15,680 research outputs found
Transverse exponential stability and applications
We investigate how the following properties are related to each other: i)-A
manifold is "transversally" exponentially stable; ii)-The "transverse"
linearization along any solution in the manifold is exponentially stable;
iii)-There exists a field of positive definite quadratic forms whose
restrictions to the directions transversal to the manifold are decreasing along
the flow. We illustrate their relevance with the study of exponential
incremental stability. Finally, we apply these results to two control design
problems, nonlinear observer design and synchronization. In particular, we
provide necessary and sufficient conditions for the design of nonlinear
observer and of nonlinear synchronizer with exponential convergence property
Contraction analysis of switched Filippov systems via regularization
We study incremental stability and convergence of switched (bimodal) Filippov
systems via contraction analysis. In particular, by using results on
regularization of switched dynamical systems, we derive sufficient conditions
for convergence of any two trajectories of the Filippov system between each
other within some region of interest. We then apply these conditions to the
study of different classes of Filippov systems including piecewise smooth (PWS)
systems, piecewise affine (PWA) systems and relay feedback systems. We show
that contrary to previous approaches, our conditions allow the system to be
studied in metrics other than the Euclidean norm. The theoretical results are
illustrated by numerical simulations on a set of representative examples that
confirm their effectiveness and ease of application.Comment: Preprint submitted to Automatic
An Energy-based Approach to Ensure the Stability of Learned Dynamical Systems
Non-linear dynamical systems represent a compact, flexible, and robust tool
for reactive motion generation. The effectiveness of dynamical systems relies
on their ability to accurately represent stable motions. Several approaches
have been proposed to learn stable and accurate motions from demonstration.
Some approaches work by separating accuracy and stability into two learning
problems, which increases the number of open parameters and the overall
training time. Alternative solutions exploit single-step learning but restrict
the applicability to one regression technique. This paper presents a
single-step approach to learn stable and accurate motions that work with any
regression technique. The approach makes energy considerations on the learned
dynamics to stabilize the system at run-time while introducing small deviations
from the demonstrated motion. Since the initial value of the energy injected
into the system affects the reproduction accuracy, it is estimated from
training data using an efficient procedure. Experiments on a real robot and a
comparison on a public benchmark shows the effectiveness of the proposed
approach.Comment: Accepted at the International Conference on Robotics and Automation
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