Comparisons between the three-phase current injection method and the forward/backward sweep method

2010 ◽  
Vol 32 (7) ◽  
pp. 825-833 ◽  
Author(s):  
Leandro Ramos de Araujo ◽  
Débora Rosana Ribeiro Penido ◽  
Sandoval Carneiro Júnior ◽  
José Luiz Rezende Pereira ◽  
Paulo Augusto Nepomuceno Garcia
Keyword(s):  
Current Injection ◽  
Sweep Method ◽  
Injection Method ◽  
Phase Current ◽  
Three Phase ◽  
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 Discrete optimal capital investment and financing policies in fishery resource harvesting with reserve area

2019 ◽  
Author(s):  
Farida Hanum ◽  
Toni Bakhtiar ◽  
Muhamad Nagib Alatas
Keyword(s):  
Capital Investment ◽  
Renewable Resource ◽  
State Variables ◽  
Sweep Method ◽  
Fishery Resource ◽  
Dividend Payout ◽  
Financing Policies ◽  
Investment And Financing ◽  
Optimal Capital ◽  
Forward Backward Sweep Method

This research discusses a problem in renewable resource (fish) harvesting on single-owner fishery where the dynamics of growth are expressed by system of difference equations. The model involves three state variables (stock of equity, resource stock in reserve zone and unreserved zone) and two control variables (effort rate and dividend payout rate). Discrete Pontryagin maximum principle was applied to obtain optimality conditions which must be satisfied by the variables. Further, the forward-backward sweep method was used to determine the numerical solution of optimal control model. Three scenarios of interest rate applied to find out the response of company in managing harvesting effort and dividend payout rate were investigated.

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.

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