Evaluation of the reachability subspace of general form polynomial matrix descriptions (PMDs)
Exact boundary controllability for quasilinear wave equations in a planar tree-like network of strings
Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
The exact boundary controllability of linear and nonlinear Korteweg-de Vries equation on bounded domains with various boundary conditions is studied. When boundary conditions bear on spatial derivatives up to order 2, the exact controllability result by Russell-Zhang is directly proved by means of Hilbert Uniqueness Method. When only the first spatial derivative at the right endpoint is assumed to be controlled, a quite different analysis shows that exact controllability holds too. From...
Exact boundary controllability of 3-D Euler equation
Exact boundary controllability of 3-D Euler equation
We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.
Exact boundary controllability of a hybrid system of elasticity by the HUM method
We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.
Exact Boundary Controllability of a Hybrid System of elasticity by the HUM Method
We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.
Exact boundary controllability of a nonlinear KdV equation with critical lengths
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
Exact boundary controllability of coupled hyperbolic equations
We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.
Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations
Exact boundary synchronization for a coupled system of 1-D wave equations
Several kinds of exact synchronizations and the generalized exact synchronization are introduced for a coupled system of 1-D wave equations with various boundary conditions and we show that these synchronizations can be realized by means of some boundary controls.
Exact controllability for a nonlinear stochastic wave equation.
Exact controllability for a semilinear wave equation with both interior and boundary controls.
Exact controllability for semilinear wave equations in one space dimension
Exact controllability for temporally wave equation.
Exact controllability for the equation of the one dimensional plate in domains with moving boundary.
Exact controllability for the semilinear string equation in non cylindrical domains
Exact controllability for the wave equation in domains with variable boundary.
Exact controllability in fluid – solid structure: The Helmholtz model
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability...