Open Access
Issue
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
Page(s) 1217 - 1246
DOI https://doi.org/10.1051/m2an/2026029
Published online 01 June 2026
  1. A.A. Ali and M. Hinze, Reduced basis methods an application to variational discretization of parametrized elliptic optimal control problems. SIAM J. Sci. Comput. 42 (2020) A271–A291. [Google Scholar]
  2. A. Alla and S. Volkwein, Asymptotic stability of POD based model predictive control for a semilinear parabolic PDE. Adv. Comput. Math. 41 (2015) 1073–1102. [Google Scholar]
  3. A. Alla, C. Gräßle and M. Hinze, Time adaptivity in model predictive control. J. Sci. Comput. 90 (2022) 24. [Google Scholar]
  4. J.I. Alora, L.A. Pabon, J. Köhler, M. Cenedese, E. Schmerling, M.N. Zeilinger, G. Haller and M. Pavone, Robust nonlinear reduced-order model predictive control, in 2023 62nd IEEE Conference on Decision and Control (CDC) (2023) 4798–4805. [Google Scholar]
  5. B. Azmi and M. Bernreuther, On the forward-backward method with nonmonotone linesearch for infinite-dimensional nonsmooth nonconvex problems. Comput. Optim. Appl. 91 (2025) 1263–1308. [Google Scholar]
  6. B. Azmi and K. Kunisch, A hybrid finite-dimensional RHC for stabilization of time-varying parabolic equations. SIAM J. Control Optim. 57 (2019) 3496–3526. [Google Scholar]
  7. B. Azmi, J. Rohleff and S. Volkwein, Finite-dimensional receding horizon control of linear time-varying parabolic PDEs: stability analysis and model-order reduction. Springer Nature, Switzerland, Cham (2025) 55–81. [Google Scholar]
  8. R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2001) 1–102. [Google Scholar]
  9. T. Breiten and L. Pfeiffer, On the turnpike property and the receding-horizon method for linear-quadratic optimal control problems. SIAM J. Control Optim. 58 (2020) 1077–1102. [Google Scholar]
  10. A. Cohen, R. Devore and C. Schwab, Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE's. Anal. Appl. 9 (2011) 11–47. [Google Scholar]
  11. S. Dietze and M.A. Grepl, Reduced order model predictive control for parametrized parabolic partial differential equations. Appl. Math. Comput. 453 (2023) 128044. [Google Scholar]
  12. J. Ghiglieri and S. Ulbrich, Optimal flow control based on POD and MPC and an application to the cancellation of Tollmien-Schlichting waves. Optim. Method. Softw. 29 (2014) 1042–1074. [Google Scholar]
  13. L. Grüne, Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. SIAM J. Control Optim. 48 (2009) 1206–1228. [Google Scholar]
  14. L. Grüne and J. Pannek, Nonlinear Model Predictive Control: Theory and Algorithms, in Communications and Control Engineering. 2nd edition. Springer, Cham (2017). [Google Scholar]
  15. L. Grüne and A. Rantzer, On the infinite horizon performance of receding horizon controllers. IEEE Trans. Automat. Control 53 (2008) 2100–2111. [Google Scholar]
  16. L. Grüne, M. Schaller and A. Schiela, Efficient model predictive control for parabolic PDEs with goal oriented error estimation. SIAM J. Sci. Comput. 44 (2022) A471–A500. [Google Scholar]
  17. M. Gubisch and S. Volkwein, Proper orthogonal decomposition for linear-quadratic optimal control, in Model Reduction and Approximation: Theory and Algorithms. Society for Industrial and Applied Mathematics (2017) 3–63. [Google Scholar]
  18. J.S. Hesthaven, G. Rozza and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations, Vol. 590. Springer, Cham (2016). [Google Scholar]
  19. M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich, Optimization with PDE Constraints, Vol. 23. Springer Science & Business Media (2008). [Google Scholar]
  20. M. Hinze, N. Kutz, O. Mula and K. Urban, Model Order Reduction and Applications: Cetraro, Italy 2021. Springer, Cham (2023). [Google Scholar]
  21. K. Ito and K. Kunisch, Receding horizon optimal control for infinite dimensional systems. ESAIM: COCV 8 (2002) 741–760. A tribute to J.L. Lions. [Google Scholar]
  22. A. Jadbabaie and J. Hauser, On the stability of receding horizon control with a general terminal cost. IEEE Trans. Automat. Control 50 (2005) 674–678. [Google Scholar]
  23. M. Kärcher, Z. Tokoutsi, M.A. Grepl and K. Veroy, Certified reduced basis methods for parametrized elliptic optimal control problems with distributed controls. J. Sci. Comput. 75 (2018) 276–307. [Google Scholar]
  24. M. Kartmann, M. Manucci, B. Unger and S. Volkwein, Certified model predictive control for switched evolution equations using model order reduction. Preprint arXiv:2412.12930 (2024). To appear in Communications on Applied Mathematics and Computation (2026). [Google Scholar]
  25. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 40 (2002) 492–515. [CrossRef] [MathSciNet] [Google Scholar]
  26. J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (1972). [Google Scholar]
  27. M. Loehning, M. Reble, J. Hasenauer, S. Yu and F. Allgöwer, Model predictive control using reduced order models: guaranteed stability for constrained linear systems. J. Process Control 24 (2014) 1647–1659. [Google Scholar]
  28. J. Lorenzetti, A. McClellan, C. Farhat and M. Pavone, Linear reduced-order model predictive control. IEEE Trans. Autom. Control 67 (2022) 5980–5995. [Google Scholar]
  29. P. Manns and S. Ulbrich, A simplified Newton method to generate snapshots for POD models of semilinear optimal control problems. SIAM J. Numer. Anal. 60 (2022) 2807–2833. [Google Scholar]
  30. J.B. Rawlings, D.Q. Mayne and M.M. Diehl, Model Predictive Control: Theory, Computation and Design, 2nd edition. Nob Hill Publishing (2019). [Google Scholar]
  31. M. Reble and F. Allgöwer, Unconstrained model predictive control and suboptimality estimates for nonlinear continuous-time systems. Automatica J. IFAC 48 (2012) 1812–1817. [Google Scholar]
  32. B. Vexler and W. Wollner, Adaptive finite elements for elliptic optimization problems with control constraints. SIAM J. Control Optim. 47 (2008) 509–534. [CrossRef] [MathSciNet] [Google Scholar]

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