Related papers: Koopman Model Dimension Reduction via Variational …

Nonlinear Negative Imaginary (NI) systems arise in various engineering applications, such as controlling flexible structures and air vehicles. However, unlike linear NI systems, their theory is not well-developed. In this paper, we propose…

A new approach to data-driven discovery of Koopman eigenfunctions without a pre-defined set of basis functions is proposed. The approach is based on a reference trajectory, for which the Koopman mode amplitudes are first identified, and the…

This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems. We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying…

Model-based diagnosis reasons backwards from a functional schematic of a system to isolate faults given observations of anomalous behavior. We develop a fully probabilistic approach to model based diagnosis and extend it to support…

A data driven, kernel-based method for approximating the leading Koopman eigenvalues, eigenfunctions, and modes in problems with high dimensional state spaces is presented. This approach approximates the Koopman operator using a set of…

Constraint handling during tracking operations is at the core of many real-world control implementations and is well understood when dynamic models of the underlying system exist, yet becomes more challenging when data-driven models are…

This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a…

An efficient way to control systems with unknown nonlinear dynamics is to find an appropriate embedding or representation for simplified approximation (e.g. linearization), which facilitates system identification and control synthesis.…

Mobile robot navigation can be challenged by system uncertainty. For example, ground friction may vary abruptly causing slipping, and noisy sensor data can lead to inaccurate feedback control. Traditional model-based methods may be limited…

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…

This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…

Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…

Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…

Given the complexity and nonlinearity inherent in traffic dynamics within vehicular platoons, there exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability. Currently, there…

We present a data-driven shared control algorithm that can be used to improve a human operator's control of complex dynamic machines and achieve tasks that would otherwise be challenging, or impossible, for the user on their own. Our method…

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…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional…