Optimal construction of Koopman eigenfunctions for prediction and control

Understand

This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control.

• The method leverages the richness of the spectrum of the Koopman operator away from attractors to construct a rich set of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion.
• The eigenfunction construction is optimization-based with no dictionary selection required.
• Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multi-step prediction error minimization, carried out by a simple linear least-squares regression.