相关论文: Physics-informed Split Koopman Operators for Data-…

Detecting anomalies and discovering driving signals is an essential component of scientific research and industrial practice. Often the underlying mechanism is highly complex, involving hidden evolving nonlinear dynamics and noise…

In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…

In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…

Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently…

Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication…

This paper presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates…

We introduce a unified framework that combines nonlinear dynamics, perceptual psychophysics and high frequency haptic rendering to enhance realism in surgical simulation. The interaction of the surgical device with soft tissue is elevated…

The prediction of photon echoes is a crucial technique for understanding optical quantum systems. However, it typically requires numerous simulations with varying parameters and input pulses, rendering numerical studies computationally…

This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spectral decomposition of the Koopman operator. The reduced…

Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…

In recent years data-driven analysis of dynamical systems has attracted a lot of attention and transfer operator techniques, namely, Perron-Frobenius and Koopman operators are being used almost ubiquitously. Since data is always obtained in…

A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly…

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…

We consider the application of Koopman theory to nonlinear partial differential equations. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear…

Autonomous Underwater Vehicles (AUVs) play an essential role in modern ocean exploration, and their speed control systems are fundamental to their efficient operation. Like many other robotic systems, AUVs exhibit multivariable nonlinear…

Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell…

The Koopman operator enables the analysis of nonlinear dynamical systems through a linear perspective by describing time evolution in the infinite-dimensional space of observables. Here this formalism is applied to shear flows, specifically…

We develop a data-driven, model-free approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator for the purpose of control. In particular, DNN…

This paper presents a model-based reinforcement learning (RL) framework for optimal closed-loop control of nonlinear robotic systems. The proposed approach learns linear lifted dynamics through Koopman operator theory and integrates the…

The mathematical properties and data-driven learning of the Koopman operator, which represents nonlinear dynamics as a linear mapping on a properly defined functional spaces, have become key problems in nonlinear system identification and…