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This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system…

Koopman operators, since introduced by the French-born American mathematician Bernard Koopman in 1931, have been employed as a powerful tool for research in various scientific domains, such as ergodic theory, probability theory, geometry,…

While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…

Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…

This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…

Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of nonlinear dynamic behavior (e.g. through normal forms). In…

A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…

This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics…

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…

This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…

The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both discrete and continuous spectra, complicating direct…

This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…

The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the recent development of the Koopman model…

In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a dynamical system. The proposed approach relies on the linear lifting of a nonlinear system using linear Perron-Frobenius (P-F) and…

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to…

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens of…

This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…