arXiv:2603.29744eess.SYcs.LG2026-03

提出两种神经状态观测器,可精准估计受外部输入影响的非自治非线性系统状态。

HyperKKL: Learning KKL Observers for Non-Autonomous Nonlinear Systems via Hypernetwork-Based Input Conditioning

  • 用超网络生成随输入变化的动态变换映射,提升观测精度
  • 在4个基准系统上平均降低29%的对称平均百分比误差
  • 理论推导了状态估计误差的最坏情况边界,适合控制与系统辨识研究者

Kazantzis-Kravaris/Luenberger(KKL)观测器是一类针对非线性系统的状态观测器,依赖于一个单射映射将非线性动态转换到稳定的准线性潜在空间,并通过该映射的左逆在原始坐标中获得状态估计。现有基于学习的方法仅适用于自治系统,难以推广到受控或非自治系统。本文提出两种基于学习的神经KKL观测器设计,用于受外生输入影响的非自治系统。为此,提出一种基于超网络的框架(HyperKKL),包含两种输入条件化策略:第一种是增强型观测器方法(HyperKKL_{obs}),在潜在空间观测器动态中加入输入相关的修正项,同时保持静态变换映射;第二种是动态观测器方法(HyperKKL_{dyn}),利用超网络生成编码器和解码器权重,实现输入依赖的时变变换映射。我们推导了状态估计误差的理论最坏情况界。在四个非线性基准系统上的数值评估表明,输入条件化显著提升了估计精度,在所有非零输入场景下平均对称均方百分比误差(SMAPE)降低了29%。

原文摘要 · Abstract (English)

Kazantzis-Kravaris/Luenberger (KKL) observers are a class of state observers for nonlinear systems that rely on an injective map to transform the nonlinear dynamics into a stable quasi-linear latent space, from where the state estimate is obtained in the original coordinates via a left inverse of the transformation map. Current learning-based methods for these maps are designed exclusively for autonomous systems and do not generalize well to controlled or non-autonomous systems. In this paper, we propose two learning-based designs of neural KKL observers for non-autonomous systems whose dynamics are influenced by exogenous inputs. To this end, a hypernetwork-based framework ($HyperKKL$) is proposed with two input-conditioning strategies. First, an augmented observer approach ($HyperKKL_{obs}$) adds input-dependent corrections to the latent observer dynamics while retaining static transformation maps. Second, a dynamic observer approach ($HyperKKL_{dyn}$) employs a hypernetwork to generate encoder and decoder weights that are input-dependent, yielding time-varying transformation maps. We derive a theoretical worst-case bound on the state estimation error. Numerical evaluations on four nonlinear benchmark systems show that input conditioning yields consistent improvements in estimation accuracy over static autonomous maps, with an average symmetric mean absolute percentage error (SMAPE) reduction of 29% across all non-zero input regimes.

状态观测非线性系统超网络控制理论

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