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The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…

Statistics Theory · Mathematics 2021-10-19 Oleksandr Masyutka , Mikhail Moklyachuk

Observer design typically requires the observability of the underlying system, which may be hard to verify for nonlinear systems, while guaranteeing asymptotic convergence of errors, which may be insufficient in order to satisfy performance…

Optimization and Control · Mathematics 2017-03-23 Shankar Mohan , Jinsun Liu , Ram Vasudevan

In this paper we propose a method to estimate the initial state of a linear dynamical system with noisy observation. The method allows the user to have estimations in real time, that is, to have a new estimation for each new observation.…

Optimization and Control · Mathematics 2021-05-06 Rocío Díaz Martín , Ivan Medri , Juliana Osorio

We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…

Machine Learning · Computer Science 2024-09-26 Yahya Sattar , Yassir Jedra , Sarah Dean

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…

Functional Analysis · Mathematics 2025-12-25 Simon Foucart

We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on the strict convexity of the reachable set…

Optimization and Control · Mathematics 2011-10-04 Giovanni Colombo , Khai Tien Nguyen

We consider a situation where the state of a system is represented by a real-valued vector. Under normal circumstances, the vector is zero, while an event manifests as non-zero entries in this vector, possibly few. Our interest is in the…

Statistics Theory · Mathematics 2011-12-30 Ery Arias-Castro

We study minimax testing in a statistical inverse problem when the associated operator is unknown. In particular, we consider observations from an inverse Gaussian regression model where the associated operator is unknown but contained in a…

Statistics Theory · Mathematics 2025-09-03 Clément Marteau , Theofanis Sapatinas

The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…

Statistics Theory · Mathematics 2025-10-29 Iryna Dubovets'ka , Mykhailo Moklyachuk

In this paper we discuss the controllability of two-point boundary value problem (TBVP) for one-dimensional wave equation. Some new concepts are introduced: TBVP input control problem, minimum-input solution (MS) and pre-minimum-input…

Analysis of PDEs · Mathematics 2020-10-06 Yuyou Gan , Sisi Huang , Dexing Kong

In this paper, we consider the problem of state estimation through observations possibly corrupted with both bad data and additive observation noises. A mixed $\ell_1$ and $\ell_2$ convex programming is used to separate both sparse bad data…

Information Theory · Computer Science 2011-05-04 Weiyu Xu , Meng Wang , Ao Tang

We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…

Systems and Control · Electrical Eng. & Systems 2023-11-14 Hussein Sibai , Sayan Mitra

Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…

Methodology · Statistics 2025-04-28 Ryad Belhakem , Franck Picard , Vincent Rivoirard , Angelina Roche

In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…

Numerical Analysis · Mathematics 2021-11-01 Asha K Dond , Thirupathi Gudi , Ramesh Ch. Sau

This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…

Probability · Mathematics 2020-02-25 Jin W. Kim , Prashant G. Mehta

We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…

Optimization and Control · Mathematics 2014-11-18 Pedro Martín Merino Rosero

This paper focuses on the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of the sequence with…

Statistics Theory · Mathematics 2025-11-11 Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei

Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…

Machine Learning · Computer Science 2026-04-23 Xuelin Zhang , Peipei Yuan

This paper focuses on the state estimation problem in distributed sensor networks, where intermittent packet dropouts, corrupted observations, and unknown noise covariances coexist. To tackle this challenge, we formulate the joint…

Machine Learning · Statistics 2026-04-06 Peng Sun , Ruoyu Wang , Xue Luo

This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…

Statistics Theory · Mathematics 2023-08-01 Simon Foucart , Grigoris Paouris