Research PaperNo Access

Analysis, Control and FPGA Implementation of a Fractional-Order Modified Shinriki Circuit

Karthikeyan Rajagopal

Centre for Non-Linear Dynamics, Defence University, Bishoftu, Oramia Regional State, Ethiopia

Institute of Energy, Mekelle University, Mekelle, Tigray Regional State, Ethiopia

E-mail Address: rkarthiekeyan@gmail.com

Corresponding author.

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Fahimeh Nazarimehr

Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran

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Laarem Guessas

Department of Electronics, Faculty of Technology, Ferhat Abbes University, Setif, Algeria

Intelligent Systems Laboratory, Faculty of Technology, Ferhat Abbes University, Setif, Algeria

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Anitha Karthikeyan

Centre for Non-Linear Dynamics, Defence University, Bishoftu, Oramia Regional State, Ethiopia

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Ashokkumar Srinivasan

Centre for Non-Linear Dynamics, Defence University, Bishoftu, Oramia Regional State, Ethiopia

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, and

Sajad Jafari

Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

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https://doi.org/10.1142/S0218126619502323Cited by:12 (Source: Crossref)

Abstract

In this paper, we introduce a novel integer-order memristor-modified Shinriki circuit (MMSC). We investigate the dynamic properties of the MMSC system and the existence of chaos is proved with positive largest Lyapunov exponent. Bifurcation plots are derived to analyze the parameter dependence of the MMSC system. The fractional-order model of the MMSC system (FOMMSC) is derived and the bifurcation analysis of the FOMMSC system with the fractional orders is carried out. Fractional-order adaptive sliding-mode controllers (FOASMCs) and genetically optimized PID controllers are designed to synchronize identical FOMMSC systems with unknown parameters. Numerical simulations are conducted to validate the theoretical results. FPGA implementation of the FOASMC controllers is presented to show that the proposed control algorithm is hardware realizable. MMSC has trigonometric functions which make the system more complex and the optimization and synchronization of such systems in the integer order itself are harder, so the paper does the same in fractional order. The proposed system is a memristive circuit which can show special features such as multistability, hyperchaos, and multiscroll attractor. Such a system with these features is very rare in the literature.

This paper was recommended by Regional Editor Emre Salman.

Keywords:

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