Fractional-Order Control Scheme for Q-S Chaos Synchronization

2019 ◽  
pp. 434-441 ◽  
Author(s):  
Adel Ouannas ◽  
Giuseppe Grassi ◽  
Ahmad Taher Azar
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Fractional Order Control ◽  
Control Scheme

scholarly journals Results for Chaos Synchronization with New Multi-Fractional Order of Neural Networks by Multi-Time Delay

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Fatin Nabila Abd Latiff ◽  
Wan Ainun Mior Othman
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Direct Method ◽  
Extensive Literature ◽  
Control Scheme ◽  
New Finding

A new finding is proposed for multi-fractional order of neural networks by multi-time delay (MFNNMD) to obtain stable chaotic synchronization. Moreover, our new result proved that chaos synchronization of two MFNNMDs could occur with fixed parameters and initial conditions with the proposed control scheme called sliding mode control (SMC) based on the time-delay chaotic systems. In comparison, the fractional-order Lyapunov direct method (FLDM) is proposed and is implemented to SMC to maintain the systems’ sturdiness and assure the global convergence of the error dynamics. An extensive literature survey has been conducted, and we found that many researchers focus only on fractional order of neural networks (FNNs) without delay in different systems. Furthermore, the proposed method has been tested with different multi-fractional orders and time-delay values to find the most stable MFNNMD. Finally, numerical simulations are presented by taking two MFNNMDs as an example to confirm the effectiveness of our control scheme.

scholarly journals On the Q–S Chaos Synchronization of Fractional-Order Discrete-Time Systems: General Method and Examples

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Adel Ouannas ◽  
Amina-Aicha Khennaoui ◽  
Giuseppe Grassi ◽  
Samir Bendoukha
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Control Strategies ◽  
Linearization Method ◽  
Discrete Time Systems ◽  
Control Scheme ◽  
The Stability ◽  
Time Systems ◽  
General Method

In this paper, we propose two control strategies for the Q–S synchronization of fractional-order discrete-time chaotic systems. Assuming that the dimension of the response system m is higher than that of the drive system n, the first control scheme achieves n-dimensional synchronization whereas the second deals with the m-dimensional case. The stability of the proposed schemes is established by means of the linearization method. Numerical results are presented to confirm the findings of the study.

scholarly journals Fractional-Order Control of a Micrometric Linear Axis

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Luca Bruzzone ◽  
Pietro Fanghella
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Tracking Error ◽  
Transient State ◽  
Step Response ◽  
Controlled System ◽  
Fractional Order Control ◽  
Control Scheme ◽  
Derivative Term ◽  
Pole Location

This paper discusses the application of a particular fractional-order control scheme, the PDD1/2, to the position control of a micrometric linear axis. The PDD1/2scheme derives from the classical PD scheme with the introduction of the half-derivative term. The PD and PDD1/2schemes are compared by adopting a nondimensional approach for the sake of generality. The linear model of the closed-loop system is discussed by analysing the pole location in theσ-plane. Then, different combinations of the derivative and half-derivative terms, characterized by the same settling energy in the step response, are experimentally compared in the real mechatronic application, with nonnegligible friction effects and a position set point with trapezoidal speed law. The experimental results are coherent with the nonlinear model of the controlled system and confirm that the introduction of the half-derivative term is an interesting option for reducing the tracking error in the transient state.

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