Data-Efficient Model Learning for Control with Jacobian-Regularized Dynamic-Mode Decomposition

Brian Edward Jackson, Jeong Hun Lee, Kevin Tracy, Zachary Manchester

Keywords: Koopman, learning, model-predictive control, optimal control

TL;DR: Using information from an approximate prior model improves sample efficiency when learning Koopman models.

Abstract: We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based on Dynamic-Mode Decomposition (DMD) by leveraging Jacobian information from an approximate prior model of the system, and improved tracking performance over traditional model-based MPC. We demonstrate JDMD’s ability to quickly learn bilinear Koopman dynamics representations across several realistic examples in simulation, including a perching maneuver for a fixed-wing aircraft with an empirically derived high-fidelity physics model. In all cases, we show that the models learned by JDMD provide superior tracking and generalization performance within a model-predictive control framework, even in the presence of significant model mismatch, when compared to approximate prior models and models learned by standard Extended DMD (EDMD).

Student First Author: yes

Website: https://roboticexplorationlab.org/projects/koopman.html

Code: https://github.com/bjack205/BilinearControl.jl