Learning-based Moving Horizon Estimation through Differentiable Convex Optimization Layers
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Date
2022-06
Publication Type
Conference Paper
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yes
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Abstract
To control a dynamical system it is essential to obtain an accurate estimate of the current system state based on uncertain sensor measurements and existing system knowledge. An optimization-based moving horizon estimation (MHE) approach uses a dynamical model of the system, and further allows for integration of physical constraints on system states and uncertainties, to obtain a trajectory of state estimates. In this work, we address the problem of state estimation in the case of constrained linear systems with parametric uncertainty. The proposed approach makes use of differentiable convex optimization layers to formulate an MHE state estimator for systems with uncertain parameters. This formulation allows us to obtain the gradient of a squared and regularized output error, based on sensor measurements and state estimates, with respect to the current belief of the unknown system parameters. The parameters within the MHE problem can then be updated online using stochastic gradient descent (SGD) to improve the performance of the MHE. In a numerical example of estimating temperatures of a group of manufacturing machines, we show the performance of tuning the unknown system parameters and the benefits of integrating physical state constraints in the MHE formulation.
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Publication status
published
Book title
Proceedings of the 4th Annual Learning for Dynamics and Control Conference
Journal / series
Volume
168
Pages / Article No.
153 - 165
Publisher
PMLR
Event
4th Annual Learning for Dynamics and Control Conference (4th L4DC 2022)
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Methods
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Date collected
Date created
Subject
Moving horizon estimation; constrained system identification; differentiable convex optimization layers
Organisational unit
09563 - Zeilinger, Melanie / Zeilinger, Melanie
Notes
Funding
157601 - Safety and Performance for Human in the Loop Control (SNF)