相关论文: Reachability of Black-Box Nonlinear Systems after …

The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…

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…

Controlling robots with strongly nonlinear, high-dimensional dynamics remains challenging, as direct nonlinear optimization with safety constraints is often intractable in real time. The Koopman operator offers a way to represent nonlinear…

Purpose of review: We review recent advances in algorithmic development and validation for modeling and control of soft robots leveraging the Koopman operator theory. Recent findings: We identify the following trends in recent research…

We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…

This short note gives a new framework for dealing with nonlinear sampled-data systems. We introduce a new idea of lifting, which is well known for linear systems, but not successfully generalized to nonlinear systems. This paper introduces…

This paper deals with diagnosability of discrete-time nonlinear systems with unknown inputs and quantized outputs. We propose a novel notion of diagnosability that we term approximate diagnosability, corresponding to the possibility of…

The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing…

Modeling of nonlinear behaviors with physical-based models poses challenges. However, Koopman operator maps the original nonlinear system into an infinite-dimensional linear space to achieve global linearization of the nonlinear system…

Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…

Public-key cryptosystems rely on computationally difficult problems for security, traditionally analyzed using number theory methods. In this paper, we introduce a novel perspective on cryptosystems by viewing the Diffie-Hellman key…

This paper proposes a Koopman-based linear model predictive control (LMPC) framework for safety-critical control of nonlinear discrete-time systems. Existing MPC formulations based on discrete-time control barrier functions (DCBFs) enforce…

Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we establish sufficient and necessary conditions under which a…

This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…

The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the…

Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…

Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine…

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…

PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction,…

The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…