Related papers: Tracking controllability on moving targets for par…

We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path at the other free end. This sidewise…

This paper is devoted to a study of the controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations with distributed controls, locally supported in space. We prove that for any $T>0$, if the…

We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized…

We study the wave equation in an interval with two linearly moving endpoints. We give the exact solution by a series formula, then we show that the energy of the solution decay at the rate $1/t$. We also establish observability results, at…

This paper addresses the study of the hierarchical control for the one-dimensional wave equation in intervals with a moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving. When…

We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary…

In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary…

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a…

This paper deals with the hierarchical control of the parabolic equation.We use Stackelberg{Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective…

The aim of this paper is to study the null controllability of a class of quasilinear parabolic equations. In a first step we prove that the associated linear parabolic equations with non-constant diffusion coefficients are approximately…

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…

The main objective of tracking control is to steer the tracking error, that is the difference between the reference and the output, to zero while the plant's operation limits are satisfied. This requires that some assumptions on the…

This paper studies the controllability problem of a parabolic system of chemotaxis. The local exact controllability to trajectories of the system imposed one control force only is obtained by applying Kakutani's fixed point theorem combined…

We prove the null controllability of a one dimensional degenerate parabolic equation with drift and a singular potential. We study the case the potential arises at the left end point and the weighted Dirichlet boundary control is located at…

This work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic-elliptic system…

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions. The control is distributed and acts on a small subset of the…

The admissible positional control problem for the canonical system with geometrical restrictions on the control is considered. The investigation is performed with the help of the controllability function method. We obtain controllability…