Stabilization of partially linear composite stochastic systems via stochastic Luenberger observers

summary:The present paper addresses the problem of the stabilization (in the sense of exponential stability in mean square) of partially linear composite stochastic systems by means of a stochastic observer. We propose sufficient conditions for the existence of a linear feedback law depending on an estimation given by a stochastic Luenberger observer which stabilizes the system at its equilibrium state. The novelty in our approach is that all the state variables but the output can be corrupted by noises whereas in the previous works at least one of the state variable should be unnoisy in order to design an observer

Exponential mean square stability of partially linear stochastic systems

AbstractThe purpose of this paper is to state sufficient conditions for the existence of linear feedback laws which render the equilibrium solution of a composite partially linear stochastic system (the linear part of which is deterministic) exponentially stable in mean square

Particle approximation for first order stochastic partial differential equations

Projet MEFISTODisponible dans les fichiers attachés à ce documen

Time discretization of the Zakai equation for diffusion processes observed in correlated noise

International audienceA time discretization scheme is provided for the Zakai equation, a stochastic PDE which gives the conditional law of a diffusion process observed in white-noise. The case where the observation noise and the state noise are correlated, is considered. The numerical scheme is based on a Trotter-like product formula, which exhibits prediction and correction steps, and for which an error estimate of order δ is proved, where δ is the time discretization step. The correction step is associated with a degenerate second-order stochastic PDE, for which a representation result is available in terms of stochastic characteristics. A discretization scheme is then provided to approximate these stochastic characteristics. Under an additional assumption on the correlation coefficient, an error estimate of order √δ is proved for the overall numerical scheme. This has been proved to be the best possible error estimate by Elliott and Glowinski

Filtrage non lineaire avec bruits correles et observation non bornee : etude numerique d'une equation de Zakai

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions

The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic dif- ferential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic–Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002)

Continuity of the Filter with Unbounded Observation Coefficients

In this article, we study the continuity with respect to the trajectories of the observation process for the filter associated with nonlinear filtering problems when the coefficients depend on both the signal and the observation and the observation coefficient is unbounded. To achieve this task we define a formal unnormalized filter and prove by limiting arguments that it is related to the original filter through a generalized Bayes formula, and is locally Lipschitz continuous with respect to the uniform norm