Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-dimensional control of the heat equation: Dirichlet actuation and
  point measurement   Recently finite-dimensional observer-based controllers were introduced for
the 1D heat equation, where at least one of the observation or control
operators is bounded. In this paper, for the first time, we manage with such
controllers for the 1D heat equation with both operators being unbounded. We
consider Dirichlet actuation and point measurement and use a modal
decomposition approach via dynamic extension. We suggest a direct Lyapunov
approach to the full-order closed-loop system, where the finite-dimensional
state is coupled with the infinite-dimensional tail of the state Fourier
expansion, and provide LMIs for finding the controller dimension and the
resulting exponential decay rate. We further study sampled-data implementation
of the controller under sampled-data measurement. We use Wirtinger-based,
discontinuous in time, Lyapunov functionals which compensate sampling in the
finite-dimensional state. To compensate sampling in the infinite-dimensional
tail, we use a novel form of Halanay's inequality, which is appropriate for
Lyapunov functions with jump discontinuities that do not grow in the jumps.
Numerical examples demonstrate the efficiency of the method.

4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc