between cities, so diseases can be spread quickly between very distant places (as was the case with the COVID-19). In our model, each region’s studied population is divided into five compartments S, L1, I, L2, and R. Further, we introduce in our discrete systems three control variables which represent the effectiveness rates of vaccination, travel-blocking operation, and treatment. We focus in our study to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Firstly, we analyze the epidemic model when the control strategy is based on the vaccination control only, and secondly, when the travel-blocking control is added, we finish with the introduction of the treatment control. The optimal control theory, based on Pontryagin’s maximum principle, is applied thrice in this paper, for the characterizations of the vaccination, travel-blocking, and treatment controls. The numerical results associated with the multipoint boundary value problems are obtained based on the forward-backward sweep method combined with progressive-regressive Runge–Kutta fourth-order schemes.

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 Implementation and acceleration of optimal control for systems biology

2021 ◽  
Author(s):  
Jesse A Sharp ◽  
Kevin Burrage ◽  
Matthew J Simpson
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Iteration Process ◽  
Sweep Method ◽  
Acceleration Techniques ◽  
Fixed Point Iteration Process ◽  
Allocation Decisions ◽  
Insight Into ◽  
Forward Backward Sweep Method ◽  
Resource Allocation Decisions

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 (TPBVPs) arising from the application of Pontryagin's Maximum Principle (PMP) in optimal control. In this review we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualising 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. Further, 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.

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