Related papers: Partial null controllability of parabolic linear s…
A robust model predictive control scheme for a class of constrained norm-bounded uncertain discrete-time linear systems is developed under the hypothesis that only partial state measurements are available for feedback. Off-line calculations…
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…
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
We analyze a bilinear control problem governed by a semilinear parabolic equation. The control variable is the Robin coefficient on the boundary. First-order necessary and second-order sufficient optimality conditions are derived. A…
A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…
In a separable Hilbert space $X$, we study the linear evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0, \end{equation*} where $A$ is an accretive self-adjoint linear operator, $B$ is a bounded linear operator on $X$, and $p\in…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…
In this article, we study the boundary null-controllability properties of the one-dimensional linearized (around $(Q_0,V_0)$ with constants $Q_0>0, V_0>0$) compressible Navier-Stokes equations in the interval $(0,1)$ when a control function…
We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
This article examines an infinite-dimensional linear control system that describes population models structured by age, size, and spatial position. The control is localized with respect to space, age and size; an estimate of the time…
This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Math\'ematiques et applications at Sorbonne University, delivered over the past few years.…
A common goal in the control of a large network is to minimize the number of driver nodes or control inputs. Yet, the physical determination of control signals and the properties of the resulting control trajectories remain widely…
We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove…
Controlling nonlinear systems, especially when data are being used to offset uncertainties in the model, is hard. A natural approach when dealing with the challenges of nonlinear control is to reduce the system to a linear one via change of…
In this work, the null controllability problem for a linear system in $\ell^2$ is considered, where the matrix of a linear operator describing the system is an infinite matrix with $\lambda\in \mathbb R$ on the main diagonal and 1s above…
This paper addresses a structural design problem in control systems, and explicitly takes into consideration the possible application to large-scale systems. More precisely, we aim to determine and characterize the minimum number of…
We consider the problem of stabilization to zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum. This problem was previously studied in…
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…
In this paper, we study the null controllability for parabolic SPDEs involving both the state and the gradient of the state. To start with, an improved global Carleman estimate for linear forward (resp. backward) parabolic SPDEs with…