Control, synchronization with linear quadratic regulator method and FFANN-based PRNG application on FPGA of a novel chaotic system

Abstract

In this work, LQR method is proposed for controlling and synchronizing newly developed chaotic system. The developed 4-D chaotic system has been investigated via time series, phase portraits and bifurcation diagrams. Calculation of the gain of linear control has been designed by LQR method, which is an optimal control method. For understanding active controller's impact on global asymptotic stability of synchronization and control errors, the Lyapunov function has been used. Numerical analyses have demonstrated to reveal the effectiveness of the applied active control method and the results have been discussed. Besides, the new chaotic system has been modeled utilizing FFANN architecture. As a result, the output response of FFANN converges to the real output response of 4-D new chaotic system obtained using Dormand-Prince numerical algorithm. The obtained good results make the hardware design in efficient manner. It has been performed using the network parameters from FFANN structure on FPGA in VHDL. The performed design can be used with high clock frequencies up to 166.3 MHz. In addition, PRNG has been implemented and synthesized using FFANN-based chaotic oscillator for Xilinx Virtex-6 FPGA chip. The output rate of the designed FFANN-based PRNG is 166.3 Mbps.