Solutions to Lyapunov stability problems of sets: Nonlinear systems with differentiable motions.
Solvable optimal control of Brownian motion in symmetric spaces and spherical polynomials
Some algorithmic aspects of subspace identificationwith inputs
It has been experimentally verified that most commonly used subspace methods for identification of linear state-space systems with exogenous inputs may, in certain experimental conditions, run into ill-conditioning and lead to ambiguous results. An analysis of the critical situations has lead us to propose a new algorithmic structure which could be used either to test difficult cases andor to implement a suitable combination of new and old algorithms presented in the literature to help fixing the...
Some applications of Girsanov's theorem to the theory of stochastic differential inclusions
The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.
Some boundary optimal control problems related to a singular cost functional
Some controllability results for the 2D Kolmogorov equation
Some controllability results for the relativistic Vlasov-Maxwell system
The goal of this note is to present the recent results concerning the controllability of the Vlasov-Maxwell system, which are proved in the paper [10] by Olivier Glass and the author.
Some decay properties for the damped wave equation on the torus
This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...
Some fundamental notions of large variable systems
Some geometrical properties of infinite-dimensional bilinear controlled systems
The study of controlled infinite-dimensional systems gives rise to many papers (see for instance [GXL], [GXB], [X]) but it is also motivated by various mathematical problems: partial differential equations ([BP]), sub-Riemannian geometry on infinite-dimensional manifolds ([Gr]), deformations in loop-spaces ([AP], [PS]). The first difference between finite and infinite-dimensional cases is that solutions in general do not exist (even locally) for every given control function. The aim of this paper...
Some ideas for comparison of Bellman chains
In this paper we are exploiting some similarities between Markov and Bellman processes and we introduce the main concepts of the paper: comparison of performance measures, and monotonicity of Bellman chains. These concepts are used to establish the main result of this paper dealing with comparison of Bellman chains.
Some inverse and control problems for fluids
This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.
Some inverse mapping theorems
Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks
This paper investigates the output controllability problem of temporal Boolean networks with inputs (control nodes) and outputs (controlled nodes). A temporal Boolean network is a logical dynamic system describing cellular networks with time delays. Using semi-tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems. Some necessary and sufficient conditions on the output controllability via two kinds of inputs are obtained by providing...
Some new results in state space decoupling of multivariable systems. I. A link between geometric approach and matrix methods
Some new results in state space decoupling of multivariable systems. II. Extensions to decoupling of systems with and output feedback decoupling
Some new results related to the null controllability of the heat equation
We address three null controllability problems related to the heat equation. First we show that the heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation can be obtained...
Some optimal control applications of real-analytic stratifications and desingularization
Some problems in modelling of real systems by formalized ones
Some problems of system identification