Related papers: Null-Control and Measurable Sets
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear…
We consider funnel control for linear infinite-dimensional systems that are impedance passive, meaning that they satisfy an energy balance in which the stored energy equals the squared norm of the state and the supplied power is the inner…
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every…
We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop…
We prove the existence of global solutions for some coupled systems of partially nonautonomous evolution inclusions comprised of a Cauchy problem with a compact resolvent semigroup generator and an evolution equation governed by a…
We study the null controllability of the parabolic equation associated with the Grushin-type operator $A=\partial_x^2+|x|^{2\gamma}\partial_y^2\,, (\gamma>0),$ in the rectangle $\Omega=(-1,1)\times(0,1)$, under an additive control supported…
In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a…
Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport…
In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We…
In this article, we study the uniform null controllability problem for a system of coupled parabolic equations with an oscillating coefficient. This is done in three steps -- first, we study the spectral properties of an elliptic operator;…
We prove the internal controllability of some systems of two coupled wave equations in one space dimension, with one control, under certain conditions on the coupling. To do this we apply the "fictitious control method" in two cases:…
The paper is devoted to the exact controllability of a system of coupled abstract wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman type condition and give a description of the…
In this article, we completely describe the control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups. We show that, if the restriction of the associate derivation to the nilradical is nontrivial, the Lie…
In this paper, we study the approximate controllability of a system governed by an evolution problem known as the sloshing problem. This problem involves a spatial, nonlocal differential operator inherent in the dynamics of a…
We develop a variational approach in order to study the qualitative properties of non-autonomous parabolic equations. Based on the method of product integrals, we discuss long-time behavior, invariance properties, and ultracontractivity of…
In this article, we study the null controllability of linearized compressible Navier-Stokes system in one and two dimension. We first study the one-dimensional compressible Navier-Stokes system for non-barotropic fluid linearized around a…
The idea of controlling the dynamics of spatially extended systems using a small number of localized perturbations is very appealing - such a setup is easy to implement in practice. However, when the distance between controllers generating…
In this paper we present a weighted $L_p$-theory of parabolic systems on a half space. The leading coefficients are assumed to be only measurable in $t$ and have small bounded mean oscillations (BMO) with respect to $x$, and the lower order…