Related papers: Sparsity structures for Koopman operators

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…

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…

In this paper we prove new connections between two frameworks for analysis and control of nonlinear systems: the Koopman operator framework and contraction analysis. Each method, in different ways, provides exact and global analyses of…

Koopman spectral theory has grown in the past decade as a powerful tool for dynamical systems analysis and control. In this paper, we show how recent data-driven techniques for estimating Koopman-Invariant subspaces with neural networks can…

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 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…

A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal…

The problem of data-driven identification of coherent observables of measure-preserving, ergodic dynamical systems is studied using kernel integral operator techniques. An approach is proposed whereby complex-valued observables with…

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…

Global information about dynamical systems can be extracted by analysing associated infinite-dimensional transfer operators, such as Perron-Frobenius and Koopman operators as well as their infinitesimal generators. In practice, these…

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their…

Sparsity in the eigenvectors of signal covariance matrices is exploited in this paper for compression and denoising. Dimensionality reduction (DR) and quantization modules present in many practical compression schemes such as transform…

We study the metastability properties of a simple prototypical bistable system using the formalism of the Koopman operator. Instead of studying noise-induced transitions by following the trajectories of the system, we track them by studying…

The accuracy of Koopman operator approximations over finite-dimensional spaces relies critically on their invariance properties. These can be rigorously quantified via the principal angles between a candidate subspace and its image under…

The extended-domain method is a strategy for applying spectral methods to complex geometries. Its stability is complicated by the ill-conditioning of the Fourier extension frame. This paper provides a rigorous analysis of the method's…

We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these infinite dimensional dynamical systems which exhibits space-time-chaos.

The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and…

Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…