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The Kalman filter computes the optimal variable-gain using prior knowledge of the initial state and random (process and measurement) noise distributions, which are assumed to be Gaussian with known variance. However, when these…
Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…
We demonstrate that the extended Kalman filter converges locally for a broad class of nonlinear systems. If the initial estimation error of the filter is not too large then the error goes to zero exponentially as time goes to infinity. To…
Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper…
We derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. We provide the first analysis of the general case when eigenvalues of the LTI…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
This document presents the study of the problem of location and trajectory that a robot must follow. It focuses on applying the Kalman filter to achieve location and trajectory estimation in an autonomous mobile differential robot. The…
Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this…
The Highly-Adaptive-Lasso(HAL)-TMLE is an efficient estimator of a pathwise differentiable parameter in a statistical model that at minimal (and possibly only) assumes that the sectional variation norm of the true nuisance parameters are…
In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not…
The subspace identification method (SIM) has been extensively employed in the identification of discrete-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. This paper focuses on the analysis of perturbation…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
One of the primary challenges of system identification is determining how much data is necessary to adequately fit a model. Non-asymptotic characterizations of the performance of system identification methods provide this knowledge. Such…
In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
This paper addresses the problem of identifying linear systems from noisy input-output trajectories. We introduce Thresholded Ho-Kalman, an algorithm that leverages a rank-adaptive procedure to estimate a Hankel-like matrix associated with…
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
We present the first finite-sample analysis of policy evaluation in robust average-reward Markov Decision Processes (MDPs). Prior work in this setting have established only asymptotic convergence guarantees, leaving open the question of…