发表机构
College of Control Science and Engineering, Zhejiang University; School of Science, Huzhou Normal University; Department of Mathematics, National University of Singapore（浙江大学控制科学与工程学院; 湖州师范学院理学院; 新加坡国立大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出两阶段训练框架，结合点引导李雅普诺夫预训练与LMI微调，实现神经网络观测器的可证明稳定性，加速训练并提升精度。
AI 中文摘要
在许多安全关键应用中，不确定动力系统的控制依赖于估计状态和外部扰动的观测器。神经网络观测器可以提高估计精度，但通过线性矩阵不等式（LMI）约束来证明其李雅普诺夫稳定性，会导致大规模半定规划（SDP），这对于大型网络来说难以求解。为了克服这一可扩展性瓶颈，我们提出了一种新颖的两阶段训练框架，用于可证明稳定的神经网络观测器。我们的方法将优化解耦为点引导的李雅普诺夫预训练阶段，该阶段在采样状态上快速实现高估计精度和局部稳定性，随后是LMI微调阶段，该阶段有效满足严格的全局李雅普诺夫稳定性证书。我们为局部稳定性半径和在指定正则性和采样假设下规定紧致误差状态域上的概率覆盖提供了正式的理论保证。在非线性控制基准和X-29飞机消融实验上的实验表明，我们的LMI认证神经网络观测器比直接基于LMI的方法训练速度显著更快，并在不同系统中稳健泛化，在多种观测器基线上实现了改进的跟踪精度。代码可在该https URL获取。
英文摘要
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.
