Related papers: Applied Koopman Operator Theory for Power Systems …
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…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
We propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment the a priori known state-space model by reformulating parameters deemed uncertain…
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…
The Koopman operator has become a celebrated tool in modern dynamical systems theory for analyzing and interpreting both models and datasets. The linearity of the Koopman operator means that important characteristics about it, and in turn…
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…
Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…
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…
The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators for nonlinear systems with control inputs. To this end, we…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…
We propose the application of Koopman operator theory for the design of stabilizing feedback controller for a nonlinear control system. The proposed approach is data-driven and relies on the use of time-series data generated from the…
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 reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…