Related papers: Global, Unified Representation of Heterogenous Rob…
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…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…
Robotic cloth folding is a challenging task, particularly when considering dynamic folding tasks, which aim at folding cloth by fast motions that leverage its dynamics. When subject to such fast motions, the complexity of cloth dynamics…
Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…
Formation control of multi-agent systems has been a prominent research topic, spanning both theoretical and practical domains over the past two decades. Our study delves into the leader-follower framework, addressing two critical,…
Developing agents that can perform complex control tasks from high-dimensional observations is a core ability of autonomous agents that requires underlying robust task control policies and adapting the underlying visual representations to…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
Suitable representations of dynamical systems can simplify their analysis and control. On this line of thought, this paper aims to answer the following question: Can a transformation of the generalized coordinates under which the actuators…
Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be…
A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…
Koopman operators, since introduced by the French-born American mathematician Bernard Koopman in 1931, have been employed as a powerful tool for research in various scientific domains, such as ergodic theory, probability theory, geometry,…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
The Koopman autoencoder, a data-driven technique, has gained traction for modeling nonlinear dynamics using deep learning methods in recent years. Given the linear characteristics inherent to the Koopman operator, controlling its…
Machine learning methods allow the prediction of nonlinear dynamical systems from data alone. The Koopman operator is one of them, which enables us to employ linear analysis for nonlinear dynamical systems. The linear characteristics of the…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
While Koopman operator lifts a nonlinear system into an infinite-dimensional function space and represents it as a linear dynamics, its definition is restricted to autonomous systems, i.e., does not incorporate inputs or disturbances. To…
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.…
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…