Neural network observer trains faster with provable stability guarantees
Learning Provable Neural Network Observer for Uncertain Dynamical Systems
Machine Learning
Summary
Controlling systems that change over time and face uncertainties requires ways to estimate current states accurately. The authors developed a new two-step training method for neural networks that observe and estimate these states more reliably and faster than before. Their approach first quickly learns to estimate well in specific cases, then fine-tunes to ensure the system remains stable overall. They prove that their method guarantees stability within a certain range and demonstrate better accuracy on various control tasks including aircraft models.
What this means in practice
- •For control systems engineers: Build reliable observers for uncertain systems that estimate states more accurately and guarantee stability in safety-critical controls.
- •For aerospace system developers: Improve real-time tracking and disturbance estimation in aircraft control by using fast-trained neural observers with provable stability.
Authors
Zhangyi Wang, Jiaxu Liu, Chen Song, Chao Xu, Shengze Cai
Abstract
In many safety-critical applications, control of uncertain dynamical systems relies on observers that estimate states and external disturbances. Neural network observers can improve estimation accuracy, but certifying their Lyapunov stability via Linear Matrix Inequality (LMI) constraints leads to large-scale semidefinite programs (SDPs) that are difficult to solve for large networks. To overcome this scalability bottleneck, we propose a novel two-stage training framework for provably stable neural network observers. Our approach decouples the optimization into a point-guided Lyapunov pre-training phase, which rapidly achieves high estimation accuracy and local stability over sampled states, followed by an LMI fine-tuning phase that efficiently satisfies a strict global Lyapunov stability certificate. We provide formal theoretical guarantees for local stability radii and probabilistic coverage over a prescribed compact error-state domain under specified regularity and sampling assumptions. Experiments on nonlinear control benchmarks and X-29 aircraft ablations show that our LMI-certified neural network observers train significantly faster than direct LMI-based methods and generalize robustly across diverse systems, achieving improved tracking accuracy over a range of observer baselines. The code is available at https://github.com/Berry-Myon/LearningNeuralNetworkObserver.