State Synchronization for Dual Digital Twin of EV Batteries by Lyapunov Stability Condition and Contraction Analysis

State synchronization is crucial in matching digital twins to physical objects dynamically in order to have trustworthy modeling and reliable prediction. This work proposes two approaches to ensure state synchronization on the introduced Dual Digital Twin (DDT). DDT is deployed on both the cloud and the edge ends for better realtime monitoring and control of EVs' batteries, especially when Internet communication is limited. In this paper, the state synchronization problem is cast as a stability problem and also a contraction problem to understand systems' evolution over time. The proposed approaches leverage the Lyapunov stability condition and contraction theory to enforce the synchronization between the twin models and real battery states with streaming data. The contraction analysis framework does not require the knowledge of initial points. The derived stability and contraction conditions that reflect the physical properties of dynamical systems can be embedded into the training process of the reduced order model (ROM) neural network. Simulation results demonstrate the effectiveness of the proposed approaches. The average ROM prediction error is 1.16% and has a 30.39% accuracy improvement with the proposed algorithm.