Related papers: Deep Learning Based Dynamics Identification and Li…

This paper investigates the application of the Koopman Operator theory to the motion of a satellite about a libration point in the Circular Restricted Three-Body Problem. Recently, the Koopman Operator has emerged as a promising alternative…

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…

This paper addresses a learning problem for nonlinear dynamical systems with incorporating any specified dissipativity property. The nonlinear systems are described by the Koopman operator, which is a linear operator defined on the…

Deep learning research has made many biometric recognition solution viable, but it requires vast training data to achieve real-world generalization. Unlike other biometric traits, such as face and ear, gait samples cannot be easily crawled…

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…

The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…

In this paper, we systematically derive a finite set of Koopman based observables to construct a lifted linear state space model that describes the rigid body dynamics based on the dual quaternion representation. In general, the Koopman…

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,…

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…

This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…

The accurate modeling and control of nonlinear dynamical effects are crucial for numerous robotic systems. The Koopman formalism emerges as a valuable tool for linear control design in nonlinear systems within unknown environments. However,…

To avoid complex constraints of the traditional nonlinear method for tethered space robot (TSR) deployment, this paper proposes a data-driven optimal control framework with an improved deep learning based Koopman operator that could be…

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…

The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…