数据驱动的非线性网络系统切换状态估计与稀疏传感器调度

中文摘要 AI 辅助

本文提出了一种数据驱动的框架，用于未知非线性网络系统的联合观测器设计和稀疏传感器调度。非线性动力学被在线近似为一系列局部线性化的离散时间系统的分段序列，从而产生一个切换线性表示，该表示通过子空间状态空间系统辨识（4SID）递归识别。为了确保模式切换之间的一致性，引入了正交Procrustes对齐，以促进连续模式切换之间的坐标一致性，并减轻由任意状态空间坐标变化引起的人为不连续性。基于辨识的局部实现，设计了一个双速率预测-校正观测器。观测器增益通过一个凸优化问题计算，该问题同时考虑估计精度、传感器稀疏性和稳定性要求。特别地，L_{2,1}范数正则化项促进增益矩阵的列稀疏性，从而自动选择信息丰富的测量通道，而谱范数约束保证估计误差动态的Schur稳定性。所提出的框架首先在Aimsun Next中模拟的交通网络上进行验证。在18条链路的网络上获得的结果表明，该观测器能够准确重建宏观交通状态，同时显著减少实时估计所需的活跃传感器数量。

英文摘要

This paper presents a data-driven framework for joint observer design and sparse sensor scheduling for unknown nonlinear networked systems. The nonlinear dynamics are approximated online as a piecewise sequence of locally linearized discrete-time systems, resulting in a switched linear representation recursively identified through Subspace State-Space System Identification (4SID). To ensure consistency across regime transitions, an Orthogonal Procrustes alignment is introduced to promote coordinate consistency across consecutive regime transitions and mitigate artificial discontinuities caused by arbitrary state-space coordinate changes. Based on the identified local realizations, a dual-rate predictor-corrector observer is designed. The observer gain is computed through a convex optimization problem that jointly addresses estimation accuracy, sensor sparsity, and stability requirements. In particular, an L_{2,1}-norm regularization term promotes column sparsity in the gain matrix, enabling the automatic selection of informative measurement channels, while a spectral-norm constraint guarantees Schur stability of the estimation error dynamics. The proposed framework is first validated on a traffic network simulated in Aimsun Next. Results obtained on an 18-link network show that the observer accurately reconstructs macroscopic traffic states while significantly reducing the number of active sensors required for real-time estimation.

发表机构

• University of Calabria（卡拉布里亚大学）

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