Tucker Product-Based Dynamical Systems

The Tucker product-based dynamical system (TPDS) representation was first introduced by Rogers et al. [Adv. Neural Inf. Process. Syst.] in 2013. The representation is a generalization of the linear dynamical system (LDS) model which can preserve the state and output of the system as tensors. TPDSs utilize multilinear operators formed by the Tucker product of matrices to govern the system evolution and can be used to capture dynamics with tensor time-series data. Techniques for TPDS model reduction and system identification have been developed. Furthermore, system-theoretic properties, including stability, reachability, and observability, have been extended to TPDSs through tensor algebra, enabling efficient computation.