Related papers: Null Controllability for Cascade systems of Couple…

This paper studies the approximate and null controllability for impulse controlled systems of heat equations coupled by a pair (A,B) of constant matrices. We present a necessary and sufficient condition for the approximate controllability,…

This work is concerned with the obtainment of new Carleman estimates for linear parabolic equations, where the second-order differential operator brings a super strong degeneracy in a positive measure subset of the spatial domain. In order…

This paper presents a delay-adaptive boundary control scheme for a $2\times 2$ coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming…

In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding…

In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under…

This paper deals with a hierarchical multi-objective control problem for forward stochastic parabolic equations with dynamic boundary conditions. The controls are divided into two classes: leaders and followers. The goal of the leaders is…

This paper is addressed to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators…

We consider a $2\times2$ nonlinear reaction-diffusion system posed on a smooth bounded domain$$\Omega$ of R N (N $\ge$ 1$). The control input is in the source term of only one equation. It is localized in some arbitrary nonempty open subset…

We describe a particular control method for a system controlled by several actuators with the same control constants. We show under certain assumptions that the control constants for the whole system can be obtained immediately from the…

In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in "New blow-up rates for…

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a semilinear parabolic equation in one-dimension defined in a non-cylindrical domain where the diffusion coefficient degenerates at one point of the…

One proves that the linear and semilinear stochastic parabolic equations with a multiplicative noise with a finite number of modes are exactly null controllable.

Using a compactness-uniqueness approach, we show that the Fattorini criterion implies the exact controllability of general compactly perturbed controlled linear systems. We then apply this perturbation result to obtain new controllability…

This paper is devoted to the analysis of the uniform null controllability for a family of nonlinear reaction-diffusion systems approximating a parabolic-elliptic system which models the electrical activity of the heart. The uniform, with…

In this work, we investigate the optimal cost of null controllability for the $n$-dimensional Stokes system when the control acts on $n-1$ scalar components. We establish a novel spectral estimate for low frequencies of the Stokes operator,…

In this paper, we investigate the controlled system described by forward-backward stochastic differential equations with the control contained in drift, diffusion and generator of BSDE. A new verification theorem is derived within the…

Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$. The null controllability properties of the equation $$u_{tt}+\Delta^2 u+\rho (\Delta)^\alpha u_t=F(x,t)$$ are studied. Let $T>0$, and assume initial conditions $(u^0,u^1)\in…

This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…

This paper extends the Carleman estimates to high dimensional parabolic equations with highly degenerate symmetric coefficients on a bounded domain of Lipschitz boundary and use these estimates to study the controlla?bility the…

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…