KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning
This work addresses the problem of state estimation in nonlinear systems for control engineering, offering a systematic method with theoretical guarantees, though it appears incremental as it builds on existing KKL observer frameworks with a learning-based enhancement.
The paper tackles the challenge of designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems by proposing a novel learning approach that uses neural networks trained with physics-informed learning to approximate the required transformations, and demonstrates its effectiveness through numerical simulations and application to sensor fault detection in Kuramoto oscillators.
This paper proposes a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems. The design of a KKL observer involves finding an injective map that transforms the system state into a higher-dimensional observer state, whose dynamics is linear and stable. The observer's state is then mapped back to the original system coordinates via the inverse map to obtain the state estimate. However, finding this transformation and its inverse is quite challenging. We propose to sequentially approximate these maps by neural networks that are trained using physics-informed learning. We generate synthetic data for training by numerically solving the system and observer dynamics. Theoretical guarantees for the robustness of state estimation against approximation error and system uncertainties are provided. Additionally, a systematic method for optimizing observer performance through parameter selection is presented. The effectiveness of the proposed approach is demonstrated through numerical simulations on benchmark examples and its application to sensor fault detection and isolation in a network of Kuramoto oscillators using learned KKL observers.