Robust Model Predictive Control with Data-Driven Koopman Operators

This paper presents robust Koopman model predictive control (RK-MPC), a framework that leverages the training errors of data-driven models to improve constraint satisfaction. Koopman-based control has enabled fast nonlinear feedback using linear tools, but existing approaches ignore the modeling error during control, which can lead to constraint violations. Our approach assumes that the unknown dynamics are Lipschitz-continuous and uses the training error of data-driven Koopman models to approximate a Lipschitz constant for the state- and control-dependent model error. We then use the Lipschitz constant to bound the prediction error along the planning horizon and formulate a convex, robust finite-horizon optimal control problem that is real-time implementable. We demonstrate the efficacy of this approach with simulation results using the dynamics of a forced Duffing oscillator and a quadrotor. Our Python implementation can run in real-time at 66Hz for the 17-dimensional duffing oscillator and at 12Hz for the 44-dimensional quadrotor on a standard laptop.