Port-Hamiltonian systems



This research line is concerned with the control of port-Hamiltonian systems with application to mechatronic systems. The people involved are (click on the name for the web page)



Port-Hamiltonian systems (PHS) are a class of non linear control systems, specially suited for systems arising from physical applications. The conservation of energy is the center of the framework. 



The main fields in which the CODE PHS team works on are listed as follows.


Distributed parameter systems


For the case of flexible structures, waves, etc., an infinite dimensional formulation of port Hamiltonian systems is used to perform modeling and control. By a physically coherent parametrization of the boundary variables the passivity properties are guaranteed, which in turn permits to:

  • Perform the interconnection with boundary control systems (Coupled PDE/PDE or PDE/ODE), 
  • Use of structural invariants (Casimir functions) to derive passivity based controllers (energy shaping), 
  • Prove the existence of closed-loop solutions and asymptotic and/or exponential stability (semi-group theory).
  • Develop power preserving discretization schemes for numerical simulations. 




Multi-physical systems and contact scenarios


The modularity of port-Hamiltonian systems represent a powerful framework for the structural modeling and control of complex multi-physical systems. In this sense a complex system can be studied as the interconnection of several simpler subsystems. This approach is used to study the contact between compliant structures in micro-assembly processes by:

  • Developing novel dynamical non-linear models that characterize the contact by switching between different energy functionals (hybrid model), 
  • Incorporate micro-scale phenomena such as pull-off and adhesion in the model, 
  • Characterize the passivity properties of the system to perform Lyapunov based control. 




 Control by the second law


The second law of thermodynamics, which states the irreversible creation of entropy, is combined with the port-Hamiltonian framework to develop stabilizing control laws for finite and infinite dimensional systems. This is applied to micro shaped memory alloys (MSAM) and systems of chemical reactions by:

  • The development of Irreversible port-Hamiltonian control systems (IPHS), which characterizes the first and second law of thermodynamics (conservation of energy and irreversible entropy creation), 
  • Systematic synthesis of non-linear control laws by combining the passivity properties related to the second law and IPHS formulation.

Research Projects


There are several projects which sustain the research activities. The main ones are:


  • LABEX Action (web page)
  • ANR APP Blanc SIMI3 HAMECMOPSYS "Hamiltonian Methods for the Control of Multidomain Distributed Parameter Systems"  (web page)
  • ECOS-CONICYT C12E08 "Modelling and stabilization of distributed port Hamiltonian systems: Application to micro and macro systems with thermodynamic phenomena". (web page)



Research is a multi-interaction-coupled human system :) Our collaborators come from all over the world, to mention some of places:


LAGEP, (Lyon, France), ISAE-SUPAERO (Toulouse, France), University of Twente (Twente, the Netherlands), University of Bologna (Bologna, Italy), University Santa Maria (Valparaiso, Chile), University of Concepcion (Concepcion, Chile), ...


Summer schools organized by the PHS team


One of the main responsibilities of researchers is to communicate their scientific results to students. In this aspect the participation and/or organization of summer schools has proven to be a fruitful mechanism. Some recent summer schools are listed below.


  1. PHCS: Introduction to port-Hamiltonian control systems. Postgraduate course at the Doctoral School of the University of Franche-Comté, Besançon, France. 18 - 20 Mars, 2015. The course had the following speakers: Yann Le Gorrec and Hector Ramirez.
  2. UTFSM'2014: Modelling and control of complex physical systems: the port-Hamiltonian approach. Postgraduate course at the Department of Electronic Engineering of the Universidad Técnica Federico Santa María, Valparaiso, Chile. 27 - 29 October, 2014. The course was organized by Juan Yuz, Eduardo Cerpa and Hector Ramirez and had the following speakers: Bernhard Maschke, Hector Ramirez and Yann Le Gorrec.
  3. MTNS'2014: Stability and stabilization of distributed port-Hamiltonian systems. Postgraduate mini-course in the frame of 21th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014) hosted by the University of Groningen, the Netherlands, 7-11 July, 2014, with the support of the Dutch Institute of Systems and Control (DISC). The course is organized by Alessandro Macchelli and Markus Schöberl and has the following speakers: Hans Zwart, Yann Le Gorrec, Birgit Jacob, Alessandro Macchelli and Hector Ramirez
  4. UTFSM'2014b: Energy based modelling and control of physical systems. Postgraduate course in the frame of the Summer School on Estimation and Control at the Department of Electronic Engineering of Universidad Técnica Federico Santa María, Valparaiso, Chile. 13 - 17 January, 2014. The course had the following speaker: Hector Ramirez.




A short selection of relevant publications


  1. H. Ramirez, Y. Le Gorrec, A. Macchelli and H. Zwart, Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems with Dynamic Feedback. Automatic Control, IEEE Transactions on , vol. 59, no.10 (2014) pp. 2849-2855.
  2. Y. Le Gorrec and D. Matignon. Coupling between hyperbolic and difusive systems: a port-Hamiltonian formulation. . European Journal of Control Vol. 19 (6), Pages 505-512, 2013.
  3. H. Hoang, F. Couenne, Y. Le Gorrec, C.L. Chen, B. Erik Ydstie. Passivity-based nonlinear control of CSTR via asymptotic observers. Annual Review on Control Vol. 37 (2), Pages 278-288, 2013.
  4. H. Ramirez, B. Maschke and D. Sbarbaro, Modelling and control of multi-energy systems: an irreversible port-Hamiltonian approach. European Journal of Control 19 (2013), pp. 513-520.
  5. H. Ramirez, B. Maschke and D. Sbarbaro, Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR, Chemical Engineering Science, Volume 89, 15 February 2013, Pages 223-234.
  6. H.Hoang, F.Couenne, C.Jallut, Y. Le Gorrec. Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamic. Journal of Process Control, Vol. 22(2), Pages :412-422, February 2012.
  7. J. A. Villegas, H. Zwart, Y. Le Gorrec, B. Maschke. Exponential Stability of a Class of Boundary Control Systems.  IEEE Transactions on Automatic Control- Vol. 54(1), Pages : 142-147, January 2009.
  8. A. Baaiu, F. Couenne, L. Lefevre, Y. Le Gorrec and M. Tayakout. Structure-preserving infinite dimensional model reduction. Application to Adsorption Processes. Journal of Process Control, Vol. 19(3), Pages : 394-404, March 2009.
  9. Y. Le Gorrec, H. Zwart and B. Maschke. Dirac structures and boundary control systems associated with skew-Symmetric differential operators. SIAM Journal of Control Optimization, Vol: 44 Issue 5, pages 1864-1892, 2005.