Reconfigurable FPGA Realization of Fractional-Order Chaotic Systems

Abstract

This paper proposes FPGA realization of an IP core for generic fractional-order derivative based on Grünwald-Letnikov approximation. This generic design is applied to achieve reconfigurable realization of fractional-order chaotic systems. The fractional-order real-time configuration boosts the suitability of this particular realization for different applications, including dynamic switching, synchronization, and encryption. The proposed design targets optimized utilization of the FPGA internal resources and efficient employment of the external peripherals: switches and I/O ports in the FPGA board. The digital design of the fractional-order dependent terms: binomial coefficients and power function is proposed. Three approximations of the power function using curve fitting are compared, settling on the quadratic approximation that balances accuracy and efficiency. Three fractional-order chaotic systems: Liu, Li and Chen four-wing, are verified for both commensurate and incommensurate orders cases, using one approach for the commensurate order case and two approaches for the incommensurate order case. The reconfigurable design is realized on the Artix-7 FPGA board, yielding throughputs of 1.1266, 1.1266, and 1.434 Gbit/s for both commensurate and incommensurate orders cases of the three systems, respectively. Compared to recent related works, the proposed implementation demonstrates its efficient hardware utilization and suitability for potential applications.

Chaotic Oscillations in Cascoded and Darlington-Type Amplifier Having Generalized Transistors

“…Note that an ideal FO integrator can be considered a special case of FO filter. FPGA realizations of chaotic systems can also be found in recent papers, for example [42]. These implementations serve as hardware solvers for given sets of discretized differential equations and form a bridge between numerical analysis and experimental verification.…”

Control Techniques for a Class of Fractional Order Systems

“…( ( )) ≥ −√ , ∀ ∈ (−∞, +∞), where ( ) is determined by ( 13), ( 28), (36), for each class of systems. This inequality can be interpreted as the Nyquist criterion for the critical point −√ .…”

“…The previous sections discussed the control laws for several classes of models described by fractional-order equations: Fractional Order Linear Systems, Fractional Order Linear Systems with nonlinear components, Time Delay Fractional Order Linear Systems, Time Delay Fractional Order Linear Systems with nonlinear components. The control law was determined for these systems as, ( ) = − ( ) where the controller gain = 1 + ( ( )) ≥ −√ , ∀ ∈ (−∞, +∞), where ( ) is determined by ( 13), ( 28), (36), for each class of systems. This inequality can be interpreted as the Nyquist criterion for the critical point −√ .…”

“…A comprehensive review of literature related to the industrial use and integration of FOPID control is presented in [35]. FPGA implementation techniques of Fractional Order Systems is discussed in [36] and analog-hardware implementation of a FOPID for a DC motor [37] is emphasized. Memristor-based implementation with neuromorphic circuits which provide guidelines for physical realization of FOPID controllers, and a discrete implementation are presented in [38,39] respectively.…”

A Unified FPGA Realization for Fractional-Order Integrator and Differentiator

“…In [25,26], a generic GL definition with a fixed-window approach employed in a chaotic system was proposed. In [27], a generic hardware realization for the GL-based differentiator was proposed. This paper proposes a generic hardware design of a GL-based differentiator and integrator, which involves an improvement in the range of order q and a decrease in the reliance on software for the calculation of different parameters of GL.…”