Related papers: KoopGen: Koopman Generator Networks for Representi…
We use Koopman theory for data-driven model reduction of nonlinear dynamical systems with controls. We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman…
The Koopman framework proposes a linear representation of finite-dimensional nonlinear systems through a generally infinite-dimensional globally linear embedding. Originally, the Koopman formalism has been derived for autonomous systems. In…
This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…
This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis…
Data-driven model predictive control based on Willems' fundamental lemma has proven effective for linear systems, but extending stability guarantees to nonlinear systems remains an open challenge. In this paper, we establish conditions…
Gas turbine engines are complex and highly nonlinear dynamical systems. Deriving their physics-based models can be challenging because it requires performance characteristics that are not always available, often leading to many simplifying…
Advanced autonomous driving systems require accurate vehicle dynamics modeling. However, identifying a precise dynamics model remains challenging due to strong nonlinearities and the coupled longitudinal and lateral dynamic characteristics.…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the…
The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such…
Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature spaces induced by a user-chosen dictionary are rarely invariant,…
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 introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…
The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear…
Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial…
The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show…
A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…
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…
Mixed vehicle platoons, comprising connected and automated vehicles (CAVs) and human-driven vehicles (HDVs), hold significant potential for enhancing traffic performance. However, most existing control strategies assume linear system…
Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal…