Related papers: Deep Learning Based Dynamics Identification and Li…
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…
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…
This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two…
Given the complexity and nonlinearity inherent in traffic dynamics within vehicular platoons, there exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability. Currently, there…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinear functions called…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a…
Autonomous driving has attracted lots of attention in recent years. An accurate vehicle dynamics is important for autonomous driving techniques, e.g. trajectory prediction, motion planning, and control of trajectory tracking. Although…
We propose deep Koopman-layered models with learnable parameters in the form of Toeplitz matrices for analyzing the transition of the dynamics of time-series data. The proposed model has both theoretical solidness and flexibility. By virtue…
This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an…
This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems. We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying…
Trajectory planning for robotic manipulators operating in dynamic orbital debris environments poses significant challenges due to complex obstacle movements and uncertainties. This paper presents Deep Koopman RRT (DK-RRT), an advanced…
Koopman operator has been recognized as an ongoing data-driven modeling method for vehicle dynamics which lifts the original state space into a high-dimensional linear state space. The deep neural networks (DNNs) are verified to be useful…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical…
Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…
This paper presents a data-driven model predictive control framework for mobile robots navigating in dynamic environments, leveraging Koopman operator theory. Unlike the conventional Koopman-based approaches that focus on the linearization…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator…