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Machine Learning Accelerated PDE Backstepping Observers

Shi, Yuanyuan and Li, Zongyi and Yu, Huan and Steeves, Drew and Anandkumar, Anima and Krstic, Miroslav (2022) Machine Learning Accelerated PDE Backstepping Observers. . (Unpublished)

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State estimation is important for a variety of tasks, from forecasting to substituting for unmeasured states in feedback controllers. Performing real-time state estimation for PDEs using provably and rapidly converging observers, such as those based on PDE backstepping, is computationally expensive and in many cases prohibitive. We propose a framework for accelerating PDE observer computations using learning-based approaches that are much faster while maintaining accuracy. In particular, we employ the recently-developed Fourier Neural Operator (FNO) to learn the functional mapping from the initial observer state and boundary measurements to the state estimate. By employing backstepping observer gains for previously-designed observers with particular convergence rate guarantees, we provide numerical experiments that evaluate the increased computational efficiency gained with FNO. We consider the state estimation for three benchmark PDE examples motivated by applications: first, for a reaction-diffusion (parabolic) PDE whose state is estimated with an exponential rate of convergence; second, for a parabolic PDE with exact prescribed-time estimation; and, third, for a pair of coupled first-order hyperbolic PDEs that modeling traffic flow density and velocity. The ML-accelerated observers trained on simulation data sets for these PDEs achieves up to three orders of magnitude improvement in computational speed compared to classical methods. This demonstrates the attractiveness of the ML-accelerated observers for real-time state estimation and control.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper ItemConference Paper
Shi, Yuanyuan0000-0002-6182-7664
Li, Zongyi0000-0003-2081-9665
Yu, Huan0000-0002-9324-0200
Anandkumar, Anima0000-0002-6974-6797
Krstic, Miroslav0000-0002-5523-941X
Additional Information:Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).
Record Number:CaltechAUTHORS:20221221-004741856
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118562
Deposited By: George Porter
Deposited On:21 Dec 2022 20:46
Last Modified:02 Jun 2023 01:30

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