A Simple Model-Predictive Control Strategy for Discrete-Time Port-Hamiltonian Boundary Control Systems

Authors

Alessandro Macchelli

Abstract

This letter deals with discrete-time linear boundary control systems (BCSs) in port-Hamiltonian form, for which the discretization is performed in time while preserving the distributed nature of the state and the passivity of the original system. The contribution is twofold. First, an explicit parametrized expression of the discrete-time state evolution is derived. Second, this parametrization is employed to design a simple model predictive control (MPC) law. The receding-horizon scheme relies on an optimization procedure based on a quadratically constrained quadratic programming (QCQP) problem. By following standard arguments and exploiting the passivity of the BCS, we prove that the MPC methodology guarantees asymptotic stability.

Citation

• Journal: IEEE Control Systems Letters
• Year: 2026
• Volume: 10
• Issue:
• Pages: 559–564
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/lcsys.2026.3700669

BibTeX

@article{Macchelli_2026,
  title={{A Simple Model-Predictive Control Strategy for Discrete-Time Port-Hamiltonian Boundary Control Systems}},
  volume={10},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2026.3700669},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Macchelli, Alessandro},
  year={2026},
  pages={559--564}
}

Download the bib file

References

• Curtain RF, Zwart H (1995) An Introduction to Infinite-Dimensional Linear Systems Theory. Springer New Yor – 10.1007/978-1-4612-4224-6
• Macchelli A (2024) A Discrete-Time Formulation of Nonlinear Distributed-Parameter Port-Hamiltonian Systems. IEEE Control Syst Lett 8:802–807. https://doi.org/10.1109/lcsys.2024.340476 – 10.1109/lcsys.2024.3404769
• Macchelli A (2026) Port-Hamiltonian Boundary Control Systems in Discrete-Time Modeling and Control Design. IEEE Trans Automat Contr 71(2):722–736. https://doi.org/10.1109/tac.2025.359306 – 10.1109/tac.2025.3593062
• Le Gorrec Y, Zwart H, Maschke B (2005) Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM J Control Optim 44(5):1864–1892. https://doi.org/10.1137/04061167 – 10.1137/040611677
• Kotyczka P, Lefèvre L (2019) Discrete-time port-Hamiltonian systems: A definition based on symplectic integration. Systems & Control Letters 133:104530. https://doi.org/10.1016/j.sysconle.2019.10453 – 10.1016/j.sysconle.2019.104530
• Moreschini A, Mattioni M, Monaco S, Normand-Cyrot D (2021) Stabilization of Discrete Port-Hamiltonian Dynamics via Interconnection and Damping Assignment. IEEE Control Syst Lett 5(1):103–108. https://doi.org/10.1109/lcsys.2020.300070 – 10.1109/lcsys.2020.3000705
• Macchelli A (2022) Trajectory Tracking for Discrete-Time Port-Hamiltonian Systems. IEEE Control Syst Lett 6:3146–3151. https://doi.org/10.1109/lcsys.2022.318284 – 10.1109/lcsys.2022.3182845
• Macchelli A (2023) Control Design for a Class of Discrete-Time Port-Hamiltonian Systems. IEEE Trans Automat Contr 68(12):8224–8231. https://doi.org/10.1109/tac.2023.329218 – 10.1109/tac.2023.3292180
• Gonzalez O (1996) Time integration and discrete Hamiltonian systems. J Nonlinear Sci 6(5):449–467. https://doi.org/10.1007/bf0244016 – 10.1007/bf02440162
• García CE, Prett DM, Morari M (1989) Model predictive control: Theory and practice—A survey. Automatica 25(3):335–348. https://doi.org/10.1016/0005-1098(89)90002- – 10.1016/0005-1098(89)90002-2
• Mayne DQ, Rawlings JB, Rao CV, Scokaert POM (2000) Constrained model predictive control: Stability and optimality. Automatica 36(6):789–814. https://doi.org/10.1016/s0005-1098(99)00214- – 10.1016/s0005-1098(99)00214-9
• Alessio A, Bemporad A (2009) A Survey on Explicit Model Predictive Control. Lecture Notes in Control and Information Sciences 345–36 – 10.1007/978-3-642-01094-1_29
• Rawlings, Model Predictive Control: Theory, Computation, and Design (2017)
• Ito K, Kunisch K (2002) Receding horizon optimal control for infinite dimensional systems. ESAIM: COCV 8:741–760. https://doi.org/10.1051/cocv:200203 – 10.1051/cocv:2002032
• Grüne L (2009) Analysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems. SIAM J Control Optim 48(2):1206–1228. https://doi.org/10.1137/07070785 – 10.1137/070707853
• Pham VT, Georges D, Besançon G (2014) Infinite-Dimensional Predictive Control for Hyperbolic Systems. SIAM J Control Optim 52(6):3592–3617. https://doi.org/10.1137/11083820 – 10.1137/110838200
• Dubljevic S, Humaloja J-P (2020) Model predictive control for regular linear systems. Automatica 119:109066. https://doi.org/10.1016/j.automatica.2020.10906 – 10.1016/j.automatica.2020.109066
• Havu V, Malinen J (2007) The Cayley Transform as a Time Discretization Scheme. Numerical Functional Analysis and Optimization 28(7–8):825–851. https://doi.org/10.1080/0163056070149332 – 10.1080/01630560701493321
• Chisci L, Lombardi A, Mosca E (1996) Dual-Receding Horizon Control of Constrained Discrete Time Systems. European Journal of Control 2(4):278–285. https://doi.org/10.1016/s0947-3580(96)70052- – 10.1016/s0947-3580(96)70052-3
• CHEN H, ALLGöWER F (1998) A Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability∗∗This paper was not presented at any IFAC meeting. This paper was accepted for publication in revised form by Associate Editor W. Bequette under the direction of Editor Prof. S. Skogestad. Automatica 34(10):1205–1217. https://doi.org/10.1016/s0005-1098(98)00073- – 10.1016/s0005-1098(98)00073-9
• Krupa P, Jaouani R, Limon D, Alamo T (2024) A Sparse ADMM-Based Solver for Linear MPC Subject to Terminal Quadratic Constraint. IEEE Trans Contr Syst Technol 32(6):2376–2384. https://doi.org/10.1109/tcst.2024.338606 – 10.1109/tcst.2024.3386062
• Mora LA, Morris K (2024) Exponential Decay Rate of Linear Port-Hamiltonian Systems: A Multiplier Approach. IEEE Trans Automat Contr 69(3):1767–1772. https://doi.org/10.1109/tac.2023.333200 – 10.1109/tac.2023.3332008
• Zeilinger MN, Jones CN, Morari M (2010) Robust stability properties of soft constrained MPC. 49th IEEE Conference on Decision and Control (CDC) 5276–528 – 10.1109/cdc.2010.5717488