Related papers: Exact Finite Koopman Embedding of Block-Oriented P…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A…
We develop a deep autoencoder architecture that can be used to find a coordinate transformation which turns a nonlinear PDE into a linear PDE. Our architecture is motivated by the linearizing transformations provided by the Cole-Hopf…
The Koopman representation is an infinite dimensional linear representation of linear or nonlinear dynamical systems. It represents the dynamics of output maps (aka observables), which are functions on the state space whose evaluation is…
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…
The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…
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…
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The…
Nonlinear dynamical systems are widely encountered in various scientific and engineering fields. Despite significant advances in theoretical understanding, developing complete and integrated frameworks for analyzing and designing these…
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,…
Nonlinearity presents a significant challenge in problems involving dynamical systems, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. In this paper, we introduce the Koopman…
In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…
This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental…
Representing nonlinear dynamical systems using the Koopman Operator and its spectrum has distinct advantages in terms of linear interpretability of the model as well as in analysis and control synthesis through the use of well-studied…
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…
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…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…