Luré-Postnikov Stability Analysis of Closed-Loop Control Systems with Gated Recurrent Neural Network-based Virtual Sensors
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917126479020032 |
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| author | Hilgert, Eric Schwung, Andreas |
| author_facet | Hilgert, Eric Schwung, Andreas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Luré-Postnikov Stability Analysis of Closed-Loop Control Systems with Gated Recurrent Neural Network-based Virtual Sensors Hilgert, Eric Schwung, Andreas Systems and Control 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. |
| title | Luré-Postnikov Stability Analysis of Closed-Loop Control Systems with Gated Recurrent Neural Network-based Virtual Sensors |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2505.11539 |