Related papers: The $H^{\infty}$-control problem for parabolic sys…
In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
This work studies the null controllability of a system of coupled parabolic PDEs. In particular, our work specializes to an important subclass of these control problems which are coupled by first and zero-order couplings and are,…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…
We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop…
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…
Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…
We study a parabolic boundary control problem with one spatial dimension, control constraints of box type, and an objective function that measures the $L^2$-distance to a desired terminal state. It is shown that, for a certain choice of the…
We address a class of systems for which the solution to an H-infinity optimal control problem can be given on a very simple closed form. In fact, both the control law and optimal performance value are explicitly given. The class of systems…
In this paper, we present a new distributional identity for the solutions of elliptic equations involving Hardy potentials with singularities located on the boundary of the domain. Then we use it to obtain the boundary isolated singular…
The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a transport equation with boundary control. A suitable viscosity solution approach is needed in view of the…
A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. Key words: Cahn-Hilliard…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
This paper examines the impulse controllability of degenerate singular parabolic equations through a modern framework focused on finite-time stabilization. Furthermore, we provide an explicit estimate for the exponential decay of the…
In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties.…
The present paper addresses the topic of boundary output feedback stabilization of parabolic-type equations, governed by linear differential operators which can be diagonalized by the introduction of adequate weighting functions (by means…
The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…
In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on a phase-field model of grain boundary motion, proposed in…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
This paper studies the controllability problem of a parabolic system of chemotaxis. The local exact controllability to trajectories of the system imposed one control force only is obtained by applying Kakutani's fixed point theorem combined…