An estimation problem is considered for a stochastic parabolic equation with an unknown random coefficient. The additional randomness in the coefficient generalizes a popular estimation problem that has been extensively studied in recent years. The filter estimate of the coefficient is constructed from a finite-dimensional projection of the solution of the equation. Under certain conditions thi...

There are several functional forms for non-linear dynamical filters. Extended Kalman filters algorithms that used to estimate more accurate values of unknown quantities internal systems from a sequence noisy observation measured over period time. This filtering process becomes computationally expensive when subjected high dimensional data which consequently has negative impact on the filter per...

This paper proposes a distributed secondary voltage control method based on extended state Kalman-Bucy filter (ESKBF) and fast terminal sliding mode (FTSM) for the resilient operation of an islanded microgrid (MG) with inverter-based generations (DGs). To tackle co-existence multiple uncertainties, unified modelling framework is proposed to represent set different types disturbances, including ...

In this paper, we study a generalized Kalman--Bucy filtering problem under uncertainty. The drift uncertainty for both signal process and observation is considered, the attitude to characterized by convex operator (convex risk measure). optimal filter or minimum mean square estimator (MMSE) calculated solving estimation operator. first part of studied $g$-expectation which special For case, pro...

Preface These lecture notes are concerned with state estimation problem of linear and particularly nonlinear discrete and continuous-discrete stochastic systems. State estimation has a great variety of applications including The general solution of the state estimation problem is based on the Bayesian recursive relations and the Fokker-Planck equation which generate conditional probability dens...

BACKGROUND Intensive chemotherapy frequently results in gut toxicity, indicated by oral and intestinal mucositis, resulting in poor treatment outcomes and increased mortality. There are no effective preventive strategies against gut toxicity and the role of diet is unknown. OBJECTIVE We hypothesized that the severity of chemotherapy-induced gut toxicity in early life is diet-dependent, and th...

In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of the Langevin SDE used in finite dimensional sampling. Here the theory is developed for conditioned Gaussian processes for which the resulting SPDE is linear...

This paper presents an algorithm for synchronizing two different chaotic systems by using a combination of Unscented Kalman–Bucy Filter (UKBF) and sliding mode controller. It is assumed that the drive chaotic system is perturbed by white noise and shows stochastic chaotic behavior. In addition the output of the system does not contain the whole state variables of the system, and it is also affe...