Related papers: Koopman Autoencoders with Continuous-Time Latent D…
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,…
Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…
This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We…
The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion…
Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary…
Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
In this paper, a unified batch-online learning approach is introduced to learn a linear representation of nonlinear system dynamics using the Koopman operator. The presented system modeling approach leverages a novel incremental…
In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict…
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…
The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing…
This paper introduces an input-output bilinear Koopman realization with an optimization algorithm of lifting functions. For nonlinear systems with inputs, Koopman-based modeling is effective because the Koopman operator enables a…
Many machine learning approaches for decision making, such as reinforcement learning, rely on simulators or predictive models to forecast the time-evolution of quantities of interest, e.g., the state of an agent or the reward of a policy.…
This paper presents a Koopman-based model predictive control (MPC) framework for safe UAV navigation in dynamic environments using real-time LiDAR data. By leveraging the Koopman operator to linearly approximate the dynamics of surrounding…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…
Achieving rapid and time-deterministic stabilization for complex systems characterized by strong nonlinearities and parametric uncertainties presents a significant challenge. Traditional model-based control relies on precise system models,…
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…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…