Estimating unknown dynamics and cost as a bilinear system with Koopman-based Inverse Optimal Control

In this work, we address the challenge of approximating unknown system dynamics and cost functions through a Koopman-based Inverse Optimal Control (IOC) framework.

Using optimal trajectories, a modified Extended Dynamic Mode Decomposition with control (EDMDc) constructs a bilinear control system in lifted coordinates.

Pontryagin's Maximum Principle (PMP) conditions are then derived, revealing structural similarities to the inverse Linear Quadratic Regulator (LQR) problem.

This allows tractable cost recovery without resorting to nonlinear IOC formulations.

The bilinear representation also inherits the analytical advantages of linear systems.

Simulation and robotic experiments validate the approach, showing accurate estimation of both dynamics and costs, and illustrating its potential for general control and modeling applications.