Related papers: Linear identification of nonlinear systems: A lift…
While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the…
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…
We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…
A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. In excavation, a bucket interacts with the surrounding soil in a highly nonlinear and complex…
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…
We consider the application of Koopman theory to nonlinear partial differential equations. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear…
We propose a novel framework for learning linear time-invariant (LTI) models for a class of continuous-time non-autonomous nonlinear dynamics based on a representation of Koopman operators. In general, the operator is infinite-dimensional…
Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand,…
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…
Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vector space. However, providing stability guarantees while…
A Koopman decomposition is a powerful method of analysis for fluid flows leading to an apparently linear description of nonlinear dynamics in which the flow is expressed as a superposition of fixed spatial structures with exponential time…
In this paper, we provide an algorithm for online computation of Koopman operator in real-time using streaming data. In recent years, there has been an increased interest in data-driven analysis of dynamical systems, with operator theoretic…
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…
Most current gait recognition methods suffer from poor interpretability and high computational cost. To improve interpretability, we investigate gait features in the embedding space based on Koopman operator theory. The transition matrix in…
The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…
Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…
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…
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…
Inferring latent dynamics from multivariate time-series defined over topological cell complexes is crucial for capturing the complex, higher-order interactions inherent in real-world systems such as in water, sensor, and transportation…