Connections between port-controlled Hamiltonian systems and differential games and their applications to decentralised control of multi-agent systems

Authors

Maria Luisa Scarpa, Thulasi Mylvaganam

Abstract

Connections between port-controlled Hamiltonian (PCH) systems and differential games are explored in this paper. First, it is shown that a given differential game can be associated with a family of PCH systems. Second, the converse is demonstrated namely that a given PCH system can be associated with a family of differential games. Third, combining these insights, we present a strategy for assigning cost matrices of a differential game, and the free parameters that arise in the context of PCH systems, to achieve a specific closed-loop behaviour, characterised by a desired closed-loop energy function. The construction of the resulting control laws only requires solving linear matrix inequalities. Finally, the latter “integrated approach” is extended to provide a method to design decentralised control laws for a class of networked multi-agent systems.

Keywords

decentralised control, differential games, linear matrix inequalities, multi-agent systems, port-controlled hamiltonian systems

Citation

• Journal: Automatica
• Year: 2026
• Volume: 187
• Issue:
• Pages: 112913
• Publisher: Elsevier BV
• DOI: 10.1016/j.automatica.2026.112913

BibTeX

@article{Scarpa_2026,
  title={{Connections between port-controlled Hamiltonian systems and differential games and their applications to decentralised control of multi-agent systems}},
  volume={187},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2026.112913},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Scarpa, Maria Luisa and Mylvaganam, Thulasi},
  year={2026},
  pages={112913}
}

Download the bib file

References

• Arcak M (2007) Passivity as a Design Tool for Group Coordination. IEEE Trans Automat Contr 52(8):1380–1390. https://doi.org/10.1109/tac.2007.90273 – 10.1109/tac.2007.902733
• Başar, (1999)
• Bullo, (2009)
• Cappello, A game theoretic framework for distributed control of multi-agent systems with acyclic communication topologies. (2019)
• Cappello D, Mylvaganam T (2020) Approximate Nash Equilibrium Solutions of Linear Quadratic Differential Games. IFAC-PapersOnLine 53(2):6685–6690. https://doi.org/10.1016/j.ifacol.2020.12.09 – 10.1016/j.ifacol.2020.12.091
• Cappello D, Mylvaganam T (2022) Distributed Differential Games for Control of Multi-Agent Systems. IEEE Trans Control Netw Syst 9(2):635–646. https://doi.org/10.1109/tcns.2021.312417 – 10.1109/tcns.2021.3124170
• Castaños F, Ortega R, van der Schaft A, Astolfi A (2009) Asymptotic stabilization via control by interconnection of port-Hamiltonian systems. Automatica 45(7):1611–1618. https://doi.org/10.1016/j.automatica.2009.03.01 – 10.1016/j.automatica.2009.03.015
• Cortes J, Martinez S, Karatas T, Bullo F (2004) Coverage Control for Mobile Sensing Networks. IEEE Trans Robot Automat 20(2):243–255. https://doi.org/10.1109/tra.2004.82469 – 10.1109/tra.2004.824698
• Dattorro, (2010)
• Dharwadker, (2011)
• Engwerda, (2005)
• Fujimoto K, Sugie T (2001) Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42(3):217–227. https://doi.org/10.1016/s0167-6911(00)00091- – 10.1016/s0167-6911(00)00091-8
• Gu D (2008) A Differential Game Approach to Formation Control. IEEE Trans Contr Syst Technol 16(1):85–93. https://doi.org/10.1109/tcst.2007.89973 – 10.1109/tcst.2007.899732
• Horn, (2012)
• Jafarian M, Vos E, De Persis C, van der Schaft AJ, Scherpen JMA (2015) Formation control of a multi-agent system subject to Coulomb friction. Automatica 61:253–262. https://doi.org/10.1016/j.automatica.2015.08.02 – 10.1016/j.automatica.2015.08.021
• Li, Lyapunov iterations for solving coupled algebraic Riccati equations of Nash differential games and algebraic Riccati equations of zero-sum games. (1995)
• Li Y, Hu X (2022) A differential game approach to intrinsic formation control. Automatica 136:110077. https://doi.org/10.1016/j.automatica.2021.11007 – 10.1016/j.automatica.2021.110077
• Yongguo Mei, Yung-Hsiang Lu, Hu YC, Lee CSG (2006) Deployment of mobile robots with energy and timing constraints. IEEE Trans Robot 22(3):507–522. https://doi.org/10.1109/tro.2006.87549 – 10.1109/tro.2006.875494
• Mesbahi, (2010)
• Nortmann B, Monti A, Sassano M, Mylvaganam T (2024) Nash Equilibria for Linear Quadratic Discrete-Time Dynamic Games via Iterative and Data-Driven Algorithms. IEEE Trans Automat Contr 69(10):6561–6575. https://doi.org/10.1109/tac.2024.337524 – 10.1109/tac.2024.3375249
• Ortega R, van der Schaft A, Castanos F, Astolfi A (2008) Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans Automat Contr 53(11):2527–2542. https://doi.org/10.1109/tac.2008.200693 – 10.1109/tac.2008.2006930
• (2001) Putting energy back in control. IEEE Control Syst 21(2):18–33. https://doi.org/10.1109/37.91539 – 10.1109/37.915398
• Ortega R, van der Schaft A, Maschke B, Escobar G (2002) Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38(4):585–596. https://doi.org/10.1016/s0005-1098(01)00278- – 10.1016/s0005-1098(01)00278-3
• Ortega R, García-Canseco E (2004) Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control 10(5):432–450. https://doi.org/10.3166/ejc.10.432-45 – 10.3166/ejc.10.432-450
• Ortega R, Spong MW (2000) Stabilization of Underactuated Mechanical Systems Via Interconnection and Damping Assignment. IFAC Proceedings Volumes 33(2):69–74. https://doi.org/10.1016/s1474-6670(17)35549- – 10.1016/s1474-6670(17)35549-0
• Possieri, An algebraic geometry approach for the computation of all linear feedback Nash equilibria in LQ differential games. (2015)
• Rodríguez, On stabilization of nonlinear distributed parameter port-controlled Hamiltonian systems via energy shaping. (2001)
• Sastry, (2013)
• van der Schaft, (2014)
• Starr AW, Ho YC (1969) Nonzero-sum differential games. J Optim Theory Appl 3(3):184–206. https://doi.org/10.1007/bf0092944 – 10.1007/bf00929443
• Vos, (2015)
• Vos E, Scherpen JMA, Schaft AJ van der, Postma A (2014) Formation Control of Wheeled Robots in the Port-Hamiltonian Framework. IFAC Proceedings Volumes 47(3):6662–6667. https://doi.org/10.3182/20140824-6-za-1003.0039 – 10.3182/20140824-6-za-1003.00394
• Vu NMT, Lefèvre L (2018) A connection between optimal control and IDA-PBC design. IFAC-PapersOnLine 51(3):205–210. https://doi.org/10.1016/j.ifacol.2018.06.05 – 10.1016/j.ifacol.2018.06.054