Related papers: Data-driven Reachability Verification with Probabi…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…
The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system.…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
Robot manipulators operating in uncertain and non-convex environments present significant challenges for safe and optimal motion planning. Existing methods often struggle to provide efficient and formally certified collision risk…
It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the…
Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network…
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under…
In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic…
This paper presents a data-driven model predictive control framework for mobile robots navigating in dynamic environments, leveraging Koopman operator theory. Unlike the conventional Koopman-based approaches that focus on the linearization…
Reachability analysis is a popular method to give safety guarantees for stochastic cyber-physical systems (SCPSs) that takes in a symbolic description of the system dynamics and uses set-propagation methods to compute an overapproximation…
This short note gives a new framework for dealing with nonlinear sampled-data systems. We introduce a new idea of lifting, which is well known for linear systems, but not successfully generalized to nonlinear systems. This paper introduces…
Conserved quantities, i.e. constants of motion, are critical for characterizing many dynamical systems in science and engineering. These quantities are related to underlying symmetries and they provide fundamental knowledge about physical…
Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have shown great success thanks to their ability to approximate…
Reachability analysis has been a prominent way to provide safety guarantees for neurally controlled autonomous systems, but its direct application to neural perception components is infeasible due to imperfect or intractable perception…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
In recent years data-driven analysis of dynamical systems has attracted a lot of attention and transfer operator techniques, namely, Perron-Frobenius and Koopman operators are being used almost ubiquitously. Since data is always obtained in…
We propose a novel targeted exploration strategy designed specifically for uncertain linear time-invariant systems with energy-bounded disturbances, i.e., without any assumptions on the distribution of the disturbances. We use classical…
Detecting anomalies and discovering driving signals is an essential component of scientific research and industrial practice. Often the underlying mechanism is highly complex, involving hidden evolving nonlinear dynamics and noise…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…