Koopman-based Deep Learning for Nonlinear System Estimation
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and invariably unmodeled dynamics present challenges in making precise predictions. In this paper, we present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear systems. The Koopman model is used together with deep reinforcement networks that learn the optimal stepwise actions to predict future states of nonlinear systems. Our estimator is also adaptive to a diffeomorphic transformation of the estimated nonlinear system, which enables it to compute optimal state estimates without re-learning.
Code (0)
등록된 구현이 없습니다.
Tasks
Deep LearningTransfer LearningSimilar Papers 제목 키워드 기반
Self-tuning moving horizon estimation of nonlinear systems via physics-informed machine learning Koopman modeling
In this paper, we propose a physics-informed learning-based Koopman modeling approach and present a Koopman-based self-tuning moving horizon estimation design for a class of nonlinear systems. Specifically, we train Koop…
Chemical ProcessPhysics-informed machine learningPyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator
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 …
Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study
We use Koopman theory for data-driven model reduction of nonlinear dynamical systems with controls. We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integ…
FormModel Predictive ControlState EstimationKoopman Operator in the Weighted Function Spaces and its Learning for the Estimation of Lyapunov and Zubov Functions
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 …
Optimal Synthesis of LTI Koopman Models for Nonlinear Systems with Inputs
A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinea…