scholarly journals Enlarged Controllability of Riemann–Liouville Fractional Differential Equations

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Touria Karite ◽  
Ali Boutoulout ◽  
Delfim F. M. Torres
Keyword(s):  
Minimum Energy ◽  
Fractional Diffusion ◽  
Liouville Type ◽  
Energy Control ◽  
Penalization Method ◽  
Diffusion Systems ◽  
Minimum Energy Control ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method ◽  
Fractional Differential

We investigate exact enlarged controllability (EEC) for time fractional diffusion systems of Riemann–Liouville type. The Hilbert uniqueness method (HUM) is used to prove EEC for both cases of zone and pointwise actuators. A penalization method is given and the minimum energy control is characterized.

scholarly journals Subdiffusive Source Sensing by a Regional Detection Method

Sensors ◽  
2019 ◽  
Vol 19 (16) ◽  
pp. 3504
Author(s):  
Weijing Song ◽  
Fudong Ge ◽  
YangQuan Chen
Keyword(s):  
Detection Method ◽  
Fractional Diffusion ◽  
Energy Resources ◽  
Source Detection ◽  
Diffusion Systems ◽  
Pollution Problem ◽  
Detection Approach ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method ◽  
Source Of Pollution

Motivated by the fact that the danger may increase if the source of pollution problem remains unknown, in this paper, we study the source sensing problem for subdiffusion processes governed by time fractional diffusion systems based on a limited number of sensor measurements. For this, we first give some preliminary notions such as source, detection and regional spy sensors, etc. Secondly, we investigate the characterizations of regional strategic sensors and regional spy sensors. A regional detection approach on how to solve the source sensing problem of the considered system is then presented by using the Hilbert uniqueness method (HUM). This is to identify the unknown source only in a subregion of the whole domain, which is easier to be implemented and could save a lot of energy resources. Numerical examples are finally included to test our results.

On the regional controllability of the sub-diffusion process with Caputo fractional derivative

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Fudong Ge ◽  
YangQuan Chen ◽  
Chunhai Kou ◽  
Igor Podlubny
Keyword(s):  
Fractional Derivative ◽  
Diffusion Process ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Minimum Energy ◽  
Energy Control ◽  
Diffusion Systems ◽  
Minimum Energy Control ◽  
The Laplace Transform ◽  
Regional Controllability

AbstractThis paper is devoted to the investigation of regional controllability of the fractional order sub-diffusion process. We first derive the equivalent integral equations of the abstract sub-diffusion systems with Caputo and Riemann-Liouville fractional derivatives by utilizing the Laplace transform. The new definitions of regional controllability of the system studied are introduced by extending the existence contributions. Then we analyze the regional controllability of the fractional order sub-diffusion system with minimum energy control in two different cases:

Approximate minimum energy control

AIAA Journal ◽  
1970 ◽  
Vol 8 (12) ◽  
pp. 2242-2244 ◽  
Author(s):  
R. O. ROGERS ◽  
D. D. SWORDER
Keyword(s):  
Minimum Energy ◽  
Energy Control ◽  
Minimum Energy Control

scholarly journals Minimum energy control of fractional positive electrical circuits

2016 ◽  
Vol 65 (2) ◽  
pp. 191-201 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Electrical Circuit ◽  
Existence Of Solution ◽  
Energy Control ◽  
Electrical Circuits ◽  
Minimum Energy Control

Abstract Minimum energy control problem for the fractional positive electrical circuits is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by an example of fractional positive electrical circuit.

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