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.

Optimization

Speech Timing ◽  
2020 ◽  
pp. 190-237
Author(s):  
Alice Turk ◽  
Stefanie Shattuck-Hufnagel
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Hierarchical Control ◽  
Component Model ◽  
Multiple Factors ◽  
Key Features ◽  
Cost Of Time ◽  
The Cost ◽  
Parameter Values

This chapter introduces a theoretical framework, Optimal Control Theory, which will enable a phonology-extrinsic-timing-based, three-component model to determine values of controlled variables, and to model the influence of multiple factors on these parameter values. Key features of Optimal Control Theory models are discussed, as well as evidence for types of movement costs (including the cost of time) used in the models, and predictions of the models for the coordination of multiple effectors and hierarchical control. Finally, the chapter reviews Optimal Control Theory models currently used to account for timing phenomena in speech.

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.

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 The Derivation of Structural Properties of LM-g Splines by Necessary Condition of Optimal Control

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Xiongwei Liu ◽  
Xinjian Zhang ◽  
Lizhi Cheng
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Structural Properties ◽  
Optimal Control Theory ◽  
State Constraints ◽  
Necessary Conditions ◽  
Necessary Condition ◽  
Interpolating Splines ◽  
The Relationship ◽  
Optimization And Optimal Control

The structural properties of LM-g splines are investigated by optimization and optimal control theory. The continuity and structure of LM-g splines are derived by using a class of necessary conditions with state constraints of optimal control and the relationship between LM-g interpolating splines and the corresponding L-g interpolating splines. This work provides a new method for further exploration of LM-g interpolating splines and its applications in the optimal control.

Optimal Control Theory

2018 ◽  
Author(s):  
John E. Prussing
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Necessary Conditions ◽  
Minimum Principle ◽  
Minimum Cost ◽  
Initial Time ◽  
Pontryagin Minimum Principle ◽  
Final Time ◽  
Terminal Constraints

Optimal Control Theory is reviewed in detail. We consider a dynamic system that operates between a specified initial time and a final time which may be specified or unspecified. Necessary conditions for a minimum cost functional are derived. Terminal constraints are considered. Pontryagin Minimum Principle is discussed.

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 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.

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