Related papers: Rough controls for Schroedinger operators on 2-tor…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
We consider in this note Furstenberg transformations on Cartesian products of infinite-dimensional tori. Under some appropriate assumptions, we show that these transformations are uniquely ergodic with respect to the Haar measure and have…
We prove approximate controllability of the bilinear Schr\"odinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and…
The determination of the spectrum of a Schr\"odinger operator is a fundamental problem in mathematical quantum mechanics. We discuss a series of results showing that Schr\"odinger operators can exhibit spectra that are remarkably thin in…
In this work, we found a non trivial topology to achieve the controllability for linear and nonlinear system in finite or infinite time horizon. We give several examples illustrating this topologizing method for the controllability results.…
We consider the problem of the observability of positively expansive maps by the time series associated to continuous real functions. For this purpose we prove a general result on the generic observability of a locally injective map of a…
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…
We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de…
We show that, after a renormalisation, one can define the square of the modulus of the solution of the fractional Schr\"odinger equations on the circle with data in Sobolev spaces of arbitrary negative index. As an application, we obtain…
We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue points. The studies yield convergence results and also a density…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
Output controllability and functional observability are properties that enable, respectively, the control and estimation of part of the state vector. These notions are of utmost importance in applications to high-dimensional systems, such…
We give a simple proof of the sharp decay of the Fourier-transform of surface-carried measures of two-dimensional generic surfaces. The estimates are applied to prove Strichartz and resolvent estimates for elliptic operators whose…
We survey results of recent activity towards studying controllability and accessibility issues for equations of dynamics of incompressible fluids controlled by low-dimensional or, degenerate, forcing. New results concerning controllability…
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are…
The paper presents a robust control technique that combines the Control Lyapunov function and Hamilton-Jacobi Reachability to compute a controller and its Region of Attraction (ROA). The Control Lyapunov function uses a linear system model…
This paper continues our study of the interconnection between controllability and mixing properties of random dynamical systems. We begin with an abstract result showing that the approximate controllability to a point and a local…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
An alternative formulation for the controllability problem of single input linear positive systems is presented. Driven by many industrial applications, this formulations focuses on the case where the region of interest is only a subset of…
For any continuous map f on a compact manifold M, we define the SRB-like (or observable) probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove that f has observable measures, even if SRB measures do not…