Related papers: Sharp control time for viscoelastic bodys
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
The paper is devoted to the controllability problem for 3D compressible Euler system. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
This work is devoted to prove the global uniform exact controllability of the inviscid and viscous Burgers-$\alpha$ systems. The state $y$ is the solution to a regularized Burgers equation, where the transport velocity $z$ consists of a…
A fundamental challenge in physics is controlling the propagation of waves in disordered media despite strong scattering from inhomogeneities. Spatial light modulators enable one to synthesize (shape) the incident wavefront, optimizing the…
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the…
When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface.…
In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the control function acts on a subdomain…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
Shear wave elastography (SWE) is a promising imaging modality for mechanical characterization of tissues, offering biomarkers with potential for early and precise diagnosis. While various methods have been developed to extract mechanical…
We give a characterization of the controllability for discrete-time linear systems with convex output constraints. It extends all previously known characterizations in the literature, as well as our previous results on controllability of…
Previously, the controllability problem of a linear time-invariant dynamical system was mapped to the maximum matching (MM) problem on the bipartite representation of the underlying directed graph, and the sizes of MMs on random bipartite…
This article is devoted to study the interior approximated controllability of the strongly damped semilinear wave equation with memory, impulses and delay terms. The problem is challenging since the state equation contains memory and…
We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…
An important characteristic of temporal graphs is how the directed arrow of time influences their causal topology, i.e., which nodes can possibly influence each other causally via time-respecting paths. The resulting patterns are often…
We consider a coupled system of partial differential equations describing the interactions between a closed free interface and two viscous incompressible fluids. The fluids are assumed to satisfy the incompressible Navier-Stokes equations…
We consider the problem of boundary control for a vibrating string with $N$ interior point masses. We assume the control is at the left end, and the string is fixed at the right end. Singularities in waves are "smoothed" out to one order as…
In this paper, we investigate the controllability of a class of formation control systems. Given a directed graph, we assign an agent to each of its vertices and let the edges of the graph describe the information flow in the system. We…
Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry…