Parameter identification of fractional order systems with nonzero initial conditions based on block pulse functions

Measurement ◽  
2020 ◽  
Vol 158 ◽  
pp. 107684 ◽  
Author(s):  
Yao Lu ◽  
Yinggan Tang ◽  
Xuguang Zhang ◽  
Shuen Wang
Keyword(s):  
Parameter Identification ◽  
Fractional Order ◽  
Initial Conditions ◽  
Fractional Order Systems ◽  
Block Pulse Functions

Parameter identification of fractional order systems using block pulse functions

2015 ◽  
Vol 107 ◽  
pp. 272-281 ◽  
Author(s):  
Yinggan Tang ◽  
Haifang Liu ◽  
Weiwei Wang ◽  
Qiusheng Lian ◽  
Xinping Guan
Keyword(s):  
Parameter Identification ◽  
Fractional Order ◽  
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.

Parameter identification of nonlinear fractional-order systems by enhanced response sensitivity approach

2018 ◽  
Vol 95 (2) ◽  
pp. 1495-1512 ◽  
Author(s):  
Zhong-Rong Lu ◽  
Guang Liu ◽  
Jike Liu ◽  
Yan-Mao Chen ◽  
Li Wang
Keyword(s):  
Parameter Identification ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Response Sensitivity ◽  
Sensitivity Approach

ON STABILITY OF COMMENSURATE FRACTIONAL ORDER SYSTEMS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250084 ◽  
Author(s):  
JOCELYN SABATIER ◽  
CHRISTOPHE FARGES
Keyword(s):  
Fractional Order ◽  
Original Work ◽  
Closed Loop ◽  
Initial Conditions ◽  
Stability Theorem ◽  
Fractional Order Systems ◽  
Fractional Differentiation ◽  
Starting Point ◽  
Definition Of

This paper proposes a new proof of the Matignon's stability theorem. This theorem is the starting point of numerous results in the field of fractional order systems. However, in the original work, its proof is limited to a fractional order ν such that 0 < ν < 1. Moreover, it relies on Caputo's definition for fractional differentiation and the study of system trajectories for non-null initial conditions which is now questionable in regard of recent works. The new proof proposed here is based on a closed loop realization and the application of the Nyquist theorem. It does not rely on a peculiar definition of fractional differentiation and is valid for orders ν such that 1 < ν < 2.

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