Related papers: Neural Koopman Lyapunov Control
This paper presents a class of linear predictors for nonlinear controlled dynamical systems. The basic idea is to lift the nonlinear dynamics into a higher dimensional space where its evolution is approximately linear. In an uncontrolled…
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…
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…
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…
An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models. Advances in extended dynamic mode decomposition approaches and machine learning…
Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…
The challenge of finding exact and finite-dimensional Koopman embeddings of nonlinear systems has been largely circumvented by employing data-driven techniques to learn models of different complexities (e.g., linear, bilinear, input…
This paper extends the Willems' Fundamental Lemma to nonlinear control-affine systems using the Koopman bilinear realization. This enables us to bypass the Extended Dynamic Mode Decomposition (EDMD)-based system identification step in…
Koopman operator theory enables a global linear representation of a given nonlinear dynamical system by transforming the nonlinear dynamics into a higher dimensional observable function space where the evolution of observable functions is…
Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we establish sufficient and necessary conditions under which a…
This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in…
Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…
We derive novel deterministic bounds on the approximation error of data-based bilinear surrogate models for unknown nonlinear systems. The surrogate models are constructed using kernel-based extended dynamic mode decomposition to…
In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…
This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional…
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
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…