Luré-Postnikov Stability Analysis of Closed-Loop Control Systems with Gated Recurrent Neural Network-based Virtual Sensors

Eric Hilgert; Andreas Schwung

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arXiv · 2505.11539

Luré-Postnikov Stability Analysis of Closed-Loop Control Systems with Gated Recurrent Neural Network-based Virtual Sensors

Eric Hilgert·Andreas Schwung

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Abstract

This article addresses certification of closed-loop stability when a virtual-sensor based on a gated recurrent neural network operates in the feedback path of a nonlinear control system. The Hadamard gating used in standard GRU/LSTM cells is shown to violate the Luré-Postnikov Lyapunov conditions of absolute-stability theory, leading to conservative analysis. To overcome this limitation, a modified architecture-termed the Luré-Postnikov gated recurrent neural network (LP-GRNN)-is proposed; its affine update law is compatible with the Luré-Postnikov framework while matching the prediction accuracy of vanilla GRU/LSTM models on the NASA CMAPSS benchmark. Embedding the LP-GRNN, the plant, and a saturated PI controller in a unified standard nonlinear operator form (SNOF) reduces the stability problem to a compact set of tractable linear matrix inequalities (LMIs) whose feasibility certifies global asymptotic stability. A linearized boiler case study illustrates the workflow and validates the closed-loop performance, thereby bridging modern virtual-sensor design with formal stability guarantees.

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BibTeX RIS

Eric Hilgert, Andreas Schwung. 2025-12-05. Luré-Postnikov Stability Analysis of Closed-Loop Control Systems with Gated Recurrent Neural Network-based Virtual Sensors. https://arxiv.org/abs/2505.11539

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