相关论文: PyKoopman: A Python Package for Data-Driven Approx…

In this paper, we systematically derive a finite set of Koopman based observables to construct a lifted linear state space model that describes the rigid body dynamics based on the dual quaternion representation. In general, the Koopman…

We develop a data-driven, model-free approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator for the purpose of control. In particular, DNN…

This paper demonstrates the benefits of imposing stability on data-driven Koopman operators. The data-driven identification of stable Koopman operators (DISKO) is implemented using an algorithm \cite{mamakoukas_stableLDS2020} that computes…

In this paper we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has been considerable interests in operator theoretic methods for data-driven analysis of dynamical systems.…

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…

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…

This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error…

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear…

Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…

Long-horizon dynamical prediction is fundamental in robotics and control, underpinning canonical methods like model predictive control. Yet, many systems and disturbance phenomena are difficult to model due to effects like nonlinearity,…

Sparked by the Willems' fundamental lemma, a class of data-driven control methods has been developed for LTI systems. At the same time, the Koopman operator theory attempts to cast a nonlinear control problem into a standard linear one…

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…

Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under…

We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environments. Our approach leverages Koopman operator theory, which enables a linear representation of nonlinear dynamics by lifting…

Koopman operator theory and Willems' fundamental lemma both can provide (approximated) data-driven linear representation for nonlinear systems. However, choosing lifting functions for the Koopman operator is challenging, and the quality of…

We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…

The Koopman Operator (KO) is a mathematical construct that maps nonlinear (state space) dynamics to corresponding linear dynamics in an infinite-dimensional functional space. For practical applications, finite-dimensional approximations can…

Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…

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…

This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are…