An experimental set-up design for synchronization and control of coupled Hindmarsh–Rose neurons with Markov-jump dynamics: A case study on finite-time sliding-mode synchronization

This paper introduces a real-time experimental set-up design to realize the robust synchronization of chaotic systems with Markov-Jump behavior, where the control law is designed based on a finite-time sliding-mode controller. First, master and slave chaotic systems are designed with the dynamics of biological Hindmarsh–Rose (HR) neurons using electronic circuit elements. In order to create the Markov-Jump behavior, the printed circuit board is adjusted to add or remove the resistors so that it is possible to obtain the time-varying dynamic of a chaotic system in the synchronization process. In the realization of chaotic neurons, Matlab and Multisim environments are used for the simulations, and Proteus software is utilized for the design of PCB layout. The Arduino microcontroller is used for signal processing and closed-loop control, where the states of chaotic neurons are recorded and control signals are produced and applied to the slave chaotic system to be synchronized. The real-time data corresponding to the behavior of the circuits was recorded, and Lyapunov exponents were calculated to check whether the neuron circuits are chaotic or not. Second, a sliding-mode controller (SMC) was designed to guarantee a finite-time convergence of synchronization error where its parameters are optimized using a recently developed efficient optimization method, namely the adolescent-identity search algorithm. Robust finite-time synchronization results with sliding-mode control were recorded in simulation and real-time experiments. Finally, the difficulties encountered in general and unachievable results related to experimental system design and finite-time synchronization are discussed for future studies.