让非自主系统状态估计不再依赖重训练，通过输入动态生成观测器参数。
HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning
- 用超网络将外部输入编码为观测器参数，实时调整
- 在杜芬、范德波尔等系统上实现稳定状态估计
- 适合需要快速适应新驱动信号的控制场景
本文提出HyperKKL，一种针对非自主非线性系统的新型学习方法，用于设计卡赞茨斯-克劳瓦里斯/吕恩伯格（KKL）观测器。尽管KKL观测器可通过将非线性动力学浸入稳定线性隐空间提供严格的理论框架，但其实际实现依赖于难以解析求解的偏微分方程（PDE）。现有基于学习的近似方法多仅适用于自治系统，难以泛化到受驱动力系统，需昂贵的重新训练或在线梯度更新。HyperKKL通过超网络架构，将外生输入信号编码为即时生成的观测器参数，有效学习由外部驱动参数化的沉浸映射族。我们在四个基准数值仿真中验证该方法：杜芬、范德波尔、洛伦兹和罗素系统，结果表明其优于仅依赖训练启发式策略的课程学习方法。
原文摘要 · Abstract (English)
This paper proposes HyperKKL, a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for non-autonomous nonlinear systems. While KKL observers offer a rigorous theoretical framework by immersing nonlinear dynamics into a stable linear latent space, its practical realization relies on solving Partial Differential Equations (PDE) that are analytically intractable. Current existing learning-based approximations of the KKL observer are mostly designed for autonomous systems, failing to generalize to driven dynamics without expensive retraining or online gradient updates. HyperKKL addresses this by employing a hypernetwork architecture that encodes the exogenous input signal to instantaneously generate the parameters of the KKL observer, effectively learning a family of immersion maps parameterized by the external drive. We rigorously evaluate this approach against a curriculum learning strategy that attempts to generalize from autonomous regimes via training heuristics alone. The novel approach is illustrated on four numerical simulations in benchmark examples including the Duffing, Van der Pol, Lorenz, and Rössler systems.
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