A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees

References

• Abbas, H. S., Tóth, R., Petreczky, M., Meskin, N., Mohammadpour Velni, J., & Koelewijn, P. J. (2021). LPV modeling of nonlinear systems: A multi-path feedback linearization approach. International Journal of Robust and Nonlinear Control, 31(18), 9436–9465. https://doi.org/10.1002/rnc.v31.18
   PubMed Web of Science ®Google Scholar
• Aswani, A., Gonzalez, H., Sastry, S. S., & Tomlin, C. (2013). Provably safe and robust learning-based model predictive control. Automatica, 49(5), 1216–1226. https://doi.org/10.1016/j.automatica.2013.02.003
   Web of Science ®Google Scholar
• Bao, Y., Chan, K. J., Mesbah, A., & Velni, J. M. (2022). Learning-based adaptive-scenario-tree model predictive control with probabilistic safety guarantees using Bayesian neural networks. In 2022 American control conference (ACC) (pp. 3260–3265). IEEE. https://doi.org/10.23919/ACC53348.2022.9867798
   Google Scholar
• Bao, Y., Chan, K. J., Mesbah, A., & Velni, J. M. (2023). Learning-based adaptive-scenario-tree model predictive control with improved probabilistic safety using robust Bayesian neural networks. International Journal of Robust and Nonlinear Control, 33(5), 3312–3333. https://doi.org/10.1002/rnc.v33.5
   Web of Science ®Google Scholar
• Bao, Y., & Mohammadpour Velni, J. (2022). Safe control of nonlinear systems in LPV framework using model-based reinforcement learning. International Journal of Control, 96(4), 1079–1090. https://doi.org/10.1080/00207179.2022.2117083.
   Web of Science ®Google Scholar
• Bao, Y., Mohammadpour Velni, J., & Shahbakhti, M. (2020). An online transfer learning approach for identification and predictive control design with application to RCCI engines. In Dynamic systems and control conference (Vol. 84270, pp. V001T21A003). ASME.
   Google Scholar
• Bao, Y., Mohammadpour Velni, J., & Shahbakhti, M. (2021). Epistemic uncertainty quantification in state-space LPV model identification using Bayesian neural networks. IEEE Control Systems Letters, 5(2), 719–724. https://doi.org/10.1109/LCSYS.7782633
   Google Scholar
• Bao, Y., Velni, J. M., Basina, A., & Shahbakhti, M. (2020). Identification of state-space linear parameter-varying models using artificial neural networks. IFAC-PapersOnLine, 53(2), 5286–5291. https://doi.org/10.1016/j.ifacol.2020.12.1209
   Google Scholar
• Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017Feb). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859–877. https://doi.org/10.1080/01621459.2017.1285773
   Web of Science ®Google Scholar
• Blundell, C., Cornebise, J., Kavukcuoglu, K., & Wierstra, D. (2015, June). Weight uncertainty in neural network. In International conference on machine learning (pp. 1613–1622). PMLR.
   Google Scholar
• Bonzanini, A. D., Paulson, J. A., & Mesbah, A. (2020). Safe learning-based model predictive control under state- and input-dependent uncertainty using scenario trees. In 2020 59th IEEE conference on decision and control (CDC) (pp. 2448–2454). IEEE. https://doi.org/10.1109/CDC42340.2020.9304310
   Google Scholar
• Calafiore, G. C., & Fagiano, L. (2013). Stochastic model predictive control of LPV systems via scenario optimization. Automatica, 49(6), 1861–1866. https://doi.org/10.1016/j.automatica.2013.02.060
   Web of Science ®Google Scholar
• Casavola, A., Famularo, D., & Franze, G. (2008). A predictive control strategy for norm-bounded LPV discrete-time systems with bounded rates of parameter change. International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal, 18(7), 714–740. https://doi.org/10.1002/(ISSN)1099-1239
   Web of Science ®Google Scholar
• Clevert, D. A., Unterthiner, T., & Hochreiter, S. (2015). Fast and accurate deep network learning by exponential linear units (elus). arXiv preprint arXiv:1511.07289.
   Google Scholar
• Cox, P. B. (2018). Towards efficient identification of linear parameter-varying state-space models [Unpublished doctoral dissertation]. Eindhoven University of Technology.
   Google Scholar
• Defourny, B. (2010). Machine learning solution methods for multistage stochastic programming [PhD diss.]. University of Liege. https://www.lehigh.edu/defourny/PhDthesis_B_Defourny.pdf.
   Google Scholar
• Ellis, M., Liu, J., & Christofides, P. D. (2017). Economic model predictive control. Springer, 5(7), 65. https://doi.org/10.1007/978-3-319-41108-8
   Google Scholar
• Gilbert, E. G., & Tan, K. T. (1991). Linear systems with state and control constraints: The theory and application of maximal output admissible sets. IEEE Transactions on Automatic Control, 36(9), 1008–1020. https://doi.org/10.1109/9.83532
   Web of Science ®Google Scholar
• Gowal, S., Dvijotham, K., Stanforth, R., Bunel, R., Qin, C., Uesato, J., Arandjelovic, R., Mann, T., & Kohli, P. (2018). On the effectiveness of interval bound propagation for training verifiably robust models. arXiv preprint arXiv:1810.12715.
   Google Scholar
• Hanema, J. (2018). Anticipative model predictive control for linear parameter-varying systems [Unpublished doctoral dissertation]. Technische Universiteit Eindhoven, Eindhoven, The Netherlands.
   Google Scholar
• Hanema, J., Lazar, M., & Tóth, R. (2020). Heterogeneously parameterized tube model predictive control for LPV systems. Automatica, 111, 108622. https://doi.org/10.1016/j.automatica.2019.108622
   Web of Science ®Google Scholar
• Hanema, J., Tóth, R., & Lazar, M. (2021). Stabilizing non-linear model predictive control using linear parameter-varying embeddings and tubes. IET Control Theory & Applications, 15(10), 1404–1421. https://doi.org/10.1049/cth2.v15.10
   Web of Science ®Google Scholar
• Hastie, T., Tibshirani, R., & Friedman, J. (2009). Model assessment and selection. In The elements of statistical learning (pp. 219–259). Springer. https://doi.org/10.1007/978-0-387-21606-5_7
   Google Scholar
• Hewing, L., Wabersich, K. P., Menner, M., & Zeilinger, M. N. (2020). Learning-based model predictive control: Toward safe learning in control. Annual Review of Control, Robotics, and Autonomous Systems, 3(1), 269–296. https://doi.org/10.1146/control.2020.3.issue-1
   Google Scholar
• Høyland, K., Kaut, M., & Wallace, S. W. (2003). A heuristic for moment-matching scenario generation. Computational Optimization and Applications, 24(2/3), 169–185. https://doi.org/10.1023/A:1021853807313
   Web of Science ®Google Scholar
• Høyland, K., & Wallace, S. W. (2001). Generating scenario trees for multistage decision problems. Management Science, 47(2), 295–307. https://doi.org/10.1287/mnsc.47.2.295.9834
   Web of Science ®Google Scholar
• Ji, X., Zhu, S., Wang, S., & Zhang, S. (2005). A stochastic linear goal programming approach to multistage portfolio management based on scenario generation via linear programming. Iie Transactions, 37(10), 957–969. https://doi.org/10.1080/07408170591008082
   Web of Science ®Google Scholar
• Koller, T., Berkenkamp, F., Turchetta, M., Boedecker, J., & Krause, A. (2019). Learning-based model predictive control for safe exploration and reinforcement learning. arXiv preprint arXiv: 1906.12189.
   Google Scholar
• Koller, T., Berkenkamp, F., Turchetta, M., & Krause, A. (2018, December). Learning-based model predictive control for safe exploration. In 2018 IEEE conference on decision and control (CDC) (pp. 6059–6066). IEEE.
   Google Scholar
• Lee, J., & Yu, Z. (1997). Worst-case formulations of model predictive control for systems with bounded parameters. Automatica, 33(5), 763–781. https://doi.org/10.1016/S0005-1098(96)00255-5
   Web of Science ®Google Scholar
• Liu, H., Ong, Y. S., Shen, X., & Cai, J. (2020). When Gaussian process meets big data: A review of scalable GPs. IEEE Transactions on Neural Networks and Learning Systems, 31(11), 4405–4423. https://doi.org/10.1109/TNNLS.5962385
   PubMed Web of Science ®Google Scholar
• Lloyd, S. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129–137. https://doi.org/10.1109/TIT.1982.1056489
   Web of Science ®Google Scholar
• Lucia, S., Finkler, T., & Engell, S. (2013). Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty. Journal of Process Control, 23(9), 1306–1319. https://doi.org/10.1016/j.jprocont.2013.08.008
   Web of Science ®Google Scholar
• Luo, Q., Nguyen, A. T., Fleming, J., & Zhang, H. (2021). Unknown input observer based approach for distributed tube-based model predictive control of heterogeneous vehicle platoons. IEEE Transactions on Vehicular Technology, 70(4), 2930–2944. https://doi.org/10.1109/TVT.2021.3064680
   Web of Science ®Google Scholar
• Maiworm, M., Bäthge, T., & Findeisen, R. (2015). Scenario-based model predictive control: Recursive feasibility and stability. IFAC-PapersOnLine, 48(8), 50–56. https://doi.org/10.1016/j.ifacol.2015.08.156
   Google Scholar
• Mayne, D. Q., Rawlings, J. B., Rao, C. V., & Scokaert, P. O. (2000). Constrained model predictive control: Stability and optimality. Automatica, 36(6), 789–814. https://doi.org/10.1016/S0005-1098(99)00214-9
   Web of Science ®Google Scholar
• Mesbah, A. (2018). Stochastic model predictive control with active uncertainty learning: A survey on dual control. Annual Reviews in Control, 45, 107–117. https://doi.org/10.1016/j.arcontrol.2017.11.001
   Web of Science ®Google Scholar
• Morato, M. M., Normey-Rico, J. E., & Sename, O. (2020). Model predictive control design for linear parameter varying systems: A survey. Annual Reviews in Control, 49, 64–80. https://doi.org/10.1016/j.arcontrol.2020.04.016
   Web of Science ®Google Scholar
• Nguyen, H.-N. (2014). Set theoretic methods in control. In Constrained control of uncertain, time-varying, discrete-time systems (pp. 7–42). Springer International Publishing. https://doi.org/10.1007/978-3-319-02827-9_2
   Google Scholar
• Pandey, A., & de Oliveira, M. C. (2017). Quadratic and poly-quadratic discrete-time stabilizability of linear parameter-varying systems. IFAC-PapersOnLine, 50(1), 8624–8629. https://doi.org/10.1016/j.ifacol.2017.08.1512
   Google Scholar
• Rizvi, S. Z., Mohammadpour Velni, J., Abbasi, F., Tóth, R., & Meskin, N. (2018). State-space LPV model identification using kernelized machine learning. Automatica, 88, 38–47. https://doi.org/10.1016/j.automatica.2017.11.004
   Web of Science ®Google Scholar
• Shapiro, A. (2003). Monte Carlo sampling methods. Handbooks in Operations Research and Management Science, 10, 353–425. https://doi.org/10.1016/S0927-0507(03)10006-0
   Google Scholar
• Wicker, M., Laurenti, L., Patane, A., & Kwiatkowska, M. (2020). Probabilistic safety for Bayesian neural networks. arXiv preprint arXiv:2004.10281.
   Google Scholar
• Wills, A., & Ninness, B. (2012). System identification of linear parameter varying state-space models. In P. Lopes dos Santos, T. P. Azevedo Perdicoulis, & C. Novara (Eds.), Linear parameter-varying system identification: New developments and trends (pp. 295–315). World Scientific.
   Google Scholar
• Xu, D., Chen, Z., & Yang, L. (2012). Scenario tree generation approaches using K-means and LP moment matching methods. Journal of Computational and Applied Mathematics, 236(17), 4561–4579. https://doi.org/10.1016/j.cam.2012.05.020
   Web of Science ®Google Scholar
• Zhang, H., Weng, T. W., Chen, P. Y., Hsieh, C. J., & Daniel, L. (2018). Efficient neural network robustness certification with general activation functions. Advances in Neural Information Processing Systems, 31.
   Google Scholar