Enhanced FPGA realization of the fractional-order derivative and application to a variable-order chaotic system

被引：23

作者：

Tolba, Mohammed F. ^{[1
]}

Saleh, Hani ^{[1
]}

Mohammad, Baker ^{[1
]}

Al-Qutayri, Mahmoud ^{[1
]}

Elwakil, Ahmed S. ^{[2
,3
,4
]}

Radwan, Ahmed G. ^{[4
,5
]}

机构：

[1] Khalifa Univ, SoC Ctr, POB 127788, Abu Dhabi, U Arab Emirates

[2] Univ Sharjah, Dept Elect & Comp Engn, PO 27272, Sharjah, U Arab Emirates

[3] Univ Calgary, Dept Elect & Comp Engn, Calgary, AB, Canada

[4] Nile Univ, NISC Res Ctr, Cairo 12588, Egypt

[5] Cairo Univ, Dept Engn Math & Phys, Cairo, Egypt

来源：

NONLINEAR DYNAMICS | 2020年 / 99卷 / 04期

关键词：

Fractional-order systems; Chaotic oscillators; FPGA; IMPLEMENTATION; OSCILLATOR; EQUILIBRIA; POWER;

D O I：

10.1007/s11071-019-05449-w

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The efficiency of the hardware implementations of fractional-order systems heavily relies on the efficiency of realizing the fractional-order derivative operator. In this work, a generic hardware implementation of the fractional-order derivative based on the Grunwald-Letnikov's approximation is proposed and verified on a field-programmable gate array. The main advantage of this particular realization is its flexibility in applications which enable easy real-time configuration of the values of the fractional orders, step sizes, and/or other system parameters without changing the hardware architecture. Different approximation techniques are used to improve the hardware performance including piece-wise linear/quadratic methods. As an application, a variable-order chaotic oscillator is implemented and verified using fractional orders that vary in time.

引用

页码：3143 / 3154

页数：12

共 35 条

[1] Some basic cryptographic requirements for chaos-based cryptosystems [J].

Alvarez, Gonzalo ;

Li, Shujun .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2006, 16 (08) :2129-2151

[2]

Assadi I., 2015, 2nd IET International Conference on Intelligent Signal Processing 2015 (ISP)

[3] Generalized Hardware Post-processing Technique for Chaos-Based Pseudorandom Number Generators [J].

Barakat, Mohamed L. ;

Mansingka, Abhinav S. ;

Radwan, Ahmed G. ;

Salama, Khaled N. .

ETRI JOURNAL, 2013, 35 (03) :448-458

[4] Low-Power ECG-Based Processor for Predicting Ventricular Arrhythmia [J].

Bayasi, Nourhan ;

Tekeste, Temesghen ;

Saleh, Hani ;

Mohammad, Baker ;

Khandoker, Ahsan ;

Ismail, Mohammed .

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, 2016, 24 (05) :1962-1974

[5] Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrodinger equations [J].

Bhrawy, A. H. ;

Zaky, M. A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) :1100-1117

[6] Integrated technology fractional order proportional-integral-derivative design [J].

Caponetto, Riccardo ;

Dongola, Giovanni ;

Maione, Guido ;

Pisano, A. .

JOURNAL OF VIBRATION AND CONTROL, 2014, 20 (07) :1066-1075

[7] FPGA-based implementation of different families of fractional-order chaotic oscillators applying Grunwald-Letnikov method [J].

Dalia Pano-Azucena, Ana ;

Ovilla-Martinez, Brisbane ;

Tlelo-Cuautle, Esteban ;

Manuel Munoz-Pacheco, Jesus ;

Gerardo de la Fraga, Luis .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 72 :516-527

[8] Computation of fractional order derivative and integral via power series expansion and signal modelling [J].

Ferdi, Youcef .

NONLINEAR DYNAMICS, 2006, 46 (1-2) :1-15

[9] Dynamics and control of initialized fractional-order systems [J].

Hartley, TT ;

Lorenzo, CF .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :201-233

[10]

Howard R.M., 2002, Principles of Random Signal Analysis and Low Noise Design, DOI [10.1002/0471439207.ch4, DOI 10.1002/0471439207.CH4]

← 1 2 3 4 →