FPGA implementation and control of chaotic systems involving the variable-order fractional operator with Mittag–Leffler law

Abstract

This paper presents the simulation and control implementation on a Field Programmable Gate Array (FPGA) for a class of variable-order fractional chaotic systems by using sliding mode control strategy. Four different fractional variable-order chaotic systems via Atangana–Baleanu–Caputo fractional-order derivative were considered; Dadras, Aizawa, Thomas and 4 Wings attractors. A methodology has been developed to construct variable-order fractional chaotic systems using LabVIEW® software for its implementation in the National Instruments myRio-1900 (Xilinx FPGA Z-7010)® device. The variable-order fractional differential equations and the control law were solved using the variable-order Adams algorithm. Finally, simulation results show that FPGA provides high-speed realizations with the desired accuracy and demonstrate the effectiveness of the proposed sliding mode control.