Optimal control problem for linear fractional-order systems

2014 ◽  
Author(s):  
Victor Kubyshkin ◽  
Sergey Postnov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Fractional Order Systems

Finite-Time Controllability of Fractional-Order Systems

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Jay L. Adams ◽  
Tom T. Hartley
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Finite Time ◽  
Special Consideration ◽  
Fractional Order Systems ◽  
System Output ◽  
Fractional Order Integrator ◽  
Integrator Output

In this paper, the conditions that lead to a system output remaining at zero with zero input are considered. It is shown that the initialization of fractional-order integrators plays a key role in determining whether the integrator output will remain at a zero with zero input. Three examples are given that demonstrate the importance of initialization for integrators of order less than unity, inclusive. Two examples give a concrete illustration of the role that initialization plays in keeping the output of a fractional-order integrator at zero once it has been driven to zero. The implications of these results are considered, with special consideration given to the formulation of the fractional-order optimal control problem.

Finite-Time Controllability of Fractional-Order Systems

2007 ◽  
Author(s):  
Jay L. Adams ◽  
Tom T. Hartley
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Finite Time ◽  
Special Consideration ◽  
Fractional Order Systems ◽  
System Output ◽  
Fractional Order Integrator ◽  
Integrator Output

In this paper the conditions that lead to a system output remaining at zero with zero input are considered. It is shown that the initialization of fractional-order integrators plays a key role in determining whether the integrator output will remain at a zero with zero input. Three examples are given that demonstrate the importance of initialization for integrators of order less than unity, inclusive. Two examples give a concrete illustration of the role that initialization plays in keeping the output of a fractional-order integrator at zero once it has been driven to zero. The implications of these results are considered, with special consideration given to the formulation of the fractional-order optimal control problem.

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.

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