Related papers: The cost of approximate controllability for semili…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation…
In this paper we study a first extension of the theory of mild solutions for HJB equations in Hilbert spaces to the case when the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear…
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 consider the semilinear heat equation posed on a smooth bounded domain $\Omega$ of $\mathbb{R}^{N}$ with Dirichlet or Neumann boundary conditions. The control input is a source term localized in some arbitrary nonempty open subset…
We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…
We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting)which…
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris S{\'e}r. I,…
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.
Motivated by infinite-dimensional optimal control problems with endpoint state constraints, in this Note, we introduce the notion of finite codimensional exact controllability for evolution equations. It is shown that this new…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
We obtain necessary conditions and sufficient conditions for the solvability of the heat equation in a half-space of ${\bf R}^N$ with a nonlinear boundary condition. Furthermore, we study the relationship between the life span of the…
A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…
This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…
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 show that a bilinear control system is approximately controllable if and only if it is controllable in $\mathbb{R}^{n}\setminus\{0\}$. We approach this problem by looking at the foliation made by the orbits of the system, and by showing…
This article is devoted to study the interior approximated controllability of the strongly damped semilinear wave equation with memory, impulses and delay terms. The problem is challenging since the state equation contains memory and…
The paper deals with the controllability of finite-dimensional linear difference delay equations, i.e., dynamics for which the state at a given time $t$ is obtained as a linear combination of the control evaluated at time $t$ and of the…