Fractional-Order sliding mode control of a 4D memristive chaotic system

Abstract

Chaotic systems depict complex dynamics, thanks to their nonlinear behaviors. With recent studies on fractional-order nonlinear systems, it is deduced that fractional-order analysis of a chaotic system enriches its dynamic behavior. Therefore, the investigation of the chaotic behavior of a 4D memristive Chen system is aimed in this study by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Based on these analyses, two different fractional orders (i.e., q = 0.948 and q = 0.97) are determined where the 4D memristive system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the fractional-order memristive chaotic system on the equilibrium points. Then, control method results are obtained by both numerical simulations and different illustrative experiments of microcontroller-based realization. As expected, voltage outputs of the microcontroller-based realization are in good agreement with the time series of numerical simulations.

Circuit Realization of the Fractional-Order Sprott K Chaotic System with Standard Components

“…In recent years, several researchers have investigated the digital and analog applications of fractional-order chaotic systems [7][8][9][10][11][12][13][14][15][16][17][18][19]. Altun [20] investigated and realized both fractional-order numerical calculations and field-programmable analog array (FPAA) hardware implementations of Rössler and Sprott H systems.…”