相关论文: Insensitizing controls for stochastic parabolic eq…

It is well known that both the heat equation with Dirichlet or Neumann boundary conditions are null controlable as soon as the control acts in a non trivial domain (i.e. a set of positive measure, see [10, 11, 12, 1, 6]. In this article, we…

In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat…

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…

This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the…

This paper concerns the null controllability of the two-phase 1D Stefan problem with distributed controls. This is a free-boundary problem that models solidification or melting processes. In each phase, a parabolic equation, completed with…

This paper deals with the hierarchical control of the anisotropic heat equation with dynamic boundary conditions and drift terms. We use the Stackelberg-Nash strategy with one leader and two followers. To each fixed leader, we find a Nash…

The main purpose of this article is to prove a logarithmic convexity estimate for the solution of a linear heat equation subject to dynamic boundary conditions in a bounded convex domain. As an application, we prove the impulsive null…

In this work, we establish a Carleman inequality for the heat equation with Fourier boundary conditions of the form $\partial_\nu y+by=f1_\gamma$, where the control acts on a small portion $\gamma$ of the boundary. We apply this inequality…

This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…

We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.

In this paper, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an anti-stable stochastic heat equation with Neumann boundary actuation and unknown boundary…

In this paper, we study the tracking controllability of a 1D parabolic type equation. Notably, with controls acting on the boundary, we seek to approximately control the solution of the equation on specific points of the domain. We prove…

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving…

We study the null controllability of three parabolic equations. The control is acting only on one of the three equations. The three equations are coupled by means of two cubic nonlinearities. The linearized control system around 0 is not…

In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy…

In this paper we consider a linear hybrid system which composed by two non-homogeneous rods connected by a point mass and generated by the equation\bea\left\{ \begin{array}{ll} \rho_{1}(x)u_{t}=(\sigma_{1}(x)u_{x})_{x}-q_{1}(x)u,&…

We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class…

This paper focuses on boundary approximate controllability under positivity constraints of a wide range of infinite-dimensional control systems. We develop frequency domain controllability criteria. Firstly, we derive a controllability…

We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the…