Related papers: Control of the Grushin equation: non-rectangular c…

We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove…

This paper investigates the link between the null controllability property for some abstract parabolic problems and an inequality that can be seen as a quantified Fattorini-Hautus test. Depending on the hypotheses made on the abstract…

In this paper, we study small-time local controllability of real analytic control-affine systems under small perturbations of their vector fields. Consider a real analytic control system $\mathcal{X}$ which is small-time locally…

We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We…

In this paper we deal with the controllability problem for some Sobolev type equations. We show that the equations cannot be driven to zero if the control region is strictly supported within the domain. Nevertheless, we also prove that it…

This paper aims to answer an open problem posed by Morancey in 2015 concerning the null controllability of the heat equation on (-1, 1) with an internal inverse square potential located at x = 0. For the range of singularity under study,…

In this paper, we are concerned with the internal control of a class of one-dimensional nonlinear parabolic systems with nonlocal and weakly degenerate diffusion coefficients. Our main theorem establishes a local null controllability result…

This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…

This work is concerned with the possibility of proving the boundary null controllability for the degenerate wave equation, developing the asymptotic analysis of a suitable family of state-control pairs $((u_\varepsilon ,…

We establish existence, approximate controllability and optimal control of a class of impulsive non-local non-linear fractional dynamical systems in Banach spaces. We use fractional calculus, sectorial operators and Krasnoselskii fixed…

This paper is devoted to the partial null controllability issue of parabolic linear systems with n equations. Given a bounded domain in R N, we study the effect of m localized controls in a nonempty open subset only controlling p components…

The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an…

We consider the linear Zakharov-Kuznetsov equation on a rectangle with a left Dirich-let boundary control. Using the flatness approach, we prove the null controllability of this equation and provide a space of analytic reachable states.

We obtain a novel interior control result for wave equations on time dependent domains. This is done by deriving a suitable Carleman estimate and proving the corresponding observability inequality. We consider the wave equation with time…

This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system…

The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…

It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…

In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial…

In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions.…

We consider the bilinear Schroedinger equation on a bounded one-dimensional domain and we provide explicit times such that the global exact controllability is verified. In addition, we show how to construct controls for the global…