相关论文: A Simulation Preorder for Koopman-like Lifted Cont…

Catheter-based interventions are widely used for the diagnosis and treatment of cardiac diseases. Recently, robotic catheters have attracted attention for their ability to improve precision and stability over conventional manual approaches.…

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…

The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, a wealth of numerical methods providing finite-dimensional approximations of the operator have been proposed (e.g.…

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…

In this paper, we introduce a new notion of Koopman operator which faithfully encodes the dynamics of controlled systems by leveraging the tools of set-valued analysis. In this context, we propose generalisations of the Liouville and…

This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…

In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…

We address the problem of learning a neural Koopman operator model that provides dissipativity guarantees for an unknown nonlinear dynamical system that is known to be dissipative. We propose a two-stage approach. First, we learn an…

We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…

We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction…

The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…

In the paper, we consider the problem of robust approximation of transfer Koopman and Perron-Frobenius (P-F) operators from noisy time series data. In most applications, the time-series data obtained from simulation or experiment is…

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…

Sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented. An approximate predictor is a mapping which approximates the exact values of the stabilizing input for…

The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the…

We present a data-driven approach to use the Koopman generator for prediction and optimal control of control-affine stochastic systems. We provide a novel conceptual approach and a proof-of-principle for the determination of optimal control…

For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control…

We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator. The key idea is to identify the linear (infinitedimensional) Koopman operator in the lifted space of observables,…

The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the…

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…