Fixed-time cross-combination synchronization of complex chaotic systems with unknown parameters and perturbations

Abstract

In the field of secure communication, chaotic synchronization plays a vital role, while fixed-time synchronization has realistic application prospects and needs. For the synchronization problem of complex chaotic systems containing unknown parameters and perturbations in the complex domain, a fixed-time cross-combination synchronization method based on a novel adaptive sliding mode control is proposed. The scheme takes three complex chaotic driving systems and one complex chaotic response system containing unknown parameters and perturbations as the research objects, and firstly, the synchronization controller and parameter updating law are designed based on the adaptive rate and fixed-time stability theory to realize the synchronization of the system and the identification of the unknown parameters, and the feasibility of the scheme is verified by the detailed Lyapunov stability theory analysis. Subsequently, four classical complex chaotic systems with universality are selected for model analysis and synchronization scheme design, and numerical simulations are carried out. The feasibility and superiority of the scheme are verified by comparison experiments with the conventional finite-time synchronization scheme and robustness experiments. In this study, adaptive sliding mode control is combined with fixed-time combinatorial synchronization of complex-domain chaotic systems, and a cross-combination strategy is introduced to enhance the safety and anti-interference ability of the system. This not only theoretically expands the application of control theory to the combinatorial synchronization problem of complex systems, but also significantly enhances the stability and reliability of the system under uncertainty and disturbance environments.