Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Unknown Input Observability: The Analytic Solution in the case
  of a Single Unknown Input   This work presents the analytic solution of a fundamental open problem in the
framework of nonlinear observability, which is the unknown input observability
problem (UIO problem). The solution here provided holds in the case of a single
unknown input. The first part of the work presents this analytic solution. As
for the observability rank condition, the proposed analytic criterion is based
on the computation of the observable codistribution. Similarly to the case of
only known inputs, the observable codistribution is obtained by recursively
computing the Lie derivatives of the outputs along the vector fields that
characterize the dynamics. However, in correspondence of the unknown input, the
corresponding vector field must be suitably rescaled. Additionally, the Lie
derivatives of the outputs must also be computed along a new set of vector
fields that are obtained by recursively performing suitable Lie bracketing of
the vector fields that define the dynamics. In practice, the entire observable
codistribution is obtained by a very simple recursive algorithm. Finally, it is
shown that the recursive algorithm converges in a finite number of steps and
the criterion to establish that the convergence has been reached is provided.
The proposed analytic extension of the observability rank condition is
illustrated by checking the weak local observability of several nonlinear
systems driven by multiple known inputs and a single unknown input. For these
systems, extensive simulations are also provided. It is shown that, a simple
estimator based on an Extended Kalman Filter, provides results that agree with
our observability analysis. Finally, it is shown that the analytic criterion is
not only a key analytical tool to automatically obtain the state observability
(and so the analytic solution of a fundamental open problem) but it can be also
a fundamental tool for unknown input observer design.

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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an