aiqbench analysis
This paper introduces HyperKKL, a hypernetwork-based method that enables real-time state estimation for non-autonomous nonlinear systems by dynamically conditioning observer parameters on external inputs. By bypassing the need for expensive retraining or online gradient updates typically required for driven dynamics, this approach bridges theoretical control frameworks with practical machine learning adaptability. The work demonstrates rigorous evaluation across classic chaotic benchmarks like the Lorenz and Duffing systems, offering a scalable solution for complex system monitoring.
HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning
arXiv:2602.22630v3 Announce Type: replace-cross 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 R\"ossler systems.
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.
Systems and Control (eess.SY); Machine Learning (cs.LG)
arXiv:2602.22630 [eess.SY]
(or arXiv:2602.22630v3 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2602.22630 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 250 words
