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Closed-loop training of static output feedback neural network controllers for large systems: A distillation case study (2402.19309v1)

Published 29 Feb 2024 in eess.SY, cs.SY, and math.OC

Abstract: The online implementation of model predictive control for constrained multivariate systems has two main disadvantages: it requires an estimate of the entire model state and an optimisation problem must be solved online. These issues have typically been treated separately. This work proposes an integrated approach for the offline training of an output feedback neural network controller in closed loop. Online this neural network controller computers the plant inputs cheaply using noisy measurements. In addition, the controller can be trained to only make use of certain predefined measurements. Further, a heuristic approach is proposed to perform the automatic selection of important measurements. The proposed method is demonstrated by extensive simulations using a non-linear distillation column model of 50 states.

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References (29)
  1. On-line implementation of nonlinear mpc: an experimental case study, Control Engineering Practice 9 (2001) 847–857.
  2. R. Findeisen, F. Allgöwer, Computational delay in nonlinear model predictive control, IFAC Proceedings Volumes 37 (2004) 427–432.
  3. A real-time iteration scheme for nonlinear optimization in optimal feedback control, SIAM Journal on control and optimization 43 (2005) 1714–1736.
  4. V. M. Zavala, L. T. Biegler, The advanced-step nmpc controller: Optimality, stability and robustness, Automatica 45 (2009) 86–93.
  5. Fast economic model predictive control based on nlp-sensitivities, Journal of Process Control 24 (2014) 1260–1272.
  6. Convex neural network-based cost modifications for learning model predictive control, IEEE Open Journal of Control Systems 1 (2022) 366–379.
  7. Learning a convex cost-to-go for single step model predictive control (2023). URL: http://arxiv.org/abs/2312.02650. arXiv:2312.02650.
  8. S. Ramchandran, R. R. Rhinehart, A very simple structure for neural network control of distillation, Journal of Process Control 5 (1995) 115–128.
  9. T. Parisini, R. Zoppoli, A receding-horizon regulator for nonlinear systems and a neural approximation, Automatica 31 (1995) 1443–1451. URL: https://linkinghub.elsevier.com/retrieve/pii/000510989500044W. doi:10.1016/0005-1098(95)00044-W.
  10. B. Karg, S. Lucia, Efficient representation and approximation of model predictive control laws via deep learning, IEEE Transactions on Cybernetics 50 (2020) 3866–3878. doi:10.1109/TCYB.2020.2999556. arXiv:1806.10644.
  11. Industrial, large-scale model predictive control with structured neural networks, Computers and Chemical Engineering 150 (2021). doi:10.1016/j.compchemeng.2021.107291.
  12. Fast approximate learning-based multistage nonlinear model predictive control using gaussian processes and deep neural networks, Computers & Chemical Engineering 145 (2021) 107174.
  13. Differentiable predictive control: Deep learning alternative to explicit model predictive control for unknown nonlinear systems, Journal of Process Control 116 (2022) 80–92. URL: https://doi.org/10.1016/j.jprocont.2022.06.001. doi:10.1016/j.jprocont.2022.06.001.
  14. E. M. Turan, J. Jäschke, Closed-loop optimisation of neural networks for the design of feedback policies under uncertainty, Journal of Process Control 133 (2024) 103144. doi:10.1016/j.jprocont.2023.103144.
  15. The explicit linear quadratic regulator for constrained systems, Automatica 38 (2002) 3–20. doi:10.1016/S0005-1098(01)00174-1.
  16. Using stochastic programming to train neural network approximation of nonlinear mpc laws, Automatica 146 (2022) 110665.
  17. E. M. Turan, J. Jäschke, Designing neural network control policies under parametric uncertainty: A koopman operator approach, IFAC-PapersOnLine 55 (2022) 392–399.
  18. Multilayer feedforward networks are universal approximators, Neural networks 2 (1989) 359–366.
  19. G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems 2 (1989) 303–314.
  20. J. Feng, N. Simon, Sparse-input neural networks for high-dimensional nonparametric regression and classification, arXiv preprint arXiv:1711.07592 (2017).
  21. S. Skogestad, Dynamics and control of distillation columns: A tutorial introduction, Chemical Engineering Research and Design 75 (1997) 539–562.
  22. S. Skogestad, The dos and don’ts of distillation column control, Chemical Engineering Research and Design 85 (2007) 13–23.
  23. Fashionable modelling with flux, CoRR abs/1811.01457 (2018). URL: https://arxiv.org/abs/1811.01457. arXiv:1811.01457.
  24. M. Innes, Don’t unroll adjoint: Differentiating ssa-form programs, arXiv preprint arXiv:1810.07951 (2018).
  25. C. Rackauckas, Q. Nie, DifferentialEquations.jl–a performant and feature-rich ecosystem for solving differential equations in Julia, Journal of Open Research Software 5 (2017).
  26. JuMP 1.0: recent improvements to a modeling language for mathematical optimization, Mathematical Programming Computation (2023). doi:10.1007/s12532-023-00239-3. arXiv:2206.03866.
  27. A. Wächter, L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming 106 (2006) 25–57. URL: http://link.springer.com/10.1007/s10107-004-0559-y. doi:10.1007/s10107-004-0559-y.
  28. R. L. Iman, W.-J. Conover, A distribution-free approach to inducing rank correlation among input variables, Communications in Statistics-Simulation and Computation 11 (1982) 311–334.
  29. A. Foss, Critique of chemical process control theory, IEEE Transactions on Automatic Control 18 (1973) 642–652.
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