Finite-Time Integral Backstepping Nonsingular Terminal Sliding Mode Control to Synchronize a New Six-Term Chaotic System and Its Circuit Implementation

This work presents the finite-time synchronization of a new six-term chaotic system with only stable equilibria and its circuitry implementation. The chaotic system is designed in such a way that its complex dynamical behavior, including hidden attractors, can be adjusted through only one parameter, whilst allowing transformation to chaotic flows via invariant transformations. A finite-time chaotic synchronizer is designed via a nonsingular terminal integral backstepping sliding mode controller, with reduced theoretical finite-time convergence, and a modified sliding surface, to accommodate analog circuitry implementations. A comparison between the proposed controller against conventional integral backstepping sliding mode controller showed that active synchronization is achieved in finite time. Finally, analog circuitry implementation for both open-loop and closed-loop configurations is realized via commercially available active components such as LF357 and AD633. The descriptive circuitry equations for both configurations are designed to mimic the actual governing control equations for simplicity and ease of circuit troubleshooting. The workability of both configurations was tested in OrCAD PSpice. Results show that the master and slave systems were found to be in synchronization with less than 0.95% maximum errors.

Automated summary

This work presents a method for finite-time synchronization of a new six-term chaotic system with only stable equilibria and its circuitry implementation. The chaotic system allows adjustment of its complex dynamical behavior and transformation to chaotic flows through a single parameter. A finite-time chaotic synchronizer is designed using a nonsingular terminal integral backstepping sliding mode controller, with reduced theoretical finite-time convergence and a modified sliding surface for analog circuitry implementations. Comparison with conventional integral backstepping sliding mode controller showed successful active synchronization in finite time. Analog circuitry implementation for both open-loop and closed-loop configurations is achieved using commercially available active components. The master and slave systems were found to be in synchronization with less than 0.95% maximum errors.