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.

When Is a Linear Control System Optimal?

1964 ◽  
Vol 86 (1) ◽  
pp. 51-60 ◽  
Author(s):  
R. E. Kalman
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Control Variable ◽  
Point Of View ◽  
Complete Analysis ◽  
Control Law ◽  
Quadratic Loss ◽  
Mathematical Form ◽  
State Variables

The purpose of this paper is to formulate, study, and (in certain cases) resolve the Inverse Problem of Optimal Control Theory, which is the following: Given a control law, find all performance indices for which this control law is optimal. Under the assumptions of (a) linear constant plant, (b) linear constant control law, (c) measurable state variables, (d) quadratic loss functions with constant coefficients, (e) single control variable, we give a complete analysis of this problem and obtain various explicit conditions for the optimality of a given control law. An interesting feature of the analysis is the central role of frequency-domain concepts, which have been ignored in optimal control theory until very recently. The discussion is presented in rigorous mathematical form. The central conclusion is the following (Theorem 6): A stable control law is optimal if and only if the absolute value of the corresponding return difference is at least equal to one at all frequencies. This provides a beautifully simple connecting link between modern control theory and the classical point of view which regards feedback as a means of reducing component variations.

Optimal Time Control for a Magnetic Levitation Linear Servo System

2013 ◽  
Vol 416-417 ◽  
pp. 670-675
Author(s):  
Bao Quan Kou ◽  
Feng Xing ◽  
Chao Ning Zhang ◽  
Lu Zhang
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Magnetic Levitation ◽  
Control Variable ◽  
Target Function ◽  
Servo System ◽  
Optimal Time ◽  
Feed Speed ◽  
Time Control

The paper presents a new way to control the feed speed of the magnetic levitation linear servo system by adopting optimal time control theory. The optimal switch curve is obtained by building the system model and determining the control variable, control condition and target function. According to the optimal switch curve, the system can realize the optimal control of the speed. The validity of the optimal control theory in this servo system has been proven by modeling and simulating in Matlab/Simulink. The simulation result shows that the execution efficiency of the magnetic linear servo system can be improved by applying the optimal control theory.

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>

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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