mlsanityData to 7 Oct 2026

Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks

arXiv 2103.02383 ↗First posted 3 Mar 2021eess.SY cs.LG cs.SYcited by 11

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Abstract (arXiv)

The use of Recurrent Neural Networks (RNNs) for system identification has recently gathered increasing attention, thanks to their black-box modeling capabilities.Albeit RNNs have been fruitfully adopted in many applications, only few works are devoted to provide rigorous theoretical foundations that justify their use for control purposes. The aim of this paper is to describe how stable Gated Recurrent Units (GRUs), a particular RNN architecture, can be trained and employed in a Nonlinear MPC framework to perform offset-free tracking of constant references with guaranteed closed-loop stability. The proposed approach is tested on a pH neutralization process benchmark, showing remarkable performances.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 6 of its 19 references that are in the map. First posted on arXiv 3 Mar 2021.

Builds on

6 of 19 references.

References · 6

  1. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,341
  2. 2020On the stability properties of Gated Recurrent Units neural networkscited by 17
  3. 2019Model structures and fitting criteria for system identification with neural networkscited by 16
  4. 2019LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verificationcited by 12
  5. 2018Recurrent Neural Network-based Model Predictive Control for Continuous Pharmaceutical Manufacturingcited by 8
  6. 2019Model predictive control design for dynamical systems learned by Long Short-Term Memory Networkscited by 2

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Cited by year

Citing papers per year: 2021: 2; 2022: 2; 2023: 3; 2024: 0; 2025: 4.

11 papers.

  1. 2023Deep networks for system identification: a Surveycited by 35
  2. 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
  3. 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systemscited by 5
  4. 2023Nonlinear MPC design for incrementally ISS systems with application to GRU networkscited by 5
  5. 2025Deep Operator Neural Network Model Predictive Controlcited by 3
  6. 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX modelscited by 2
  7. 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validationcited by 1
  8. 2025Reservoir Predictive Path Integral Control for Unknown Nonlinear Dynamicscited by 1
  9. 2022Towards lifelong learning of Recurrent Neural Networks for control designcited by 0
  10. 2025Recurrent neural network-based robust control systems with regional properties and application to MPC designcited by 0
  11. 2025PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehiclescited by 0