The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Observers are computational algorithms designed to estimate unmeasured state variables
due to the lack of appropriate estimating devices or to replace high-priced sensors in a plant …

In this paper we develop a new approach for observer synthesis for discrete time
autonomous nonlinear systems based on Koopman operator theoretic framework. Koopman …

We propose a new observer form based on Koopman operator theoretic framework for input-
output nonlinear systems with control affine inputs. Based on this observer form, we describe …

This paper addresses the problems of navigation and source localization by mobile agents
based on the range to a single source, in addition to relative velocity readings. The …

Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …

Abstract The Koopman and Perron Frobenius transport operators are fundamentally
changing how we approach dynamical systems, providing linear representations for even …

Why do some mental activities feel harder than others? The answer to this question is
surprisingly controversial. Current theories propose that cognitive effort affords a …

Air quality has been an important issue in public health for many years. Sensing the level
and distributions of impurities help in the control of building systems and mitigate long term …

This thesis is concerned with the stochastic filtering problem for a hidden Markov model
(HMM) with the white noise observation model. For this filtering problem, we make three …