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In this paper, we deal with a minimum time problem in presence of a time delay $\tau.$ The value function of the considered optimal control problem is no longer defined in a subset of $\mathbb{R}^{n}$, as it happens in the undelayed case,…
A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general…
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy…
We study the controllability of a coupled system of linear parabolic equations, with non-negativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with…
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…
In this paper, we prove the null controllability of some parabolic-elliptic systems. The control is distributed, locally supported in space and appears only in one PDE. The arguments rely on fixed-point reformulation and suitable Carleman…
In this paper we study the local boundary controllability for a non linear system of two degenerate parabolic equations with a control acting on only one equation. We analyze boundary null controllability properties for the linear system…
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…
For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure…
We prove the interior and boundary null-controllability of some parabolic evolutions with controls acting over measurable sets.
In this paper we consider output controllability for linear time-invariant systems. In a recent paper by Danhane, Loh{\'e}ac and Jungers it has been pointed out that although output controllability is a classical notion in control theory,…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on the kind of problems arising for example when controlling the anisotropic Allen-Cahn equation as a model for crystal growth.…
In this paper we investigate the Hierarchical null controllability of a coupled degenerate semilinear parabolic equation in domains which are moving in time. We show the local null controllability of the semilinear system using Liusternik's…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
In this paper we prove a uniform controllability result for a fourth order parabolic partial differential equation which includes a transport term, when the coefficients of higher order terms vanish. We prove the null controllability of the…
This paper is concerned with the existence of insensitizing controls for a fourth order semilinear parabolic equation. Here, the initial data is partially unknown, we would like to find controls such that a specific functional is…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…
We consider a system of two parabolic equations with a forcing term present in one equation and a cubic coupling term in the other one. We prove that the system is locally null controllable.
In this article, we present two different approaches for obtaining quantitative inequalities in the context of parabolic optimal control problems. Our model consists of a linearly controlled heat equation with Dirichlet boundary condition…