Bang-bang control of a second-order non-linear stable plant with second-order nonlinearity
Behaviour near the boundary for solutions of elasticity systems.
Bilateral polynomial equations with unimodular right-hand-side matrices
Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.
Bilinear characterizations of companion matrices
Companion matrices of the second type are characterized by properties that involve bilinear maps.
Boundary control of the Maxwell dynamical system : lack of controllability by topological reasons
Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons
The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain Ω ⊂ R3. Let ΩT ⊂ Ω be the subdomain filled by waves at the moment T, T* the moment at which the waves fill the whole of Ω. The following effect occurs: for small enough T the system is approximately controllable in ΩT whereas for larger T < T* a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics of ΩT.
Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain
Boundary controllability in problems of transmission for a class of second order hyperbolic systems
Boundary controllability in problems of transmission for a class of second order hyperbolic systems
We consider transmission problems for general second order linear hyperbolic systems having piecewise constant coefficients in a bounded, open connected set with smooth boundary and controlled through the Dirichlet boundary condition. It is proved that such a system is exactly controllable in an appropriate function space provided the interfaces where the coefficients have a jump discontinuity are all star-shaped with respect to one and the same point and the coefficients satisfy a certain...
Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses.
Boundary controllability of hyperbolic equations.
Boundary controllability of nonlinear fractional integrodifferential systems.
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Boundary exact controllability for a porous elastic Timoshenko system
In this paper, we consider a one-dimensional system governed by two partial differential equations. Such a system models phenomena in engineering, such as vibrations in beams or deformation of elastic bodies with porosity. By using the HUM method, we prove that the system is boundary exactly controllable in the usual energy space. We will also determine the minimum time allowed by the method for the controllability to occur.
Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach
In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...
Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach
In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...
Boundary sentinels in cylindrical domains.
We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains pollution terms in the boundary data and missing terms in the initial data. The method of sentinels'' of J. L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value...
Boundary sentinels with given sensitivity.
Boundary stabilization of Maxwell’s equations with space-time variable coefficients
We consider the stabilization of Maxwell’s equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard” identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks.