scholarly journals Geometric Methods for Efficient Planar Swimming of Copepod Nauplii

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 706
Author(s):  
Corey Shanbrom ◽  
Jonas Balisacan ◽  
George Wilkens ◽  
Monique Chyba
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Theory ◽  
Mechanical Energy ◽  
Two Dimensional ◽  
Ecological Functions ◽  
Singular Configurations ◽  
Abnormal Extremals ◽  
Geometric Methods ◽  
Copepod Nauplius

Copepod nauplii are larval crustaceans with important ecological functions. Due to their small size, they experience an environment of low Reynolds number within their aquatic habitat. Here we provide a mathematical model of a swimming copepod nauplius with two legs moving in a plane. This model allows for both rotation and two-dimensional displacement by the periodic deformation of the swimmer’s body. The system is studied from the framework of optimal control theory, with a simple cost function designed to approximate the mechanical energy expended by the copepod. We find that this model is sufficiently realistic to recreate behavior similar to those of observed copepod nauplii, yet much of the mathematical analysis is tractable. In particular, we show that the system is controllable, but there exist singular configurations where the degree of non-holonomy is non-generic. We also partially characterize the abnormal extremals and provide explicit examples of families of abnormal curves. Finally, we numerically simulate normal extremals and observe some interesting and surprising phenomena.

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.

Controlling Asthma Due to Air Pollution

2020 ◽  
pp. 1-22
Author(s):  
Ankush H. Suthar ◽  
Purvi M. Pandya
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Air Pollution ◽  
Control Theory ◽  
Global Stability ◽  
Optimal Control Theory ◽  
Positive Impact ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Number Of Individuals

The health of our respiratory systems is directly affected by the atmosphere. Nowadays, eruption of respiratory disease and malfunctioning of lung due to the presence of harmful particles in the air is one of the most sever challenge. In this chapter, association between air pollution-related respiratory diseases, namely dyspnea, cough, and asthma, is analysed by constructing a mathematical model. Local and global stability of the equilibrium points is proved. Optimal control theory is applied in the model to optimize stability of the model. Applied optimal control theory contains four control variables, among which first control helps to reduce number of individuals who are exposed to air pollutants and the remaining three controls help to reduce the spread and exacerbation of asthma. The positive impact of controls on the model and intensity of asthma under the influence of dyspnea and cough is observed graphically by simulating the model.

scholarly journals Optimal Control Applications in the Study of Production Management

2020 ◽  
Vol 15 (2) ◽  
Author(s):  
Liviu Popescu ◽  
Nicolae Daniel Militaru ◽  
Ovidiu Mircea Mituca
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Production Management ◽  
Economic Problem ◽  
Lie Algebroid ◽  
Numerical Application ◽  
Control Applications ◽  
Geometric Methods ◽  
New Space ◽  
The Pontryagin Maximum Principle

A mathematical model for an economic problem of production management is proposed. The continuous optimal control problem is solved, by using the Pontryagin Maximum Principle at the level of a new space, called Lie algebroid. The controllability of the economic system is studied by using Lie geometric methods and involves restrictions on the final stock quantities. Finally, a numerical application is given.

Design and simulation of a control for the opening and closing of the side ventilation windows in a greenhouse

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 100
Author(s):  
E. M. Gutierrez Arias ◽  
J. E. Flores Mena ◽  
G. Perez Osorio ◽  
M. M. Morin Castillo ◽  
G. Pantle Cuatle ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Mathematical Model ◽  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Carbon Dioxide Concentration ◽  
Windward Side ◽  
Control Input ◽  
Model Control ◽  
Opening And Closing

An optimal control for the opening and closing of the side ventilation windows of a greenhouse can be obtained from a mathematical model of the crop and the greenhouse. In the greenhouse model, control input is the ventilation, and to carry out the instrumentation in the immediate future, this term we related with the aperture of the lee and windward side ventilation windows. We consider a model with four states variables: the structural biomass of leaves, the structural biomass of fruit, the nonstructural biomass (nutrients) and the carbon dioxide. Even though the control of carbon dioxide concentration inside the greenhouse is not directly addressed in this study, optimal control of the opening and closing of vents significantly complements the regulation of the carbon dioxide concentration. To apply the optimal control theory, we select a functional cost in order to increase the benefit of the farmer.

scholarly journals An Optimal Control for a Two-Dimensional Spatiotemporal SEIR Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Khalid Adnaoui ◽  
Adil El Alami Laaroussi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Control Theory ◽  
Epidemic Model ◽  
Optimal Control Theory ◽  
State Function ◽  
Two Dimensional ◽  
The Cost

In this paper, we present an application of optimal control theory on a two-dimensional spatial-temporal SEIR (susceptible, exposed, infected, and restored) epidemic model, in the form of a partial differential equation. Our goal is to minimize the number of susceptible and infected individuals and to maximize recovered individuals by reducing the cost of vaccination. In addition, the existence of the optimal control and solution of the state system is proven. The characterization of the control is given in terms of state function and adjoint. Numerical results are provided to illustrate the effectiveness of our adopted approach.

scholarly journals Optimized Planning of Different Crops in a Field Using Optimal Control in Portugal

2018 ◽  
Vol 10 (12) ◽  
pp. 4648
Author(s):  
Rui Pereira ◽  
Sofia Lopes ◽  
Amélia Caldeira ◽  
Victor Fonte
Keyword(s):  
Climate Change ◽  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Theory ◽  
Decision Makers ◽  
Agricultural Field ◽  
Water Requirements ◽  
Best Management ◽  
The World ◽  
Near Future

Climate change is a proven fact. In the report of 2007 from IPCC, one can read that global warming is an issue to be dealt with urgently. In many parts of the world, the estimated rise of temperature (in a very near future) is significant. One of the most affected regions is the Iberian Peninsula, where the increasing need for water will very soon be a problem. Therefore, it is necessary that decision makers are able to decide on all issues related to water management. In this paper, we show a couple of mathematical models that can aid the decision making in the management of an agricultural field at a given location. Having a field, in which different crops can be produced, the solution of the first model indicates the area that should be used for each crop so that the profit is as large as possible, while the water spent is the smallest possible guaranteeing the water requirements of each crop. Using known data for these crops in Portugal, including costs of labour, machines, energy and water, as well as the estimated value of the products obtained, the first mathematical model developed, via optimal control theory, obtains the best management solution. It allows creating different scenarios, thus it can be a valuable tool to help the farmer/decision maker decide the crop and its area to be cultivated. A second mathematical model was developed. It improves the first one, in the sense that it allows considering that water from the rainfall can be collected in a reservoir with a given capacity. The contribution of the collected water from the rainfall in the profit obtained for some different scenarios is also shown.

scholarly journals Modelling Optimal Control of Cholera in Communities Linked by Migration

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
J. B. H. Njagarah ◽  
F. Nyabadza
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Temporal Relationship ◽  
Latin Hypercube Sampling ◽  
Living Conditions ◽  
Model Parameters ◽  
Reproduction Numbers

A mathematical model for the dynamics of cholera transmission with permissible controls between two connected communities is developed and analysed. The dynamics of the disease in the adjacent communities are assumed to be similar, with the main differences only reflected in the transmission and disease related parameters. This assumption is based on the fact that adjacent communities often have different living conditions and movement is inclined toward the community with better living conditions. Community specific reproduction numbers are given assuming movement of those susceptible, infected, and recovered, between communities. We carry out sensitivity analysis of the model parameters using the Latin Hypercube Sampling scheme to ascertain the degree of effect the parameters and controls have on progression of the infection. Using principles from optimal control theory, a temporal relationship between the distribution of controls and severity of the infection is ascertained. Our results indicate that implementation of controls such as proper hygiene, sanitation, and vaccination across both affected communities is likely to annihilate the infection within half the time it would take through self-limitation. In addition, although an infection may still break out in the presence of controls, it may be up to 8 times less devastating when compared with the case when no controls are in place.

scholarly journals OPTIMAL CONTROL OF A TWO-DIMENSIONAL RICHARDS-KLUTE EQUATION

2019 ◽  
pp. 39-48
Author(s):  
Andrii Tymoshenko
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
External Pressure ◽  
Point Sources ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Initial State ◽  
Source Power ◽  
The Mathematical Model

This article demonstrates an approach to optimal control of humidity using point sources for the two-dimensional problem. The mathematical model is based on Richards-Klute equation. The desired humidity state at the last moment is set and the solution should reach it from the known initial state by optimal source power. The moisture is assumed incompressible, the temperature and external pressure are constant.

Maximizing Distance of the Golf Drive: An Optimal Control Study

1975 ◽  
Vol 97 (4) ◽  
pp. 362-367 ◽  
Author(s):  
M. A. Lampsa
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Variational Formulation ◽  
Necessary Conditions ◽  
Model Parameter ◽  
Steepest Ascent ◽  
Parameter Values ◽  
Control Study

Optimal control theory is used to search for the optimal control torques necessary to maximize distance of the golf drive. In the method, a mathematical model of a generalized golf swing is first developed. Film of the author’s swing serves to verify the model and to supply parameter values, constraints, and actual torques. The variational formulation of optimal control theory is utilized to establish necessary conditions for optimal control, in which constraint violations are discouraged by inclusion of penalty functions. Finally, the method of steepest ascent is used to compute optimal control torques. Also, comparison of optimal and actual torques is made, and the sensitivity of the results to small changes in model parameter values is investigated.

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