Related papers: Identification of Linear Systems with Multiplicati…
This paper proposes an identification algorithm for Single Input Single Output (SISO) Linear Time-Invariant (LTI) systems. In the noise-free setting, where the first $T$ Markov parameters can be precisely estimated, all Markov parameters…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
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…
This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…
The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires only one additional column of the system matrix in each…
We develop the no-propagate algorithm for sampling the linear response of random dynamical systems, which are non-uniform hyperbolic deterministic systems perturbed by noise with smooth density. We first derive a Monte-Carlo type formula…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
In this study, we consider the experimentally-obtained, periodically-forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions…
We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic…
This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
The algorithm with compensation of parametric uncertainties, external disturbances and measurement noises for linear time-invariant plants is designed. It is assumed, that the dimension of the noise can be equaled to the state vector…
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…
We assume a second-order source separation model where the observed multivariate time series is a linear mixture of latent, temporally uncorrelated time series with some components pure white noise. To avoid the modelling of noise, we…
This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
We propose a policy iteration algorithm for solving the multiplicative noise linear quadratic output feedback design problem. The algorithm solves a set of coupled Riccati equations for estimation and control arising from a partially…
We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus…
This paper proposes a new multi-linear projection method for denoising and estimation of high-dimensional matrix-variate factor time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent,…
When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…