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Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…
This paper investigates the distributionally robust filtering of signals generated by state-space models driven by exogenous disturbances with noisy observations in finite and infinite horizon scenarios. The exact joint probability…
This paper presents a state estimation approach for an uncertain linear equation with a non-invertible operator in Hilbert space. The approach addresses linear equations with uncertain deterministic input and noise in the measurements,…
Systems equipped with modern sensing modalities such as vision and lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of…
This article is concerned with the convergence of the state estimate obtained from the discrete time Kalman filter to the continuous time estimate as the temporal discretization is refined. We derive convergence rate estimates for different…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
This paper studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer the $n$-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of optimal steady-state…
This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the…
The paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain…
A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface…
In this technical note, we prove that the ODEFTC algorithm constitutes the first optimal distributed state estimator for continuous-time linear time-varying systems subject to stochastic disturbances. Particularly, we formally show that it…
In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any…
This paper describes a method for the online state estimation of systems described by a general class of linear noncausal time-varying difference descriptor equations subject to uncertainties. The method is based on the notions of a linear…
State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
Given a plant subject to delayed sensor measurement, there are several approaches to compensate for the delay. An obvious approach is to address this problem in state space, where the $n$-dimensional plant state is augmented by an…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…