Synchronization of a Seven-Term Chaotic 4D System Using a Simplified Fixed-Time Adaptive Integral Nonsingular Terminal Sliding Mode Control and Its Circuit Realization

This work presents an adaptive gain fixed-time synchronization of a seven-term hyperchaotic 4D system, along with its analog circuitry realizations. To facilitate a simplistic circuit realization of the closed loop system, the control design process initiates with the design of a novel, simplified fixed-time stability lemma that gives a lower convergence time, while being easier to compute. A nonlinear, fixed-time adaptive-gain nonsingular terminal sliding mode controller was then designed to synchronize the hyperchaotic 4D system. Theoretical analyses indicated that fixed-time synchronization was successfully achieved, and computer simulations verified that the zero-error convergence across all states was reached within 1 second, irrespective of the initial conditions, even in the presence of significant changes in the parameters as well as the disturbances. Analog circuitry implementations of the adaptive gain fixed-time chaotic synchronization configuration were realized using commercially available components, for instance, LF357 and AD633. The circuit equations were formulated to imitate those employed in the controller, aiming for simplicity in troubleshooting. Electronics workability was tested using OrCAD PSPICE. The results showed that active synchronization was achieved in fixed time with less than 1% error across the states in the presence of disturbances. Finally, the developed fixed-time chaotic synchronization was applied to a secure communication system. Results show that the original and recovered messages are nearly identical to one another after a fixed time of 0.5 seconds.