In this seminar, we will introduce the Dynamical Sampling Problem and explore its connections with the Observability Problem in Control Theory. Essentially, the task is that of recovering the initial state of a dynamical system. To establish a "dictionary" between these two areas, we will review key concepts such as exact and approximate controllability, Gramian matrices, Bessel sequences in Hilbert spaces, and frames. By analyzing the interplay between these two perspectives, we will uncover relations between discrete-time and continuous-time dynamical systems, utilizing insights from both fields and our established dictionary. Additionally, time permitting, we will present a simple method, based on Kalman filter techniques, for estimating the initial state of a linear dynamical system using noisy observations. The seminar will cover aspects of joint work with Ivan Medri (Vanderbilt University, USA), Ursula Molter (Universidad de Buenos Aires, Argentina), and Juliana Osorio (Universidad de Buenos Aires, Argentina).

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* Os participantes dos seminários não poderão acessar às dependências da FGV usando bermuda, chinelos, blusa modelo top ou cropped, minissaia ou camiseta regata. O uso da máscara é facultativo, porém é obrigatória a apresentação do comprovante de vacinação (físico ou digital).