Related papers: A Koopman Operator Tutorial with Othogonal Polynom…
We define an observable-space framework of Quantum Koopman Algorithms (QKAs) for simulating the dynamics of both linear quantum and nonlinear classical systems, based on approximately closed sets of observables and efficient coherent…
The motivation of our research is to establish a Laplace-domain theory that provides principles and methodology to analyze and synthesize systems with nonlinear dynamics. A semigroup of composition operators defined for nonlinear autonomous…
This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We…
It has become common to perform kinetic analysis using approximate Koopman operators that transforms high-dimensional time series of observables into ranked dynamical modes. Key to a practical success of the approach is the identification…
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…
Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This paper describes how the Koopman operator can be used…
Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic techniques to analyze nonlinear dynamics in state space. The…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens 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…
Koopman Operator Theory has opened the doors to data-driven learning of globally linear representations of complex nonlinear systems. However, current methodologies for Koopman Operator discovery struggle with uncertainty quantification and…
This paper proposes an original methodology to compute the regions of attraction in hyperbolic and polynomial nonlinear dynamical systems using the eigenfunctions of the discrete-time approximation of the Koopman operator given by the…
Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…
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,…
This paper proposes a novel approach for modeling and controlling nonlinear systems with varying parameters. The approach introduces the use of a parameter-varying Koopman operator (PVKO) in a lifted space, which provides an efficient way…
Koopman operator recently gained increasing attention in the control systems community for its abilities to bridge linear and nonlinear systems. Data driven Koopman operator approximations have established themselves as key enablers for…
The present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory. A reduced-order modelling…
In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to…
Dictionary methods for system identification typically rely on one set of measurements to learn governing dynamics of a system. In this paper, we investigate how fusion of output measurements with state measurements affects the dictionary…