Summary
We extend the current theory for spectral submanifolds (SSMs) to ones covering slowly varying dynamical systems. Restricting the dynamics onto these SSMs provides one with a mathematically rigorous model reduction technique. We also observe a justified approximation of adiabtic SSMs can be obtained from data. We demonstrate these capabilities for controlling a high- dimensional nonlinear finite element model describing a soft trunk robot. We formulate a novel model predictive control scheme using adiabatic SSMs constructed from data. We find our method outperforms the state-of-the-art techniques for trajectory tracking control tasks.
