Learned Lifted Linearization Applied to Unstable Dynamic Systems Enabled by Koopman Direct Encoding

This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It known DMD other standard data-driven methods face fundamental difficulty in constructing model when applied systems. Here we solve the problem by incorporating knowledge about state equation with learning for finding an effective set of observables. In lifted space, regions are separated into independent subspaces. Based on this property, propose find observables through neural net training where data trajectories. The resultant learned used linear transition matrix using as Direct Encoding, which transforms inner product computations proposed shows dramatic improvement over existing methods.