Computation-Aided Data Transmission for Remote Reconstruction of Trajectories of Dynamical Systems

Abstract

Remote reconstruction of trajectories of dynamical systems is now emerging as a mission-critical application in Industry 4.0 and beyond. Unfortunately, the statistical properties of signals generated by dynamical systems usually remain unknown, which prohibits the use of classic source coding methods relying on a statistical source model. To overcome this difficulty, we present a paradigm shift data transmission scheme, assuring that the reconstruction error is limited with the aid of the computation unit. It is found that the bit rate for transmitting trajectories has a significant relationship with the predictability of dynamical systems. Together with the concept of the Lyapunov exponent, an error growth function is introduced in this paper to classify the dynamical systems according to their predictability. A general expression of the bit rate is obtained in this paper. Furthermore, it is shown that the asymptotic value of the bit rate to reconstruct trajectories of a chaotic system is given by its Lyapunov exponent. The bit rate to reconstruct trajectories of non-chaotic systems is also presented. Simulation results show that our scheme outperforms conventional information-theory-based coding schemes, and can significantly reduce bandwidth requirements.