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...

In this paper, the reduced order unbiased optimal H∞ filtering problem for discrete-time descriptor linear systems is considered. Necessary and sufficient conditions for the existence of unbiased causal time invariant filters are obtained. Solutions of the filtering problems are given in terms of linear matrix inequalities (LMIs). Parametrization of all optimal causal unbiased filters is provid...

Abstract: In this paper, robust H2 optimal filtering is addressed for continuoustime stochastic systems with polytopic parameter uncertainty. A new robust stability condition is presented. A continuous-time robust H2 optimal filter is obtained by solving a sufficient linear matrix inequality condition characterizing a solution of a minimum variance filtering problem which takes into account the...

This article is a survey of the early development of selected areas in nonlinear continuous-time stochastic control. Key developments in optimal control and the dynamic programming principle, existence of optimal controls under complete and partial observations, nonlinear filtering, stochastic stability, the stochastic maximum principle and ergodic control are discussed. Issues concerning wide ...

Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closed-form expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the optimal filtering problem numerically. The posterior distribution of the state is approximated by ...

In this paper, we present an optimal filter for the enhancement or estimation of signals on the 2-sphere corrupted by noise, when both the signal and noise are realizations of anisotropic processes on the 2-sphere. The estimation of such a signal in the spatial or spectral domain separately can be shown to be inadequate. Therefore, we develop an optimal filter in the joint spatio-spectral domai...

A theory for optimal filtering of infinite sets of random signals is presented. There are several new distinctive features of the proposed approach. First, a single optimal filter for processing any signal from a given infinite signal set is provided. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Ea...

Nonlinear target tracking is a well known problem and its Bayes optimal solution, based on particle filtering techniques, is nowadays applied in high performance surveillance systems. Oftentimes, additional information about the environment and the target is available, and can be formalized in terms of constraints on target dynamics. Hence, a Constrained version of the Bayesian Filtering proble...

A simple design method for robust PID controllers is presented. It is based on a multi criteria H∞ optimal control formulation, which is shown to be easily solved by a few lines of MATLAB code. This optimal solution for PID controllers including low pass filtering, is complemented by a simple paper and pen solution that can be used to obtain nearly optimal solutions. The presented approach is s...