Generic properties of linear control systems depending on a parameter
Geometric methods in linearization of control systems
Geometrical aspects of exact boundary controllability for the wave equation. A numerical study
Geometrical aspects of exact boundary controllability for the wave equation - a numerical study
This essentially numerical study, sets out to investigate various geometrical properties of exact boundary controllability of the wave equation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry of the controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and an energetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical solutions...
Global boundary controllability of the de St. Venant equations between steady states
Global Carleman estimate for stochastic parabolic equations, and its application
This paper is addressed to proving a new Carleman estimate for stochastic parabolic equations. Compared to the existing Carleman estimate in this respect (see [S. Tang and X. Zhang, SIAM J. Control Optim. 48 (2009) 2191–2216.], Thm. 5.2), one extra gradient term involving in that estimate is eliminated. Also, our improved Carleman estimate is established by virtue of the known Carleman estimate for deterministic parabolic equations. As its application, we prove the existence of insensitizing controls...
Global controllability and stabilization for the nonlinear Schrödinger equation on an interval
We prove global internal controllability in large time for the nonlinear Schrödinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use Bourgain spaces to prove this result on L2. We also get a regularity result about the control if the data are assumed smoother.
Global controllability properties for the semilinear heat equation with superlinear term.
We discuss several global approximate controllability properties for the semilinear heat equation with superlinear reaction-convection term, governed in a bounded domain by locally distributed controls. First, based on the asymptotic analysis in vanishing time, we study the steering of the projections of its solution on any finite dimensional space spanned by the eigenfunctions for the truncated linear part. We show that, if the control-supporting area is properly chosen, then they can approximately...
Global existence and controllability to a stochastic integro-differential equation.
Globality in semisimple Lie groups
In the first section of this paper we give a characterization of those closed convex cones (wedges) in the Lie algebra which are invariant under the maximal compact subgroup of the adjoint group and which are controllable in the associated simply connected Lie group , i.e., for which the subsemigroup generated by the exponential image of agrees with the whole group (Theorem 13). In Section 2 we develop some algebraic tools concerning real root decompositions with respect to compactly...
Heavy viable trajectories of controlled systems
High order inverse function theorems
High-Order Control Variations and Small-Time Local Controllability
The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is studied and...
Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft.
Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques
Dans ce travail, nous donnons une estimation logarithmique des données de la solution u, d'un problème hyperbolique avec condition aux limites de type Neumann, par la trace de u restreinte à un ouvert du bord, pendant un temps suffisamment grand qui nous permet d'estimer la fonction de coût de ce problème.
Inégalités de Carleman globales pour les problèmes elliptiques non homogènes
On établit ici, suivant [5], une inégalité de Carleman globale optimale pour les solutions faibles (au sens ) d’équations elliptiques générales avec second membre dans et trace non nulle.La motivation, qui est expliquée dans l’introduction, réside dans l’obtention d’inégalités de Carleman globale pour l’opérateur de Navier-Stokes linéarisé afin, notamment, d’étudier les questions de contrôlabilité exacte sur les trajectoires pour les équations de Navier-Stokes. Une étape majeure consiste à obtenir...
Ingham-type inequalities and Riesz bases of divided differences
We study linear combinations of exponentials e^{iλ_nt} , λ_n ∈ Λ in the case where the distance between some points λ_n tends to zero. We suppose that the sequence Λ is a finite union of uniformly discrete sequences. In (Avdonin and Ivanov, 2001), necessary and sufficient conditions were given for the family of divided differences of exponentials to form a Riesz basis in space L^2 (0,T). Here we prove that if the upper uniform density of Λ is less than T/(2π), the family of divided differences can...
Integral observability operators of nonlinear dynamical systems.
Interior controllability of a reaction-diffusion system with cross-diffusion matrix.
Interior controllability of a broad class of reaction diffusion equations.