Related papers: Learning Neural Koopman Operators with Dissipativi…

Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, behaviors with sudden accelerations that waste energy and lack…

Sparked by the Willems' fundamental lemma, a class of data-driven control methods has been developed for LTI systems. At the same time, the Koopman operator theory attempts to cast a nonlinear control problem into a standard linear one…

This paper presents a novel identification approach of Koopman models of nonlinear systems with inputs under rather general noise conditions. The method uses deep state-space encoders based on the concept of state reconstructability and an…

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…

In many learning based control methodologies, learning the unknown dynamic model precedes the control phase, while the aim is to control the system such that it remains in some safe region of the state space. In this work, our aim is to…

It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the…

In this paper, a unified batch-online learning approach is introduced to learn a linear representation of nonlinear system dynamics using the Koopman operator. The presented system modeling approach leverages a novel incremental…

With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…

Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to…

The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the recent development of the Koopman model…

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 paper, we propose…

Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample…

Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…

In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…

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…

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…

In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on…

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 analysis plays a crucial role in understanding and modeling nonlinear dynamical systems as it reveals key system behaviors and long-term dynamics. However, the presence of measurement noise poses a significant challenge to…

This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty…