scholarly journals Modeling student engagement using optimal control theory

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Debra Lewis
Keyword(s):  
Optimal Control ◽  
Student Engagement ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Learning Task ◽  
Cognitive Effort ◽  
Cognitive Resources ◽  
State Variable ◽  
Body Of Knowledge ◽  
And Control

<p style='text-indent:20px;'>Student engagement in learning a prescribed body of knowledge can be modeled using optimal control theory, with a scalar state variable representing mastery, or self-perceived mastery, of the material and control representing the instantaneous cognitive effort devoted to the learning task. The relevant costs include emotional and external penalties for incomplete mastery, reduced availability of cognitive resources for other activities, and psychological stresses related to engagement with the learning task. Application of Pontryagin's maximum principle to some simple models of engagement yields solutions of the synthesis problem mimicking familiar behaviors including avoidance, procrastination, and increasing commitment in response to increasing mastery.</p>

scholarly journals Application of optimal control theory on optimal advertising expenditure in monopoly

2020 ◽  
Vol 83 ◽  
pp. 01017
Author(s):  
Nora Grisáková ◽  
Peter Štetka
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Market Share ◽  
Optimal Control Theory ◽  
Control Variable ◽  
New Product ◽  
Advertising Expenditure ◽  
Advertising Rate ◽  
State Variable ◽  
Economic Application

Presented paper is being focused on Optimal control theory, Variation Calculus and its economic application. Aim of this research paper is to shortly describe Optimal control and Variation Calculus and to present how can we deal with these type of issues. The last part of this paper is presenting possible economic application of Optimal control, based on the maximization of profit in monopoly while introducing new product on the market. Our control variable is the advertising rate, which affects the profit of monopoly through advertising expenditures and as a state variable was the market share defined.

scholarly journals Applying optimal control theory to complex epidemiological models to inform real-world disease management

2019 ◽  
Vol 374 (1776) ◽  
pp. 20180284 ◽  
Author(s):  
E. H. Bussell ◽  
C. E. Dangerfield ◽  
C. A. Gilligan ◽  
N. J. Cunniffe
Keyword(s):  
Infectious Disease ◽  
Optimal Control ◽  
Disease Management ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Management Strategies ◽  
Disease Outbreaks ◽  
Theme Issue ◽  
Infectious Disease Outbreaks ◽  
And Control

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach—optimal control theory—allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.

Dispersion of nanoparticles with optimal control theory based on destabilization

2014 ◽  
Vol 2 ◽  
pp. 86-86
Author(s):  
Miki U. Kobayashi ◽  
Nobuaki Aoki ◽  
Noriyoshi Manabe ◽  
Tadafumi Adschiri
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Dispersion Of Nanoparticles

scholarly journals Recoil control of deepwater drilling riser system based on optimal control theory

2020 ◽  
pp. 108473
Author(s):  
Xiuquan Liu ◽  
Zhaowei Liu ◽  
Xianglei Wang ◽  
Nan Zhang ◽  
Na Qiu ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Deepwater Drilling

scholarly journals Optimal Control for a COVID-19 Model Accounting for Symptomatic and Asymptomatic

2020 ◽  
Vol 8 (1) ◽  
pp. 168-179
Author(s):  
Jead M. Macalisang ◽  
Mark L. Caay ◽  
Jayrold P. Arcede ◽  
Randy L. Caga-anan
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Medical Care ◽  
Optimal Control Theory ◽  
Comparable Result ◽  
Type Model ◽  
Hospital Beds ◽  
Transmission Reduction ◽  
Bed Capacity ◽  
The Government

AbstractBuilding on an SEIR-type model of COVID-19 where the infecteds are further divided into symptomatic and asymptomatic, a system incorporating the various possible interventions is formulated. Interventions, also referred to as controls, include transmission reduction (e.g., lockdown, social distancing, barrier gestures); testing/isolation on the exposed, symptomatic and asymptomatic compartments; and medical controls such as enhancing patients’ medical care and increasing bed capacity. By considering the government’s capacity, the best strategies for implementing the controls were obtained using optimal control theory. Results show that, if all the controls are to be used, the more able the government is, the more it should implement transmission reduction, testing, and enhancing patients’ medical care without increasing hospital beds. However, if the government finds it very difficult to implement the controls for economic reasons, the best approach is to increase the hospital beds. Moreover, among the testing/isolation controls, testing/isolation in the exposed compartment is the least needed when there is significant transmission reduction control. Surprisingly, when there is no transmission reduction control, testing/isolation in the exposed should be optimal. Testing/isolation in the exposed could seemingly replace the transmission reduction control to yield a comparable result to that when the transmission reduction control is being implemented.

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