相关论文: EDMD for expanding circle maps and their complex p…

Future cellular networks that utilize millimeter wave signals provide new opportunities in positioning and situational awareness. Large bandwidths combined with large antenna arrays provide unparalleled delay and angle resolution, allowing…

The Koopman operator is a powerful approach to global stability analysis of nonlinear systems, which provides a systematic procedure for Lyapunov function design. In this framework, Lyapunov functions are obtained through the eigenfunctions…

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…

An elliptic partial differential equation Lu=f with a zero Dirichlet boundary condition is converted to an equivalent elliptic equation on the unit ball. A spectral Galerkin method is applied to the reformulated problem, using multivariate…

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…

By means of the operator extension theory, we construct an explicitly solvable model of a simple-cubic three-dimensional regimented array of quantum dots in the presence of a uniform magnetic field. The spectral properties of the model are…

Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…

We demonstrate that numerically computed approximations of Koopman eigenfunctions and eigenvalues create a natural framework for data fusion in applications governed by nonlinear evolution laws. This is possible because the eigenvalues of…

We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…

We study classical continuous automorphisms of the torus (cat maps) from the viewpoint of the Koopman theory. We find analytical formulae for Koopman modes defined coherently on the whole of the torus, and their decompositions associated…

This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary…

The multivariate Kendall-$\tau$ statistic, denoted by $K_n$, plays a significant role in robust statistical analysis. This paper establishes the limiting properties of the empirical spectral distribution (ESD) of $K_n$. We demonstrate that…

Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…

MPC is widely used in real-time applications, but practical implementations are typically restricted to convex QP formulations to ensure fast and certified execution. Koopman-based MPC enables QP-based control of nonlinear systems by…

Gradient-based hyperparameter optimization methods update hyperparameters using hypergradients, gradients of a meta criterion with respect to hyperparameters. Previous research used two distinct update strategies: optimizing hyperparameters…

In some previous works, the analytic structure of the spectrum of a quantum graph operator as a function of the vertex conditions and other parameters of the graph was established. However, a specific local coordinate chart on the…

We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state,…

Koopman Mode Decomposition (KMD) is a technique of nonlinear time-series analysis that originates from point spectrum of the Koopman operator defined for an underlying nonlinear dynamical system. We present a numerical algorithm of KMD…

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…

We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band…