scholarly journals Optimal Control for a Mathematical Model of Nerve Impulse Spreading

2015 ◽  
Vol 8 (4) ◽  
pp. 120-126 ◽  
Author(s):  
N.A. Manakova ◽  
◽  
O.V. Gavrilova ◽  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Nerve Impulse

Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach

2021 ◽  
Vol 145 ◽  
pp. 110789
Author(s):  
Parthasakha Das ◽  
Samhita Das ◽  
Pritha Das ◽  
Fathalla A. Rihan ◽  
Muhammet Uzuntarla ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Combinatorial Therapy ◽  
Model Based ◽  
Cancer Remission

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Identification of Neural Network Model of Robot to Solve the Optimal Control Problem

2021 ◽  
Vol 20 (6) ◽  
pp. 1254-1278
Author(s):  
Elizaveta Shmalko ◽  
Yuri Rumyantsev ◽  
Ruslan Baynazarov ◽  
Konstantin Yamshanov
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Mathematical Model ◽  
Optimal Control ◽  
Neural Network Model ◽  
Software Package ◽  
Control Object ◽  
Robotic Systems ◽  
Object Model ◽  
Modern Machine

To calculate the optimal control, a satisfactory mathematical model of the control object is required. Further, when implementing the calculated controls on a real object, the same model can be used in robot navigation to predict its position and correct sensor data, therefore, it is important that the model adequately reflects the dynamics of the object. Model derivation is often time-consuming and sometimes even impossible using traditional methods. In view of the increasing diversity and extremely complex nature of control objects, including the variety of modern robotic systems, the identification problem is becoming increasingly important, which allows you to build a mathematical model of the control object, having input and output data about the system. The identification of a nonlinear system is of particular interest, since most real systems have nonlinear dynamics. And if earlier the identification of the system model consisted in the selection of the optimal parameters for the selected structure, then the emergence of modern machine learning methods opens up broader prospects and allows you to automate the identification process itself. In this paper, a wheeled robot with a differential drive in the Gazebo simulation environment, which is currently the most popular software package for the development and simulation of robotic systems, is considered as a control object. The mathematical model of the robot is unknown in advance. The main problem is that the existing mathematical models do not correspond to the real dynamics of the robot in the simulator. The paper considers the solution to the problem of identifying a mathematical model of a control object using machine learning technique of the neural networks. A new mixed approach is proposed. It is based on the use of well-known simple models of the object and identification of unaccounted dynamic properties of the object using a neural network based on a training sample. To generate training data, a software package was written that automates the collection process using two ROS nodes. To train the neural network, the PyTorch framework was used and an open source software package was created. Further, the identified object model is used to calculate the optimal control. The results of the computational experiment demonstrate the adequacy and performance of the resulting model. The presented approach based on a combination of a well-known mathematical model and an additional identified neural network model allows using the advantages of the accumulated physical apparatus and increasing its efficiency and accuracy through the use of modern machine learning tools.

scholarly journals Dynamics and optimal control of chemotherapy for low grade gliomas: Insights from a mathematical model

2016 ◽  
Vol 21 (6) ◽  
pp. 1895-1915 ◽  
Author(s):  
Clara Rojas ◽  
Juan Belmonte-Beitia ◽  
Víctor M. Pérez-García ◽  
Helmut Maurer
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Low Grade ◽  
Low Grade Gliomas

Information dualism of the problem of optimum terminal control of dynamic object

2021 ◽  
pp. 85-90
Author(s):  
V.P. Ivanov
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Law ◽  
Computational Algorithms ◽  
Terminal Control ◽  
Dynamic Object ◽  
Nonlinear Mathematical Model ◽  
Dynamical Object

The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

Sign in / Sign up

Export Citation Format

Share Document