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This paper is concerned with the constrained approximate null controllability of heat equation coupled by a real matrix $P$, where the controls are impulsive and periodically acted into the system through a series of real matrices…
In the paper, problems of controllability, approximate controllability, reachability and approximate reachability are studied for the control system $w_t=w_{xx}$, $w(0,\cdot)=u$, $x>0$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a control.…
In the paper, the problems of controllability and approximate controllability are studied for the control system $w_t=\frac{1}{\rho}\left(kw_x\right)_x+\gamma w$, $\left.\left(\sqrt{\frac{k}{\rho}}w_x\right)\right|_{x=0}=u$, $x>0$,…
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…
This paper is devoted to prove the exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We consider the case where the coupling matrix A…
In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control…
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…
The paper deals with exact null-controllability problem for a linear control system consisting of two serially connected abstract control systems. Controllability conditions are obtained. Applications to the exact null-controllability for…
This paper considers the controllability of a class of coupled Stokes systems with distributed controls. The coupling terms are of a different nature. The first coupling is through the principal part of the Stokes operator with a constant…
In this paper, we study approximate and exact controllability of the linear difference equation $x(t) = \sum\_{j=1}^N A\_j x(t - \Lambda\_j) + B u(t)$ in $L^2$, with $x(t) \in \mathbb C^d$ and $u(t) \in \mathbb C^m$, using as a basic tool a…
In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…
In this paper, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the…
One proves that the $n$-D stochastic controlled equation $dX+AXdt=\sigma(X)dW+Bu\,dt$, where $\sigma\in\mbox{Lip}((\R^n,\L(\R^d,\R^n))$ and the pair $A\in\L(\R^n)$, $B\in\L(\R^m,\R^n)$ satisfies the Kalman rank condition, is exactly…
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…
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…
The semilinear heat equation with non-instantaneous impulses \textbf{(NII)}, memory, and delay is considered and its approximate controllability is obtained. This is done by employing a technique that avoids fixed point theorems and pulls…
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by…
This paper is devoted to the theoretical and numerical analysis of the null controllability of a coupled ODE-heat system internally and at the boundary with Neumann boundary control. First, we establish the null controllability of the…
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…
We consider the heat equation with dynamic bounary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and…