Related papers: Estimating initial conditions for dynamical system…

This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or partially known. In particular, we focus on the design of data-driven…

Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…

The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. This is entirely a data-driven approach that extracts all necessary information from data snapshots which are commonly supposed to be sampled…

In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi…

This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system…

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…

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…

We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…

The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

The problem of state estimation has a long history with many successful algorithms that allow analytical derivation or approximation of posterior filtering distribution given the noisy observations. This report tries to conclude previous…

This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…

The study of theoretical conditions for recovering sparse signals from compressive measurements has received a lot of attention in the research community. In parallel, there has been a great amount of work characterizing conditions for the…

Takens' Embedding Theorem asserts that when the states of a hidden dynamical system are confined to a low-dimensional attractor, complete information about the states can be preserved in the observed time-series output through the delay…

We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…

Internal ice layers imaged by radar provide key evidence of snow accumulation and ice dynamics, but radar-derived layer boundary observations are often incomplete, with discontinuous traces and sometimes entirely missing layers, due to…

This paper proposes a simple interval observer which can generate tighter interval estimates of variables in transient states than the standard interval observer. The simple nonlinear dynamics shrinks the estimated intervals to true state…

Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…