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TZID:Europe/Paris
BEGIN:STANDARD
DTSTART:20191027T030000
TZOFFSETFROM:+0200
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DTSTART:20200329T020000
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UID:calendar.18954.field_data.0@diag.uniroma1.it
DTSTAMP:20230206T085357Z
CREATED:20191119T095547Z
DESCRIPTION:In this talk I provide the analytic solution of an important op
en problem in control theory. Specifically\, I provide the analytic proced
ure to obtain the state observability of nonlinear systems in presence of
multiple unknown inputs. This problem\, called the Unknown Input Observabi
lity (UIO) problem\, was introduced in the seventies. As for the observabi
lity rank condition (that is the analytic procedure to obtain the observab
ility in absence of unknown inputs)\, the analytic solution of the nonline
ar UIO problem is based on the computation of the observable codistributio
n by a recursive and convergent algorithm. As in the standard case of only
known inputs\, the observable codistribution is obtained by recursively c
omputing the Lie derivatives along the vector fields that characterize the
dynamics. However\, in correspondence of the unknown inputs\, the corresp
onding vector fields must be suitably rescaled. Additionally\, the Lie der
ivatives must also be computed along a new set of vector fields that are o
btained by recursively performing suitable Lie bracketing of the vector fi
elds that define the dynamics. The analytic derivations and all the proofs
necessary to analytically derive the algorithm and its convergence proper
ties and to prove their general validity are very complex and they are bas
ed on new concepts borrowed from theoretical physics (specifically\, from
the standard model of particle physics and from the theory of general rela
tivity). In practice\, these proofs requires the introduction of the Group
of Invariance of Observability and the twofold role of time in system the
ory. In the seminar\, I only provide the strategy of the proof and an intu
itive description of the above concepts.The analytic solution is illustrat
ed by checking the observability of several nonlinear systems driven by mu
ltiple known inputs and multiple unknown inputs\, ranging from planar robo
tics up to advanced navigation systems in 3D that can be important also in
the framework of neuroscience.
DTSTART;TZID=Europe/Paris:20191129T140000
DTEND;TZID=Europe/Paris:20191129T140000
LAST-MODIFIED:20220404T120141Z
LOCATION:Aula A5
SUMMARY:Nonlinear Unknown Input Observability: the General Analytic Solutio
n - Agostino Martinelli (INRIA Grenoble\, France)
URL;TYPE=URI:https://diag.uniroma1.it/node/18954
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