Learning Provable Neural Network Observer for Uncertain Dynamical Systems

2026-09-25

AI Summary

This study addresses the scalability bottleneck in certifying Lyapunov stability for large-scale neural network observers, where linear matrix inequality (LMI) constraints render semidefinite programming computationally intractable. To overcome this limitation, the authors propose a two-stage decoupled training framework that first employs point-guided pretraining to achieve high-precision local stability, followed by LMI-based fine-tuning to obtain globally rigorous stability certificates while balancing computational efficiency with safety guarantees. The work contributes theoretically guaranteed stability radii and probabilistic coverage analyses that transcend conventional scalability constraints. Compared to direct LMI approaches, the proposed method significantly accelerates training and demonstrates superior generalization capability and tracking accuracy on nonlinear control benchmarks as well as in X-29 aircraft tests.

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.

Problem

• Neural Network Observer
• Uncertain Dynamical Systems
• Lyapunov Stability
• Linear Matrix Inequality
• Scalability

Innovation

• Neural Network Observer
• Lyapunov Stability
• Linear Matrix Inequality
• Two-stage Training Framework
• Uncertain Dynamical Systems