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

Abstract

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 successfully achieved fixed-time synchronization, and computer simulations verified the achievement of zero-error convergence across all states within 1 second, irrespective of the initial conditions and even in the presence of significant parameter and disturbance changes. 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 devised to replicate those used in the controller, with the goal of facilitating troubleshooting by ensuring simplicity. Electronics workability was tested using PSPICE simulation program. The results demonstrated 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. The results indicate that the original and recovered messages exhibit a high degree of similarity to each other after a fixed duration of 1 second.

Keywords

• Chaotic synchronization
• adaptive gain fixed-time control
• terminal sliding mode control
• closed-loop circuit implementation