Chattering-free control of chaotic synchronization within a fixed timeframe

This study presents an economical chattering-free strategy for chaotic synchronization within a fixed timeframe. By constructing a smoothed variant of Sign function, the strategy provides a continuous controller minimizing the likelihood of inducing chattering phenomena of chaotic synchronization. In addition, the use of a distinctive exponential-function-based control term simplifies parameter set and enhances economic efficiency and practicality, making this method apart from traditional fixed-time techniques. The design of the proposed controller allows for flexibility regarding the Lipschitz condition, making it suitable for systems with bounded intrinsic functions. When compared to existing strategies, this controller offers notable benefits such as a more straightforward design, fewer parameters, improved convergence rates, and stricter convergence timing. Theoretical discussions within the study shed light on the aspects driving the controller's enhanced convergence capabilities. Extensive numerical testing on the complex systems including the Chua's Circuit System with non-Lipschitz disturbance confirms the approach's reliability, efficiency, and practicality for real-world applications.