Koopman-based Deep Learning for Nonlinear System Estimation

• URL: http://arxiv.org/abs/2405.00627v2
• Date: Sat, 14 Sep 2024 21:57:26 GMT
• Title: Koopman-based Deep Learning for Nonlinear System Estimation
• Authors: Zexin Sun, Mingyu Chen, John Baillieul,
• Abstract summary: We present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear 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.
• Score: 1.3791394805787949
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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