Robust constrained nonlinear Model Predictive Control with Gated Recurrent Unit model - Extended version

In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input-output dynamic of the system under control. Robust satisfaction of input and output constraints and recursive feasibility in presence of model uncertainties are achieved using a constraint tightening approach. Moreover, new terminal cost and terminal set are introduced in the Model Predictive Control formulation to guarantee Input-to-State Stability of the closed loop system with respect to the uncertainty term.

[1]  L. Magni,et al.  Robust offset-free constrained Model Predictive Control with Long Short-Term Memory Networks - Extended version , 2023, ArXiv.

[2]  Mohammed S. Alhajeri,et al.  A tutorial review of neural network modeling approaches for model predictive control , 2022, Comput. Chem. Eng..

[3]  R. Scattolini,et al.  On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments , 2021, Journal of Process Control.

[4]  R. Scattolini,et al.  Learning model predictive control with long short‐term memory networks , 2021, International Journal of Robust and Nonlinear Control.

[5]  Caio Fabio Oliveira da Silva,et al.  Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks , 2021, IFAC-PapersOnLine.

[6]  R. Scattolini,et al.  On the stability properties of Gated Recurrent Units neural networks , 2020, Syst. Control. Lett..

[7]  Frank Allgöwer,et al.  A simple framework for nonlinear robust output-feedback MPC , 2019, 2019 18th European Control Conference (ECC).

[8]  Alberto Bemporad,et al.  Performance-Oriented Model Learning for Data-Driven MPC Design , 2019, IEEE Control Systems Letters.

[9]  Juraj Kabzan,et al.  Cautious Model Predictive Control Using Gaussian Process Regression , 2017, IEEE Transactions on Control Systems Technology.

[10]  Igor Mezic,et al.  Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control , 2016, Autom..

[11]  Yoshua Bengio,et al.  Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling , 2014, ArXiv.

[12]  Yoshua Bengio,et al.  Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation , 2014, EMNLP.

[13]  Manfred Morari,et al.  Nonlinear offset-free model predictive control , 2012, Autom..

[14]  Jairo Espinosa,et al.  A comparative analysis of distributed MPC techniques applied to the HD-MPC four-tank benchmark , 2011 .

[15]  D. Limón,et al.  Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[16]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[17]  S. Hochreiter,et al.  Long Short-Term Memory , 1997, Neural Computation.

[18]  Riccardo Scattolini,et al.  Stabilizing Predictive Control of Nonlinear ARX Models , 1997, Autom..

[19]  Paulo Renato da Costa Mendes,et al.  Model Predictive Control when utilizing LSTM as dynamic models , 2023, Engineering Applications of Artificial Intelligence.

[20]  Fabio Bonassi.  Reconciling deep learning and control theory : recurrent neural networks for model-based control design , 2023 .

[21]  Eduardo F. Camacho,et al.  Min-max Model Predictive Control of Nonlinear Systems: A Unifying Overview on Stability , 2009, Eur. J. Control.

[22]  David Q. Mayne,et al.  Robust model predictive control using tubes , 2004, Autom..

[23]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..