Related papers: Observability of Nonlinear Dynamical Systems over …
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
The strong performance of simple neural networks is often attributed to their nonlinear activations. However, a linear view of neural networks makes understanding and controlling networks much more approachable. We draw from a dynamical…
The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is…
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…
In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…
This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…
Some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant (LTI) dynamics. The topology of this system is fixed but arbitrary, and every subsystem is…
Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…
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 framework proposes a linear representation of finite-dimensional nonlinear systems through a generally infinite-dimensional globally linear embedding. Originally, the Koopman formalism has been derived for autonomous systems. In…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
In this paper we are interested in the problem of state observation of state-affine nonlinear systems. Our main contribution is to propose a globally exponentially convergent observer that requires only the necessary assumption of…
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…
Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…