Identification of fractional-order systems via a switching differential evolution subject to noise perturbations

2012 ◽  
Vol 376 (45) ◽  
pp. 3113-3120 ◽  
Author(s):  
Wu Zhu ◽  
Jian-an Fang ◽  
Yang Tang ◽  
Wenbing Zhang ◽  
Yulong Xu
Keyword(s):  
Differential Evolution ◽  
Fractional Order ◽  
Fractional Order Systems

Fractional Active Disturbance Rejection Controller Based on Improved Differential Evolution Algorithm

2021 ◽  
Author(s):  
Henghui Liang ◽  
Wei Yu ◽  
Rui Chen ◽  
Ying Luo
Keyword(s):  
Differential Evolution ◽  
Fractional Order ◽  
Disturbance Rejection ◽  
Differential Evolution Algorithm ◽  
Order Information ◽  
Fractional Order Systems ◽  
Control Performance ◽  
Active Disturbance Rejection ◽  
Evolution Algorithm ◽  
Improved Differential Evolution Algorithm

Abstract Although the active disturbance rejection controller can obtain good control performance without relying on specific model information, it targets integer-order systems. Fractional-order characteristics are commonly existed in practical systems. For fractional-order systems, it is more targeted to use the order information of the fractional-order model to design the active disturbance rejection controller, so as to obtain better control performance. A fractional active disturbance rejection controller composed of FOESO and FOPID (IDE-FOPID-FOESO) is proposed in this paper. The fractional-order extended state observer (FOESO) is designed based on the order information and the nonlinear state error feedback is replaced by the fractional-order PID controller (FOPID) whose parameters are obtained by the improved differential evolution algorithm (IDE). For IDE algorithm, the basis vector is randomly selected from the optimal individual population in the mutation strategy, and the scaling factor and cross-probability factor are adaptively adjusted according to the information of the successfully mutated individual in the search process to improve the exploration and mining capabilities of the algorithm. The simulation results show that the IDE algorithm can obtain the better parameters of FOPID faster compared with traditional DE algorithm and the IDE-FOPID-FOESO controller can be better applied to fractional-order systems with better control performance.

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

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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