Fractional Order Systems—Control Theory and Applications

2022 ◽  
Keyword(s):  
Control Theory ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Systems Control

A Brief Overview on Fractional Order Systems in Control Theory

2021 ◽  
pp. 29-47
Author(s):  
Assaad Jmal ◽  
Omar Naifar ◽  
Abdellatif Ben Makhlouf ◽  
Nabil Derbel ◽  
Mohamed Ali Hammami
Keyword(s):  
Control Theory ◽  
Fractional Order ◽  
Fractional Order Systems

scholarly journals A NEW EVOLUTIONARY METHOD TO PARAMETERS AND ORDERS IDENTIFICATION AND SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS

2021 ◽  
Vol 16 (9) ◽  
Author(s):  
Ali Soleimanizadeh
Keyword(s):  
System Identification ◽  
Control Theory ◽  
Fractional Order ◽  
Chaotic Systems ◽  
High Accuracy ◽  
Important Task ◽  
Fractional Order Systems ◽  
Integer Order ◽  
Systems Identification ◽  
Classical Control

System identification is an important task in the control theory. Classical control theory is usually known for integer-order processes. Nowadays real processes are fractional order usually. According to a large number of fractional-order systems, identification of these systems is so important. This paper aims to evaluate an improved Biogeography-based Optimization (BBO) approach to estimate the parameters and orders of fractional-order systems. After that, a method based on this algorithm has been introduced to synchronization of chaotic systems. Results show that the proposed scheme has high accuracy.

State-space analysis of linear fractional-order systems

2008 ◽  
Vol 42 (6-8) ◽  
pp. 825-838 ◽  
Author(s):  
Saïd Guermah ◽  
Saïd Djennoune ◽  
Maâmar Bettayeb
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Space Analysis ◽  
State Space Analysis

The identification of fractional order systems by multiscale multivariate analysis

2021 ◽  
Vol 144 ◽  
pp. 110735
Author(s):  
Boyi Zhang ◽  
Pengjian Shang ◽  
Qin Zhou
Keyword(s):  
Multivariate Analysis ◽  
Fractional Order ◽  
Fractional Order Systems

scholarly journals A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Variable Order ◽  
Fractional Order Systems ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

scholarly journals Realization of a fractional-order RLC circuit via constant phase element

2021 ◽  
Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano
Keyword(s):  
Experimental Data ◽  
Carbon Black ◽  
Fractional Order ◽  
Constant Phase Element ◽  
Polymeric Matrix ◽  
Fractional Order Systems ◽  
New Device ◽  
Rlc Circuit ◽  
Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

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