For an unknown linear system, starting from noisy open-loop input-state data collected during a finite-length experiment, we directly design feedback controller that guarantees robust invariance of given polyhedral set the state in presence disturbances. The main result is necessary and sufficient condition for existence such controller, amounts to solution program. benefits large rich sets pro...

Experimental and computational data field obtained from measurements are often sparse noisy. Consequently, interpolating unknown functions under these restrictions to provide accurate predictions is very challenging. This study compares machine-learning methods cubic splines on the sparsity of training they can handle, especially when samples We compare deviation a true function f using mean sq...

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension incompressible Navier–Stokes equations, observational measurements given by finite volume elements or nodal points of the velocity field and measurement errors which...

Compressed sensing aims at recovering a sparse signal x ∈ RN from few nonadaptive, linear measurements Φ(x) given by a measurement matrix Φ. One of the fundamental recovery algorithms is an `1 minimisation. In this paper we investigate the situation when our measurement Φ(x) is contaminated by arbitrary noise under the assumption that the matrix Φ satisfies the restricted isometry property. Thi...

This paper studies the recovery of a superposition of point sources from noisy bandlimited data.In the fewest possible words, we only have information about the spectrum of an object in the low-frequency band[−flo, flo] and seek to obtain a higher resolution estimate by extrapolating the spectrumup to a frequency fhi > flo. We show that as long as the sources are separated b...