HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning

2026-02-26

AI Summary

This work addresses the challenge of efficiently estimating states in non-autonomous nonlinear systems driven by external inputs, a setting where existing learning-based Kazantzis–Kravaris/Luenberger (KKL) observers often require costly retraining or online updates. To overcome this limitation, we propose HyperKKL, the first approach that integrates hypernetworks into KKL observer design. By conditioning the hypernetwork on exogenous inputs, HyperKKL dynamically generates observer parameters in real time, enabling accurate state estimation without repeated training. Combining hypernetwork architecture, KKL observer theory, and nonlinear dynamical system modeling, the method demonstrates superior performance over curriculum-learning-based baselines across four canonical systems—Duffing, Van der Pol, Lorenz, and Rössler—highlighting its effectiveness and strong generalization capability.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Auto ML and Hyperparameter Tuning
• Search and Optimization: Learning to Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• non-autonomous systems
• state estimation
• KKL observer
• exogenous input
• nonlinear dynamics

Innovation

• Hypernetwork
• KKL observer
• Non-autonomous systems
• Dynamic weight conditioning
• State estimation