Adaptive sliding mode control for synchronizing chaotic systems under external disturbances and uncertainties: circuit implementation and analysis

This article introduces the synchronization of a specific category of hyperchaotic systems characterized by unknown variables such as uncertainty and disturbance. It achieves synchronization using an adaptive sliding mode controller, while notably utilizing a reduced number of control signals compared to the system's dimension. An early step in the first part of this investigation comprises the development of a sliding mode control scheme. This approach involves two control signals with the primary goal of synchronizing two Lorenz-Stenflo (LS) hyperchaotic systems. These systems are distinguished by well-defined parameters and the systems are sensitive to disturbance inputs as well as uncertainties. Further, in the pursuit of synchronizing two LS hyperchaotic systems marked by unknown parameters and influenced by disturbance inputs and uncertainties, two control signals come into play. Notably, in this context, the determination of these elusive parameters is facilitated through the employment of an adaptive rule, thereby enhancing the synchronization process. The effectiveness of the anticipated control mechanism is assessed by employing the Lyapunov stability approach, with a focus on determining its stability level. Synchronization and stability have been shown by numerical simulations. Analog circuit designs of the LS hyperchaotic system, along with the synchronization of the proposed pair using known system parameters through the Sliding Mode Control (SMC) approach, are implemented using NI Multisim software. The results from the NI Multisim circuit realization validate the outcomes of the matlab simulations.