Disturbance Observer-based Adaptive Synchronization of Heterogeneous Chaotic Systems with Uncertainties via DNA Strand Displacement

The application of DNA strand displacement (DSD) for synchronizing chaotic systems has made remarkable progress in recent years. However, uncertainty may exist in the systems, and interference is unavoidable during the synchronization process. This article endeavors to tackle the issue of performance degradation in synchronization caused by disturbances and system uncertainties. Primarily, in order to introduce perturbations in chaotic systems using DSD, the corresponding chemical reaction networks (CRNs) is derived from the ordinary differential equations of the perturbation signal in this paper, leading to the establishment of a composite function that combines trigonometric and exponential functions. Furthermore, combining the design of nonlinear observers with adaptive control methods not only simplifies the derivation process but also allows for the construction of observers using fewer DSD reactions. Through the collaborative efforts of the adaptive law and the observer, it enables the estimation of perturbations and system uncertainties, thereby achieving the synchronization of heterogeneous chaotic systems. Finally, the proposed method successfully synchronizes the Lorenz system and Yang system, even in the presence of system uncertainties and disturbances, demonstrating its effectiveness.