Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses.
Boundary observability for the space semi-discretizations of the wave equation
Boundary observability for the space semi-discretizations of the 1 – d wave equation
We consider space semi-discretizations of the 1-d wave equation in a bounded interval with homogeneous Dirichlet boundary conditions. We analyze the problem of boundary observability, i.e., the problem of whether the total energy of solutions can be estimated uniformly in terms of the energy concentrated on the boundary as the net-spacing h → 0. We prove that, due to the spurious modes that the numerical scheme introduces at high frequencies, there is no such a uniform bound. We prove however a...
Boundary observability of a numerical approximation scheme of Maxwell's system in a cube
Carleman estimates and boundary observability for a coupled parabolic-hyperbolic system.
Carleman estimates for the Euler-Bernoulli plate operator.
Categorical approach to nonlinear constant continuous-time systems
Continuity of solutions of Riccati equations for the discrete-time JLQP
The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems.
Continuous-time deadbeat observation problem with application to predictive control of systems with delay
Control for Schrödinger operators on 2-tori: rough potentials
For the Schrödinger equation, on a torus, an arbitrary non-empty open set provides control and observability of the solution: . We show that the same result remains true for where , and is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for and conjectured for . The higher dimensional generalization remains open for .
Contrôle et stabilisation d'ondes électromagnétiques
We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.
Controllability and observability of control systems under uncertainty
Controllability and observability of linear delay systems : an algebraic approach
Controllability and observability of linear delay systems: an algebraic approach
Interpretations of most existing controllability and observability notions for linear delay systems are given. Module theoretic characterizations are presented. This setting enables a clear and precise comparison of the various examined notions. A new notion of controllability is introduced, which is called pi-freeness.
Controllability and observability of linear discrete-time fractional-order systems
In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.
Controllability and observability of time-invariant linear dynamic systems
In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.
Controllability, observability and optimal control of continuous-time 2-D systems
We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data....
Controllability, observability, realizability, and stability of dynamic linear systems.
Controllability of a simplified model of fluid-structure interaction
This article aims at studying the controllability of a simplified fluid structure interaction model derived and developed in [C. Conca, J. Planchard and M. Vanninathan, RAM: Res. Appl. Math. John Wiley & Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, ESAIM: COCV 11 (2005) 180–203; M. Tucsnak and M. Vanninathan, Systems Control Lett. 58 (2009) 547–552]. This interaction is modeled by a wave equation surrounding a harmonic oscillator. Our main result states that, in the radially...
Convergence of a two-grid algorithm for the control of the wave equation
We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d wave equation in the square. We prove the uniform (with respect to the meshsize) boundary observability for the solutions obtained by the two-grid preconditioner introduced by Glowinski [9]. Our method uses previously known uniform observability inequalities for low frequency solutions and a dyadic spectral time decomposition. As a consequence we prove the convergence of the two-grid algorithm...