Model-Based Control using Koopman Operators

The Koopman operator is an infinite dimensional linear operator that directly acts on the functions of state. That is, the Koopman operator takes any observation of state at time t and evolves the functions of state subject to its dynamics forward in time linearly. Thus, a nonlinear dynamical system which has a discoverable Koopman operator can be represented by a linear Koopman operator in a lifted function space where the observations of state evolve linearly.

The contribution in robotics is that now a highly nonlinear robotic system can be represented as a linear dynamical system which contains all the nonlinear information (as opposed to a Taylor expansion of the dynamics centered at an equilibrium state).