Exact controllability of a second-order integro-differential equation with a pressure term.
Exact controllability of an elastic membrane coupled with a potential fluid
We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the elastic membrane to insure that the uncoupled membrane is exactly controllable. The main result is that if the density of the fluid is sufficiently small, then the coupled system is exactly controllable....
Exact controllability of the linear elasticity system with evolutive Ventcel conditions. (Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité.)
Exact controllability of the radial solutions of the semilinear wave equation in R3.
The exact internal controllability of the radial solutions of a semilinear heat equation in R3 is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.
Exact controllability of the wave equation in a thin domain with a wave-like boundary. (Contrôlabilité exacte de l'équation des ondes dans un domaine mince à frontière ondulée.)
Exact controllability of the wave equation with Neumann boundary condition and time-dependent coefficients
Exact controllability of vibrations of thin bodies.
Exact decomposition of linear singularly perturbed -optimal control problem
Exact internal controllability of the elasticity system.
Exact null controllability of structurally damped and thermo-elastic parabolic models
We show exact null-controllability for two models of non-classical, parabolic partial differential equations with distributed control: (i) second-order structurally damped equations, except for a limit case, where exact null controllability fails; and (ii) thermo-elastic equations with hinged boundary conditions. In both cases, the problem is solved by duality.
Exact null internal controllability for the heat equation on unbounded convex domains
The liner parabolic equation ∂y ∂t − 1 2 Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.
Exact observability of diagonal systems with a one-dimensional output operator
In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.
Example of the function (behaviour) of a system element consisting in rudimentary properties. I
Existence and determination of the set of Metzler matrices for given stable polynomials
The problem of the existence and determination of the set of Metzler matrices for given stable polynomials is formulated and solved. Necessary and sufficient conditions are established for the existence of the set of Metzler matrices for given stable polynomials. A procedure for finding the set of Metzler matrices for given stable polynomials is proposed and illustrated with numerical examples.
Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays
Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.
Existence of classical solutions and feedback stabilization for the flow in gas networks
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
Existence of classical solutions and feedback stabilization for the flow in gas networks
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
Existence of different kind of solutions for discrete time equations
The aim of this paper is to extend the classical linear condition concerning diagonal dominant bloc matrix to fully nonlinear equations. Even if assumptions are strong, we obtain an explicit condition which exactly extend the one known in linear case, and the setting allows also to consider bicontinuous operator instead of the schift and as particular case, we receive periodic or almost periodic solutions for discrete time equations.
Existence of optimal controls for control systems governed by nonlinear partial differential equations
Existence of optimal solutions in general discrete systems