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We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust $H_\infty$ estimation for…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…
Duality of control and estimation allows mapping recent advances in data-guided control to the estimation setup. This paper formalizes and utilizes such a mapping to consider learning the optimal (steady-state) Kalman gain when process and…
This paper introduces a unified approach for state estimation and control of nonlinear dynamic systems, employing the State-Dependent Riccati Equation (SDRE) framework. The proposed approach naturally extends classical linear quadratic…
We consider the problem of selecting an optimal set of sensor precisions to estimate the states of a non-linear dynamical system using an Ensemble Kalman filter and an Unscented Kalman filter, which uses random and deterministic ensembles…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schr\"odinger-type equations, in the $L^\infty(L^2)-$norm. For the discretization in time we use the Crank-Nicolson method, while for the space…
In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…
In the remote state estimation problem, an observer tries to reconstruct the state of a dynamical system at a remote location, where no direct sensor measurements are available. The observer only has access to information sent through a…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
In this paper, we address a partition-based distributed state estimation problem for large-scale general nonlinear processes by proposing a Kalman-based approach. First, we formulate a linear full-information estimation design within a…
Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…
We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of…
In this report we address the linear state estimation problem: to estimate a linear transformation $\ell(\varphi)$ of the state $\varphi$ through an algorithm $\widehat{\ell(\varphi)}$ operating on measurements $y$, where…
Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are…
We derive an equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. In the idealized setting where time discretization is ignored and the simulation time is large, we…
System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible leading to a dual-estimation problem.…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
Nonlinear filtering problems are encountered in many applications, and one solution approach is the extended Kalman filter, which is not always convergent. Therefore, it is crucial to identify conditions under which the extended Kalman…