Related papers: Control of Kawahara equation using flat outputs
We prove the exact controllability of linear KP-I equation if the control input is added on a vertical domain. More generally, we have obtained the least dispersion needed to insure observability for fractional linear KP I equation.
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
Flatness-based control design is a well established method to generate open-loop control signals. Several articles discuss the application of flatness-based control design of (reaction-) diffusion problems for various scenarios. Beside the…
Local exact controllability of the 1D NLS (subject to zero boundary conditions) with distributed control is shown to hold in a $H^1$--neighbourhood of the nonlinear ground state. The Hilbert Uniqueness Method (HUM), due to J.-L. Lions, is…
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.…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
Using the properties of differential flatness, a controllable system, such as a quadcoper model, may be transformed into a linear equivalent system via a coordinate change and an input mapping. This is a straightforward advantage for the…
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the…
We investigate a class of higher-order nonlinear dispersive equations posed on the circle, subject to additive forcing by a finite-dimensional control. Our main objective is to establish approximate controllability by using the…
This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the…
We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding…
An alternative formulation for the controllability problem of single input linear positive systems is presented. Driven by many industrial applications, this formulations focuses on the case where the region of interest is only a subset of…
The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…
This article will deal with the stabilization problem for the higher-order dispersive system, commonly called the Kawahara equation. To do so, we introduce a damping mechanism via a distributed memory term in the equation to prove that the…
This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…
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…
In this paper, motivated by a physics problem, we investigate some numerical and computational aspects for the problem of hierarchical controllability in a one-dimensional wave equation in domains with a moving boundary. Some controls act…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
In this paper, we study some controllability and observability properties for a coupled system of time-discrete fourth- and second-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized…
This paper is devoted to study boundary controllability of the Korteweg-de Vries equation posed on a finite interval, in which, because of the third-order character of the equation, three boundary conditions are required to secure the…