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Accelerating Numerical Methods for Optimal Control

PhD Thesis, Tech. Report, CMU-RI-TR-22-64, Robotics Institute, Carnegie Mellon University, October, 2022
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We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized DMD (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 experimentally derived high-fidelity physics model. In all cases, we show that the models learned by JDMD provide superior tracking and generalization performance in the presence of significant model mismatch within a model-predictive control framework, when compared to the approximate prior models used in training and models learned by standard extended DMD.


author = {Brian E. Jackson},
title = {Accelerating Numerical Methods for Optimal Control},
year = {2022},
month = {October},
school = {Carnegie Mellon University},
address = {Pittsburgh, PA},
number = {CMU-RI-TR-22-64},
keywords = {optimal control, optimization,, robotics, path planning},

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