Adaptive Meta-Learning-Based KKL Observer Design for Nonlinear Dynamical Systems

Abstract: 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.