Existence and optimal control problem for semilinear fractional order (1,2] control system

2020 ◽  
Author(s):  
Rohit Patel ◽  
Anurag Shukla ◽  
Shimpi Singh Jadon
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order

Solving the Problem of the Optimal Control System General Synthesis Based on Approximation of a Set of Extremals using the Symbol Regression Method

2020 ◽  
pp. 59-74
Author(s):  
S.V. Konstantinov ◽  
A.I. Diveev
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Symbolic Regression ◽  
Regression Method ◽  
Synthesis Problem ◽  
Optimal Control System ◽  
Initial States

A new approach is considered to solving the problem of synthesizing an optimal control system based on the extremals' set approximation. At the first stage, the optimal control problem for various initial states out of a given domain is being numerically sold. Evolutionary algorithms are used to solve the optimal control problem numerically. At the second stage, the problem of approximating the found set of extremals by the method of symbolic regression is solved. Approach considered in the work makes it possible to eliminate the main drawback of the known approach to solving the control synthesis problem using the symbolic regression method, which consists in the fact that the genetic algorithm used in solving the synthesis problem does not provide information about proximity of the found solution to the optimal one. Here, control function is built on the basis of a set of extremals; therefore, any particular solution should be close to the optimal trajectory. Computational experiment is presented for solving the applied problem of synthesizing the four-wheel robot optimal control system in the presence of phase constraints. It is experimentally demonstrated that the synthesized control function makes it possible for any initial state from a given domain to obtain trajectories close to optimal in the quality functional. Initial states were considered during the experiment, both included in the approximating set of optimal trajectories and others from the same given domain. Approximation of the extremals set was carried out by the network operator method

Optimal Campaign Strategies in Fractional-Order Smoking Dynamics

2014 ◽  
Vol 69 (5-6) ◽  
pp. 225-231 ◽  
Author(s):  
Anwar Zeb ◽  
Gul Zaman ◽  
Il Hyo Jung ◽  
Madad Khan
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Necessary Conditions ◽  
Order Model ◽  
Campaign Strategies ◽  
Education Campaign ◽  
Fractional Order Model

This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin’s maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.

Comparative studies for the fractional optimal control in transmission dynamics of West Nile virus

2017 ◽  
Vol 10 (07) ◽  
pp. 1750095 ◽  
Author(s):  
N. H. Sweilam ◽  
O. M. Saad ◽  
D. G. Mohamed
Keyword(s):  
Optimal Control ◽  
West Nile Virus ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Comparative Studies ◽  
Control Method ◽  
Euler Method ◽  
West Nile ◽  
Iterative Optimal Control

In this paper, optimal control for a novel West Nile virus (WNV) model of fractional order derivative is presented. The proposed model is governed by a system of fractional differential equations (FDEs), where the fractional derivative is defined in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Two numerical methods are used to study the fractional-order optimal control problem. The methods are, the iterative optimal control method (OCM) and the generalized Euler method (GEM). Positivity, boundedness and convergence of the IOCM are studied. Comparative studies between the proposed methods are implemented, it is found that the IOCM is better than the GEM.

scholarly journals An Underactuated Drift-Free Left Invariant Control System on a Specific Lie Group

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Camelia Pop Arieşanu
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Point Of View ◽  
Free Left ◽  
Invariant Control

The paper presents a geometrical overview on an optimal control problem on a special Lie group. The Hamilton-Poisson realization of the dynamics offers us the possibility to study the system from mechanical geometry point of view.

Optimal Control of Fractional Order COVID-19 Epidemic Spreading in Japan and India 2020

2020 ◽  
Vol 15 (04) ◽  
pp. 207-236 ◽  
Author(s):  
Meghadri Das ◽  
G. P. Samanta
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Incomplete Information ◽  
Fractional Order ◽  
Compartmental Model ◽  
Transmission Dynamics ◽  
Epidemic Spreading ◽  
Social Distancing ◽  
First Case

In Japan, the first case of Coronavirus disease 2019 (COVID-19) was reported on 15th January 2020. In India, on 30th January 2020, the first case of COVID-19 in India was reported in Kerala and the number of reported cases has increased rapidly. The main purpose of this work is to study numerically the epidemic peak for COVID-19 disease along with transmission dynamics of COVID-19 in Japan and India 2020. Taking into account the uncertainty due to the incomplete information about the coronavirus (COVID-19), we have taken the Susceptible-Asymptomatic-Infectious-Recovered (SAIR) compartmental model under fractional order framework for our study. We have also studied the effects of fractional order along with other parameters in transfer dynamics and epidemic peak control for both the countries. An optimal control problem has been studied by controlling social distancing parameter.

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