Finite Time Nonlinear Optimal Control using Koopman Eigenfunctions

We propose a computational method for the finite-time nonlinear optimal control problem. We compute the solutions by first performing a coordinate transformation using the principle Koopman eigenfunctions. Then, we synthesize past and present techniques for obtaining a general explicit solution to the resulting differential Riccati equation. We demonstrate our method on a numerical example, for which the analytic Koopman eigenfunctions are known.