Applying the Optimal Control Methodology to the Mathematical Model of Sales Volume Distribution in a Company

Through the study of computer control system, article puts forward a mathematical model in the computer control system which controlled object is digital, and describes the mathematical model through logic algebra to form a set of method solving optimal index control laws which has the characters of easy to understand and easy to operate.

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Using the Mathematical Model on Precision Marketing with Online Transaction Data Computing

Mathematical Problems in Engineering ◽

10.1155/2021/5539300 ◽

2021 ◽

Vol 2021 ◽

pp. 1-7

Author(s):

Jun Wu ◽

Li Shi ◽

Guangshu Xu ◽

Yu-Hsi Yuan ◽

Sang-Bing Tsai ◽

...

Keyword(s):

Mathematical Model ◽

Performance Comparison ◽

Marketing Strategies ◽

Transaction Data ◽

Recommendation Algorithms ◽

Decision Making System ◽

Data Source ◽

The Mathematical Model ◽

A Company ◽

Real World Problems

In this paper, a decision-making system for precision marketing is presented to deal with real-world problems based on real e-business data collected in a company in Beijing. During the data preprocessing, the authors conducted a cleaning course to make sure the data to be analyzed in the latter part of the paper were credential. Based on the processed data, the authors analyzed consumer purchasing behaviors using three classic recommendation algorithms and made a performance comparison of the three algorithms. At the end of this paper, the authors proposed a series of precision marketing strategies which had been adopted by the data source company and had been proved to be effective in improving the performance.

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Analisis Kontrol Optimal Pada Model Matematika Penyebaran Pengguna Narkoba Dengan Faktor Edukasi

JURNAL ILMIAH MATEMATIKA DAN TERAPAN ◽

10.22487/2540766x.2020.v17.i2.15201 ◽

2020 ◽

Vol 17 (2) ◽

pp. 238-248

Author(s):

Resmawan ◽

M Eka ◽

Nurwan ◽

N Achmad

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Optimal Control ◽

Drug Users ◽

Minimum Principle ◽

Runge Kutta Method ◽

Runge Kutta ◽

Model Drug ◽

And Control ◽

The Mathematical Model

ABSTRACT This paper discusses the mathematical model of drug users with education. Optimal control theory was used on this model with education as a control to achieve the goal of minimizing the number of drug users. The optimal control problem was analyzed using Pontryagin’s minimum principle and performed numerical simulation by using a 4th-order Runge-Kutta method. Based on the numerical simulation, there was a change in the number in each population which caused the population with education to increase, and control with education resulted in the reduced number of drug users. Keywords: Optimal control; mathematical model; drug users; education ABSTRAK Artikel ini membahas tentang model matematika penyebaran pengguna narkoba dengan faktor edukasi. Teori kontrol optimal diterapkan pada model ini dengan pemberian kontrol berupa edukasi dengan tujuan untuk meminimumkan jumlah pengguna narkoba. Kontrol optimal dianalisis menggunakan Prinsip Minimum Pontryagin dan dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde 4. Berdasarkan simulasi diperoleh bahwa terjadi perubahan jumlah di tiap populasi dan mengakibatkan jumlah populasi dengan edukasi bertambah, serta pemberian kontrol dengan edukasi mengakibatkan jumlah pengguna narkoba berkurang. Kata kunci : Kontrol optimal; model matematika; pengguna narkoba; edukasi

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A STRATEGY OF OPTIMAL EFFICACY OF T11 TARGET STRUCTURE IN THE TREATMENT OF BRAIN TUMOR

Journal of Biological System ◽

10.1142/s0218339019500104 ◽

2019 ◽

Vol 27 (02) ◽

pp. 225-255 ◽

Cited By ~ 8

Author(s):

SUBHAS KHAJANCHI ◽

SANDIP BANERJEE

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Transforming Growth Factor ◽

Treatment Strategies ◽

Target Structure ◽

Optimal Control Strategy ◽

Immunosuppressive Cytokine ◽

Quadratic Optimal Control ◽

The Mathematical Model

We report a mathematical model depicting gliomas and immune system interactions by considering the role of immunotherapeutic drug T11 target structure (T11TS). The mathematical model comprises a system of coupled nonlinear ordinary differential equations involving glioma cells, macrophages, activated cytotoxic T-lymphocytes (CTLs), immunosuppressive cytokine transforming growth factor-[Formula: see text] (TGF-[Formula: see text]), immunostimulatory cytokine interferon-[Formula: see text] (IFN-[Formula: see text]) and the concentrations of immunotherapeutic agent T11TS. For the better understanding of the circumstances under which the gliomas can be eradicated from a patient, we use optimal control strategy. We design the objective functional by considering the biomedical goal, which minimizes the glioma burden and maximizes the macrophages and activated CTLs. The existence and the characterization for the optimal control are established. The uniqueness of the quadratic optimal control problem is also analyzed. We demonstrate numerically that the optimal treatment strategies using T11TS reduce the glioma burden and increase the cell count of activated CTLs and macrophages.

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Symmetric Control Systems

Herald of the Bauman Moscow State Technical University Series Instrument Engineering ◽

10.18698/0236-3933-2021-2-37-51 ◽

2021 ◽

pp. 37-51

Author(s):

A.I. Diveev ◽

E.A. Sofronova

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Control Systems ◽

Control Object ◽

Terminal State ◽

Initial State ◽

Phase Constraints ◽

The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

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Fundamentals of Synthesized Optimal Control

Mathematics ◽

10.3390/math9010021 ◽

2020 ◽

Vol 9 (1) ◽

pp. 21

Author(s):

Askhat Diveev ◽

Elizaveta Shmalko ◽

Vladimir Serebrenny ◽

Peter Zentay

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Control Method ◽

Direct Method ◽

Equilibrium Points ◽

Control Object ◽

Optimal Control Method ◽

Optimal Value ◽

New Formulation ◽

The Mathematical Model

This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal value of the quality functional, while the uncertainty has a limited impact on the change in the value of the functional. The article introduces the concept of feasibility of the mathematical model of the object, which is associated with the contraction property of mappings if we consider the model of the object as a one-parameter mapping. It is shown that this property is sufficient for the development of stable practical systems. To find a solution to the stated problem, which would ensure the feasibility of the system, the synthesized optimal control method is proposed. This article formulates the theoretical foundations of the synthesized optimal control. The method consists in making the control object stable relative to some point in the state space and to control the object by changing the position of the equilibrium points. The article provides evidence that this approach is insensitive to the uncertainties of the mathematical model of the object. An example of the application of the method for optimal control of a group of robots is given. A comparison of the synthesized optimal control method with the direct method on the model without disturbances and with them is presented.

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Optimal Control in the Mathematical Model of Internal Waves

Journal of Computational and Engineering Mathematics ◽

10.14529/jcem200105 ◽

2020 ◽

Vol 7 (1) ◽

pp. 62-71

Author(s):

K.Yu. Kotlovanov ◽

◽

E.V. Bychkov ◽

A.V. Bogomolov ◽

◽

...

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Internal Waves ◽

The Mathematical Model

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Optimal Control of the Rotor System Motion

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.705.546 ◽

2013 ◽

Vol 705 ◽

pp. 546-552

Author(s):

Imankul Toleukhan

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Electric Drive ◽

Rotor System ◽

Flexible Shaft ◽

Experimental Works ◽

Set Up ◽

Automatic Balancing ◽

The Mathematical Model

Among the problems of the rotor machines dynamics the special attention is given to the problems of creation of the automatic balancing devices (ABD) in form of a hollow rotor, filled by a liquid, and the liquid-solidbody ABD. The theoretical and experimental works on research of the ABD on the base of a hollow rotor filled partially with a liquid and of the liquid-solidbody ABD are not enough. Therefore development of the methods of research of dynamics of the rotor machines with the ABD and such machines designs is an actual, new and perspective problem. In the present work the mathematical model of the rotor system with the ABD taking into account of the engine characteristics is offered. Lets consider the model of the rotor with electric drive with one disk, set up at the flexible shaft without skew. The shaft is lean on two bearings (fig. 1).

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Optimal Control for Wheeled Inverted Pendulum Based on Collaborative Simulation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.556-562.2444 ◽

2014 ◽

Vol 556-562 ◽

pp. 2444-2447

Author(s):

Xiang Shi ◽

Zhe Xu ◽

Ka Tian ◽

Qing Yi He

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Nonlinear System ◽

Inverted Pendulum ◽

Virtual Prototype ◽

Prototype Model ◽

Control Law ◽

Collaborative Simulation ◽

Wheeled Inverted Pendulum ◽

The Mathematical Model

To control wheeled inverted pendulum is a good way to test all kinds of theories of control. The optimal control based on MATLAB is used to control wheeled inverted pendulum, and the control law is designed, and its feasibility is verified. However the mathematical model of the wheeled inverted pendulum is linearized and inverted pendulum is a high-order nonlinear system, both of them exist errors. Then the collaborative simulation of MATLAB and ADAMS is also used to control wheeled inverted pendulum, in which wheeled inverted pendulum is built up to virtual prototype model in ADAMS based on virtual prototype technology, and the control law designed from simulation of MATLAB is consulted. At last the results of simulation demonstrate the correctness of optimal control of wheeled inverted pendulum, and it also indicates the way is worth advocating in the study.

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