Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: State Estimation of the Stefan PDE: A Tutorial on Design and
  Applications to Polar Ice and Batteries   The Stefan PDE system is a representative model for thermal phase change
phenomena, such as melting and solidification, arising in numerous science and
engineering processes. The mathematical description is given by a Partial
Differential Equation (PDE) of the temperature distribution defined on a
spatial interval with a moving boundary, where the boundary represents the
liquid-solid interface and its dynamics are governed by an Ordinary
Differential Equation (ODE). The PDE-ODE coupling at the boundary is nonlinear
and creates a significant challenge for state estimation with provable
convergence and robustness. This tutorial article presents a state estimation
method based on PDE backstepping for the Stefan system, using measurements only
at the moving boundary. PDE backstepping observer design generates an observer
gain by employing a Volterra transformation of the observer error state into a
desirable target system, solving a Goursat-form PDE for the transformation's
kernel, and performing a Lyapunov analysis of the target observer error system.
The observer is applied to models of problems motivated by climate change and
the need for renewable energy storage: a model of polar ice dynamics and a
model of charging and discharging in lithium-ion batteries. The numerical
results for polar ice demonstrate a robust performance of the designed
estimator with respect to the unmodeled salinity effect in sea ice. The results
for an electrochemical PDE model of a lithium-ion battery with a phase
transition material show the elimination of more than 15 \% error in
State-of-Charge estimate within 5 minutes even in the presence of sensor noise.

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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin