The Koopman Operator in Systems and Control:Concepts, Methodologies, and Applications
, 2020 This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of ...
core +2 more sources
Trajectory Estimation in Unknown Nonlinear Manifold Using Koopman Operator Theory
CoRR, 2023 Formation coordination is a critical aspect of swarm robotics, which involves coordinating the motion and behavior of a group of robots to achieve a specific objective. In formation coordination, the robots must maintain a specific spatial arrangement while in motion.
Yanran Wang +3 more
openaire +2 more sources
Thompson aggregators, Scott continuous Koopmans operators, and Least Fixed Point theory
Mathematical Social Sciences, 2021 We reconsider the theory of Thompson aggregators proposed by Marinacci and Montrucchio (Marinacci and Montrucchio, 2010). We prove the existence of a Least Fixed Point (LFP) solution to the Koopmans equation. It is a recursive utility function. Our proof turns on demonstrating the Koopmans operator is a Scott continuous function when its domain is an ...
Robert A. Becker +1 more
openaire +2 more sources
Koopman Operator Approximation under Negative Imaginary Constraints [PDF]
, 2023 Nonlinear Negative Imaginary (NI) systems arise in various engineering applications, such as controlling flexible structures and air vehicles. However, unlike linear NI systems, their theory is not well-developed. In this letter, we propose a data-driven
Meskin, Nader +5 more
core +1 more source
Study of the Hypergeometric Equation via Data Driven Koopman-EDMD Theory
Axioms, 2023 We consider a data-driven method, which combines Koopman operator theory with Extended Dynamic Mode Decomposition. We apply this method to the hypergeometric equation which is the Fuchsian equation with three regular singular points.
Evangelos Melas +4 more
doaj +1 more source
Data-Driven Modeling and Control via Koopman Operator Theory in Robotic Systems [PDF]
, 2023 With the development of more sophisticated robots that are increasingly aimed to venture outside of the lab, the higher dimensionality, complexity and nonlinearities of the underlying robotic systems as well as environmental uncertainty pose challenges ...
Shi, Lu
core
Koopman Kalman Particle Filter for Dynamic State Estimation of Distribution System
IEEE Access, 2022 Dynamic state estimation (DSE) plays an important role in the real-time control and monitoring of distribution systems, which are high-dimensional space–time systems. The degree of nonlinearity of distribution system increases drastically with the
Kai Wang +4 more
doaj +1 more source
Koopman Operator Theory for Nonlinear Dynamic Modeling using Dynamic Mode Decomposition
CoRR, 2021 8 pages, 16 ...
Gregory Snyder, Zhuoyuan Song
openaire +2 more sources
Data-Driven Newton Raphson Controller Based on Koopman Operator Theory
CoRR, 2023 Newton-Raphson controller is a powerful prediction-based variable gain integral controller. Basically, the classical model-based Newton-Raphson controller requires two elements: the prediction of the system output and the derivative of the predicted output with respect to the control input.
openaire +2 more sources
Nonlinear System Identification of Soft Robot Dynamics Using Koopman Operator Theory [PDF]
2019 International Conference on Robotics and Automation (ICRA), 2019 Soft robots are challenging to model due in large part to the nonlinear properties of soft materials. Fortunately, this softness makes it possible to safely observe their behavior under random control inputs, making them amenable to large-scale data collection and system identification. This paper implements and evaluates a system identification method
Daniel Bruder +2 more
openaire +2 more sources