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

TL;DR

This paper introduces JDMD, a data-efficient method for learning control models that leverages Jacobian information to improve sample efficiency and tracking performance in MPC, demonstrated on realistic simulation examples.

Contribution

The paper presents JDMD, a novel Jacobian-regularized DMD approach that enhances model learning for control by incorporating Jacobian information from prior models.

Findings

JDMD achieves superior tracking performance in simulation.

JDMD demonstrates improved sample efficiency over traditional DMD methods.

Models learned by JDMD generalize well even with significant model mismatch.

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).