Related papers: Learning Neural Koopman Operators with Dissipativi…
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…
Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural…
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…
We provide an overview of the Koopman operator analysis for a class of partial differential equations describing relaxation of the field variable to a stable stationary state. We introduce Koopman eigenfunctionals of the system and use the…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
Imitation learning enables the synthesis of controllers for complex objectives and highly uncertain plant models. However, methods to provide stability guarantees to imitation learned controllers often rely on large amounts of data and/or…
Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
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…
Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central…
We present a novel approach to shared control of human-machine systems. Our method assumes no a priori knowledge of the system dynamics. Instead, we learn both the dynamics and information about the user's interaction from observation…
Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…
This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…
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,…
We propose deep Koopman-layered models with learnable parameters in the form of Toeplitz matrices for analyzing the transition of the dynamics of time-series data. The proposed model has both theoretical solidness and flexibility. By virtue…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
Providing rigorous reachability guarantees for unknown complex systems is a crucial and challenging task. In this paper, we present a novel data-driven framework that addresses this challenge by leveraging Koopman operator theory. Instead…
This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis…
This paper proposes a distributed data-driven framework for dynamics learning, termed distributed deep Koopman learning using partial trajectories (DDKL-PT). In this framework, each agent in a multi-agent system is assigned a partial…
This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are…