Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Control and State Estimation of the One-Phase Stefan Problem via
  Backstepping Design   This paper develops a control and estimation design for the one-phase Stefan
problem. The Stefan problem represents a liquid-solid phase transition as time
evolution of a temperature profile in a liquid-solid material and its moving
interface. This physical process is mathematically formulated as a diffusion
partial differential equation (PDE) evolving on a time-varying spatial domain
described by an ordinary differential equation (ODE). The state-dependency of
the moving interface makes the coupled PDE-ODE system a nonlinear and
challenging problem. We propose a full-state feedback control law, an observer
design, and the associated output-feedback control law via the backstepping
method. The designed observer allows estimation of the temperature profile
based on the available measurement of solid phase length. The associated
output-feedback controller ensures the global exponential stability of the
estimation errors, the H1- norm of the distributed temperature, and the moving
interface to the desired setpoint under some explicitly given restrictions on
the setpoint and observer gain. The exponential stability results are
established considering Neumann and Dirichlet boundary actuations.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph