Experimental verification of the multi-scroll chaotic attractors synchronization in PWL arbitrary-order systems using direct coupling and passivity-based control

Abstract

Because one of the main applications of chaos synchronization is oriented to data encryption and random number generators, fractional-order chaotic systems showing multi-scroll attractors have pointed out as feasible solutions to improve the performance of secure communications schemes. Nowadays, recent works have reported the analysis and control of fractional-order synchronization schemes for multi-scroll chaotic systems. However, the synchronization schemes from those works present mostly theoretical numerical simulations and give circuit simulations employing a simulator software rather than physical implementations. That way, our first contribution is to describe herein the experimental realization of a synchronization scheme for a fractional-order multi-scroll chaotic oscillator with a 4-scroll attractor and fractional-order q=0.9. First, we implemented the multi-scroll systems using an opamp-based analog circuit and an RC-based fractance device to emulate a fractional-order integrator. As a second contribution, we analytically demonstrate the complete synchronization between two identical multi-scroll systems employing two fractional-order controllers and the fractional-order derivative in the Caputo sense. By utilizing the Laplace transform theory, we analyze the one-way coupling method where the response (slave) system’s behavior depends on an identical drive (master) system. As a third contribution, we propose a passivity-based synchronization controller. This synchronization strategy consists of designing a virtual state feedback input and then based on the fractional-order Lyapunov theory, a control law obtains by designing an appropriate storage function to stabilize the system around its stable zero equilibrium. The experimental measures of the implemented synchronization scheme present suitable results compared to analytical and numerical findings.