On the control of stability in nonlinear mechanics
On the controllability and stabilization of the linearized Benjamin-Ono equation
In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law which...
On the controllability and stabilization of the linearized Benjamin-Ono equation
In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law...
On the controllability of a differential equation with delayed and advanced arguments.
On the controllability of a slowly rotating Timoshenko beam.
On the controllability of a type of large scale CNN with delays.
On the controllability of fractional dynamical systems
This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.
On the controllability of the 1-D isentropic Euler equation
We study the controllability problem for the one-dimensional Euler isentropic system, both in Eulerian and Lagrangian coordinates, by means of boundary controls, in the context of weak entropy solutions. We give a sufficient condition on the initial and final states under which the first one can be steered to the latter.
On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions
On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions
For boundary or distributed controls, we get an approximate controllability result for the Navier-Stokes equations in dimension 2 in the case where the fluid is incompressible and slips on the boundary in agreement with the Navier slip boundary conditions.
On the controllability of the burger equation
On the controllability of the Burger equation
We present here a return method to describe some attainable sets on an interval of the classical Burger equation by means of the variation of the domain.
On the controllability of the fifth-order Korteweg-de Vries equation
On the controllability of the Laplace equation observed on an interior curve.
The boundary approximate controllability of the Laplace equation observed on an interior curve is studied in this paper. First we consider the Laplace equation with a bounded potential. The Lp (1 < p < ∞) approximate controllability is established and controls of Lp-minimal norm are built by duality. At this point, a general result which clarifies the relationship between this duality approach and the classical optimal control theory is given. The results are extended to the Lp (1≤...
On the controllability under constraints on the control for hyperbolic equations.
On the convergence of a time-variant linear differential equation arising in identification
On the cost of null-control of an artificial advection-diffusion problem
In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.
On the cover problems of geometric theory
On the decentralized stabilization of interconnected discrete time systems
On the decoupling of one class of multivariable systems