259,358 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
Average growth of the spectral function on a Riemannian manifold
We study average growth of the spectral function of the Laplacian on a
Riemannian manifold. Two types of averaging are considered: with respect to the
spectral parameter and with respect to a point on a manifold. We obtain as well
related estimates of the growth of the pointwise zeta-function along vertical
lines in the complex plane. Some examples and open problems regarding almost
periodic properties of the spectral function are also discussed.Comment: 35 page
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A high-dimensional regression space usually causes problems in nonlinear system identification.However, if the regression data are contained in (or spread tightly around) some manifold, thedimensionality can be reduced. This paper presents a use of dimension reduction techniques tocompose a two-step identification scheme suitable for high-dimensional identification problems withmanifold-valued regression data. Illustrating examples are also given
Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows
This paper concerns an extension of discrete gradient methods to
finite-dimensional Riemannian manifolds termed discrete Riemannian gradients,
and their application to dissipative ordinary differential equations. This
includes Riemannian gradient flow systems which occur naturally in optimization
problems. The Itoh--Abe discrete gradient is formulated and applied to gradient
systems, yielding a derivative-free optimization algorithm. The algorithm is
tested on two eigenvalue problems and two problems from manifold valued
imaging: InSAR denoising and DTI denoising.Comment: Post-revision version. To appear in SIAM Journal on Scientific
Computin
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