Identification of fractional-order systems with both nonzero initial conditions and unknown time delays based on block pulse functions

2022 ◽  
Vol 169 ◽  
pp. 108646
Author(s):  
Myong-Hyok Sin ◽  
Cholmin Sin ◽  
Song Ji ◽  
Su-Yon Kim ◽  
Yun-Hui Kang
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Initial Conditions ◽  
Fractional Order Systems ◽  
Block Pulse Functions ◽  
Unknown Time Delays

Identification of fractional-order systems with time delays using block pulse functions

2017 ◽  
Vol 91 ◽  
pp. 382-394 ◽  
Author(s):  
Yinggan Tang ◽  
Ning Li ◽  
Minmin Liu ◽  
Yao Lu ◽  
Weiwei Wang
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Fractional Order Systems ◽  
Block Pulse Functions

scholarly journals Fractional Dynamics of Computer Virus Propagation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Carla M. A. Pinto ◽  
J. A. Tenreiro Machado
Keyword(s):  
Steady State ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Initial Conditions ◽  
Computer Virus ◽  
Fractional Dynamics ◽  
Fractional Order Systems ◽  
Virus Propagation ◽  
Integer Order ◽  
Fast Transients

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Parameter Identification of Fractional Order Systems Using a Collocation Method Based on Hybrid Functions

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Y. Lu ◽  
J. Zhang ◽  
Y. G. Tang
Keyword(s):  
Integral Operator ◽  
Collocation Method ◽  
Fractional Order ◽  
Analytical Form ◽  
Fractional Order Systems ◽  
Actual System ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
The Laplace Transform ◽  
Fractional Order Integral

Abstract In this paper, we propose a novel collocation method based on hybrid functions to identify the parameters and differential orders of fractional order systems (FOS). The hybrid functions consist of block-pulse functions and Taylor polynomials. The analytical form of Riemann–Liouville fractional order integral operator of these hybrid functions is derived using the Laplace transform. Then the integral operator is utilized, in conjunction with collocation points, to convert the FOS into an algebraic system directly. The parameters and differential orders of the FOS are estimated by minimizing the error between the output of the actual system and that of the estimated system. The effectiveness of the proposed method is verified through four examples.

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