Related papers: Null Controllability of the 2D Heat Equation Using…
We study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus $\mathbb{T}=\mathbb{R}/2\pi\mathbb{Z}$. We assume that the control is acting on an open subset…
We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null controllable, i.e., can be driven to…
In this study, we study the null controllability of a multi-dimensional degenerate parabolic equation characterized by a degenerate interior point. The control domain, which is an arbitrary inner region, does not encompass the degenerate…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
This article is dedicated to insensitization issues of a quadratic functional involving the solution of the linear heat equation with respect to domains variations. This work can be seen as a continuation of [P. Lissy, Y. Privat, and Y.…
In this paper, we continue the study of some controllability issues for the forward stochastic parabolic equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
Observability inequalities on lattice points are established for non-negative solutions of the heat equation with potentials in the whole space. As applications, some controllability results of heat equations are derived by the…
This paper proposes several nonlinear control strategies for trajectory tracking of a quadcopter system based on the property of differential flatness. Its originality is twofold. Firstly, it provides a flat output for the quadcopter…
In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…
In this paper, we study the null controllability of the three-dimensional Stokes equations with a memory term. For any positive final time $T>0$, we construct initial conditions such that the null controllability does not hold even if the…
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…
There are hundreds of papers dealing with the Black-Scholes equation. Yet, no one seems to have ever used the scaling invariance coming from the heat equation. And there appears to be very few studies on the "control aspect" of the…
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).…
We consider the problem of finding an input signal which transfers a linear boundary controlled 1D parabolic partial differential equation with spatially-varying coefficients from a given initial state to a desired final state. The initial…
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,…
The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One…
A popular approach to designing finite-dimensional boundary controllers for partial differential equations (PDEs) is to decompose the PDE into independent modes and focus on the dominant ones while neglecting highly damped residual modes.…
Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this…
Complete controllability of finite dimensional quantum systems with energy level degeneracy is investigated using two different approaches. One approach is to apply a weak constant field to eliminate the degeneracy and then control it using…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…