Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control

• URL: http://arxiv.org/abs/2301.03565v1
• Date: Mon, 9 Jan 2023 18:35:32 GMT
• Title: Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control
• Authors: Adam J. Thorpe, Cyrus Neary, Franck Djeumou, Meeko M. K. Oishi, Ufuk Topcu
• Abstract summary: We present a method to incorporate priori knowledge into data-driven control algorithms using kernel embeddings. Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem. We demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline.
• Score: 22.549914935697366
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in real-world scenarios where only limited observations of the system are available. Furthermore, purely data-driven methods often neglect useful a priori knowledge, such as approximate models of the system dynamics. We present a method to incorporate such prior knowledge into data-driven control algorithms using kernel embeddings, a nonparametric machine learning technique based in the theory of reproducing kernel Hilbert spaces. Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem. We formulate the biased learning problem as a least-squares problem with a regularization term that is informed by the dynamics, that has an efficiently computable, closed-form solution. Through numerical experiments, we empirically demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline. We demonstrate an application of our method to control through a target tracking problem with nonholonomic dynamics, and on spring-mass-damper and F-16 aircraft state prediction tasks.

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