Related papers: Exact null-controllability of interconnected abstr…
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.…
A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability,…
In this paper we examine a mutual control problem for systems of two abstract evolution equations subject to a proportionality final condition. Related observability and semi-observability problems are discussed. The analysis employs a…
This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
We consider an optimal control problem $\cQ$ governed by an elliptic quasivariational inequality with unilateral constraints. The existence of optimal pairs of the problem is a well known result, see \cite{SS}, for instance. We associate to…
In this paper, we are concerned with the null controllability of a linear population dynamics cascade systems (or the so-called prey-predator models) with two different dispersion coefficients which degenerate in the boundary and with one…
To each dynamic equivalence of two control systems is associated an infinite permutation matrix. We investigate how such matrices are related to the existence of dynamic equivalences.
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural-controllability theory, we continue to lack a framework to control undirected complex networks, especially…
In this paper, we study the dynamical behavior of a linear control system on $\R^2$ when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
For linear evolution control system described by $\dot{x}=Ax(t)+Bu(t),x(0)=x_{0}$ ($A$ generates a strongly continuous semigroup ${S(t)}_{t\ge 0}$ in a Banach space $X$; $B$ is a linear unbounded operator), the attainable set $K(t)$ is…
This article is devoted to the study of null controllability for evolution equations that incorporate both memory and delay effects. The problem is particularly challenging due to the presence of memory integrals and delayed states, which…
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…
Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport…
In this paper, we investigate the two-point boundary value problems for linear wave equation defined on a circle and prove that the equation possesses the exact controllability. We also investigate the two-point boundary value problems for…
Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we…
We study the null-controllability properties of heat-like equations posed on the whole Euclidean space $\mathbb R^n$. These evolution equations are associated with Fourier multipliers of the form $\rho(\vert D_x\vert)$, where…
Partial differential equation on networks have been widely investigated in the last decades in view of their application to quantum mechanics (Schr\"odinger type equations) or to the analysis of flexible structures (wave type equations).…