Related papers: Online Estimation of the Koopman Operator Using Fo…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
Koopman theory asserts that a nonlinear dynamical system can be mapped to a linear system, where the Koopman operator advances observations of the state forward in time. However, the observable functions that map states to observations are…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
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…
For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we…
In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…
This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…
The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear…
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of…
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…
The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from…
In this paper, an extension to rules-based fault detection is demonstrated utilizing properties of the Koopman operator. The Koopman operator is an infinite-dimensional, linear operator that captures nonlinear, finite dimensional dynamics.…
The Koopman operator approach to the state estimation problem for nonlinear systems is a promising research area. The main goal of this paper is an attempt to provide a rigorous theoretical framework for this approach. In particular, the…
This paper proposes a mode-in-state contribution factor for a class of nonlinear dynamical systems by utilizing spectral properties of the Koopman operator and sensitivity analysis. Using eigenfunctions of the Koopman operator for a target…
Predictive control of power electronic systems always requires a suitable model of the plant. Using typical physics-based white box models, a trade-off between model complexity (i.e. accuracy) and computational burden has to be made. This…