Adaptive Meta-Learning-Based KKL Observer Design for Nonlinear Dynamical
  Systems
Lukas Trommer Halil Yigit Oksuz
The theory of Kazantzis-Kravaris/Luenberger (KKL) observer design introduces
a methodology that uses a nonlinear transformation map and its left inverse to
estimate the state of a nonlinear system through the introduction of a linear
observer state space. Data-driven approaches using artificial neural networks
have demonstrated the ability to accurately approximate these transformation
maps. This paper presents a novel approach to observer design for nonlinear
dynamical systems through meta-learning, a concept in machine learning that
aims to optimize learning models for fast adaptation to a distribution of tasks
through an improved focus on the intrinsic properties of the underlying
learning problem. We introduce a framework that leverages information from
measurements of the system output to design a learning-based KKL observer
capable of online adaptation to a variety of system conditions and attributes.
To validate the effectiveness of our approach, we present comprehensive
experimental results for the estimation of nonlinear system states with varying
initial conditions and internal parameters, demonstrating high accuracy,
generalization capability, and robustness against noise.