48,029 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
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
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