Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extended Kalman filter based observer design for semilinear
  infinite-dimensional systems   In many physical applications, the system's state varies with spatial
variables as well as time. The state of such systems is modelled by partial
differential equations and evolves on an infinite-dimensional space. Systems
modelled by delay-differential equations are also infinite-dimensional systems.
The full state of these systems cannot be measured. Observer design is an
important tool for estimating the state from available measurements. For linear
systems, both finite- and infinite-dimensional, the Kalman filter provides an
estimate with minimum-variance on the error, if certain assumptions on the
noise are satisfied. The extended Kalman filter (EKF) is one type of extension
to nonlinear finite-dimensional systems. In this paper we provide an extension
of the EKF to semilinear infinite-dimensional systems. Under mild assumptions
we prove the well-posedness of equations defining the EKF. Local exponential
stability of the error dynamics is shown. Only detectability is assumed, not
observability, so this result is new even for finite-dimensional systems. The
results are illustrated with implementation of finite-dimensional
approximations of the infinite-dimensional EKF on an example.

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th