138,708 research outputs found
Data-driven computation of invariant sets of discrete time-invariant black-box systems
We consider the problem of computing the maximal invariant set of
discrete-time black-box nonlinear systems without analytic dynamical models.
Under the assumption that the system is asymptotically stable, the maximal
invariant set coincides with the domain of attraction. A data-driven framework
relying on the observation of trajectories is proposed to compute
almost-invariant sets, which are invariant almost everywhere except a small
subset. Based on these observations, scenario optimization problems are
formulated and solved. We show that probabilistic invariance guarantees on the
almost-invariant sets can be established. To get explicit expressions of such
sets, a set identification procedure is designed with a verification step that
provides inner and outer approximations in a probabilistic sense. The proposed
data-driven framework is illustrated by several numerical examples.Comment: A shorter version with the title "Scenario-based set invariance
verification for black-box nonlinear systems" is published in the IEEE
Control Systems Letters (L-CSS
Conflict-driven Hybrid Observer-based Anomaly Detection
This paper presents an anomaly detection method using a hybrid observer --
which consists of a discrete state observer and a continuous state observer. We
focus our attention on anomalies caused by intelligent attacks, which may
bypass existing anomaly detection methods because neither the event sequence
nor the observed residuals appear to be anomalous. Based on the relation
between the continuous and discrete variables, we define three conflict types
and give the conditions under which the detection of the anomalies is
guaranteed. We call this method conflict-driven anomaly detection. The
effectiveness of this method is demonstrated mathematically and illustrated on
a Train-Gate (TG) system
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