Twenty years of distributed port-Hamiltonian systems: a literature review

The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups.

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[4]  A. Schaft,et al.  Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems , 2011, 1111.6403.

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[9]  Ryojun Ikeura,et al.  Boundary Integrability of Multiple Stokes-Dirac Structures , 2015, SIAM J. Control. Optim..

[10]  B. Maschke,et al.  Power preserving model reduction of 2D vibro-acoustic system: A port Hamiltonian approach , 2015 .

[11]  Ghislain Haine,et al.  Anisotropic heterogeneous n-D heat equation with boundary control and observation: II. Structure-preserving discretization , 2019, IFAC-PapersOnLine.

[12]  Arjan van der Schaft,et al.  Hamiltonian discretization of boundary control systems , 2004, Autom..

[13]  Birgit Jacob,et al.  An operator theoretic approach to infinite‐dimensional control systems , 2018, GAMM-Mitteilungen.

[14]  Yann Le Gorrec,et al.  A port-Hamiltonian formulation of a 2D boundary controlled acoustic system , 2015 .

[15]  Denis Matignon,et al.  Coupling between hyperbolic and diffusive systems: A port-Hamiltonian formulation , 2013, Eur. J. Control.

[16]  Alessandro Macchelli,et al.  Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach , 2004, SIAM J. Control. Optim..

[17]  Yann Le Gorrec,et al.  Observer-Based State Feedback Controller for a class of Distributed Parameter Systems , 2019 .

[18]  Hans Zwart,et al.  Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain , 2010 .

[19]  Stefano Stramigioli,et al.  PORT-BASED FINITE ELEMENT MODEL OF A FLEXIBLE LINK , 2007 .

[20]  Bernhard Maschke,et al.  Port-Hamiltonian formulation for systems of conservation laws: application to plasma dynamics in Tokamak reactors , 2012 .

[21]  Toshiki Oguchi,et al.  A Cluster Control of Nonlinear Network Systems with External Inputs , 2013, NOLCOS.

[22]  Arjan van der Schaft,et al.  Achievable Casimirs and its implications on control of port-Hamiltonian systems , 2007, Int. J. Control.

[23]  Markus Schöberl,et al.  On Casimir Functionals for Infinite-Dimensional Port-Hamiltonian Control Systems , 2013, IEEE Transactions on Automatic Control.

[24]  Laurent Lefèvre,et al.  Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems , 2017, J. Comput. Phys..

[25]  Alessandro Macchelli,et al.  Stability Analysis of Nonlinear Repetitive Control Schemes , 2018, IEEE Control Systems Letters.

[26]  Arjan van der Schaft,et al.  Port-Hamiltonian discretization for open channel flows , 2010, Syst. Control. Lett..

[27]  A. Schaft,et al.  On Alternative Poisson Brackets for Fluid Dynamical Systems and Their Extension to Stokes-Dirac Structures , 2013 .

[28]  Stefano Stramigioli,et al.  Port-Based Modeling and Simulation of Mechanical Systems With Rigid and Flexible Links , 2009, IEEE Transactions on Robotics.

[29]  Hans Zwart,et al.  Linear wave systems on n-D spatial domains , 2014, Int. J. Control.

[30]  Ravi N. Banavar,et al.  Stabilizing a Flexible Beam on a Cart: A Distributed Port-Hamiltonian Approach , 2009, 2009 European Control Conference (ECC).

[31]  Arjan van der Schaft,et al.  Reaction-Diffusion Systems in the Port-Hamiltonian Framework , 2010 .

[33]  Ryojun Ikeura,et al.  Multi-Input Multi-Output Integrated Ionic Polymer-Metal Composite for Energy Controls , 2012, Micromachines.

[34]  A. Macchelli.  Energy-Based Control of Spatially-Discretized Distributed Port-Hamiltonian Systems , 2012 .

[35]  Alessandro Macchelli,et al.  Dissipativity-based boundary control of linear distributed port-Hamiltonian systems , 2018, Autom..

[36]  C. Engström,et al.  Spectral properties of conservative, dispersive, and absorptive photonic crystals , 2018, GAMM-Mitteilungen.

[37]  Julien Lequeurre,et al.  The piston problem in a port-Hamiltonian formalism , 2015 .

[38]  Françoise Couenne,et al.  Structure-preserving infinite dimensional model reduction: Application to adsorption processes , 2009 .

[39]  P. Kotyczka.  On the feedforward control problem for discretized port-Hamiltonian systems , 2014 .

[40]  Alessandro Macchelli.  Energy shaping of distributed parameter port-Hamiltonian systems based on finite element approximation , 2011, Syst. Control. Lett..

[41]  Hans Zwart,et al.  On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems , 2017, IEEE Transactions on Automatic Control.

[42]  B. Maschke,et al.  Geometric pseudospectral method for spatial integration of dynamical systems , 2011 .

[43]  Stefano Stramigioli,et al.  Port-Based Modeling of a Flexible Link , 2007, IEEE Transactions on Robotics.

[44]  D. Matignon,et al.  Structure-Preserving Finite Volume Method for 2D Linear and Non-Linear Port-Hamiltonian Systems , 2018 .

[45]  Hans Zwart,et al.  Exponential Stability of a Class of Boundary Control Systems , 2009, IEEE Transactions on Automatic Control.

[46]  Yann Le Gorrec,et al.  Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct , 2018, J. Comput. Phys..

[47]  Sylvain Brémond,et al.  Symplectic spatial integration schemes for systems of balance equations , 2017 .

[48]  Hans Zwart,et al.  Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems With Dynamic Feedback , 2014, IEEE Transactions on Automatic Control.

[49]  Bernhard Maschke,et al.  Multi-scale distributed parameter modeling of ionic polymer-metal composite soft actuator , 2011 .

[50]  Daniel Alazard,et al.  Modeling and Control of a Rotating Flexible Spacecraft: A Port-Hamiltonian Approach , 2019, IEEE Transactions on Control Systems Technology.

[51]  Thomas Hélie,et al.  Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano , 2017 .

[52]  Markus Schöberl,et al.  Jet bundle formulation of infinite-dimensional port-Hamiltonian systems using differential operators , 2014, Autom..

[53]  Laurent Lefèvre,et al.  Material balance and closure equations for plasmas in Tokamaks , 2013 .

[54]  Françoise Couenne,et al.  Infinite Dimensional Port Hamiltonian Representation of reaction diffusion processes , 2015 .

[55]  Alessandro Macchelli,et al.  Passivity-based control of spatially discretized port-Hamiltonian system , 2010 .

[56]  Alessandro Macchelli.  Dirac structures on Hilbert spaces and boundary control of distributed port-Hamiltonian systems , 2014, Syst. Control. Lett..

[57]  Denis Matignon,et al.  A port-Hamiltonian model of liquid sloshing in moving containers and application to a fluid-structure system , 2017 .

[60]  Laurent Lefèvre,et al.  Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws , 2012, J. Comput. Phys..

[61]  Jacquelien M. A. Scherpen,et al.  Port-Hamiltonian Modeling of a Nonlinear Timoshenko Beam with Piezo Actuation , 2014, SIAM J. Control. Optim..

[63]  A. Schaft,et al.  CONTROL BY INTERCONNECTION FOR DISTRIBUTED PORT HAMILTONIAN SYSTEMS , 2005 .

[64]  Jacquelien M. A. Scherpen,et al.  Hamiltonian perspective on compartmental reaction-diffusion networks , 2012, Autom..

[65]  Laurent Lefèvre,et al.  A structure-preserving Partitioned Finite Element Method for the 2D wave equation , 2018 .

[66]  Ghislain Haine,et al.  Partitioned Finite Element Method for port-Hamiltonian systems with Boundary Damping: Anisotropic Heterogeneous 2D wave equations , 2019, IFAC-PapersOnLine.

[67]  H. Zwart,et al.  Port-Hamiltonian modelling of nonlocal longitudinal vibrations in a viscoelastic nanorod , 2019, Mathematical and Computer Modelling of Dynamical Systems.

[68]  Kurt Schlacher,et al.  Modelling of piezoelectric structures–a Hamiltonian approach , 2008 .

[69]  Alessandro Macchelli,et al.  Control by interconnection of mixed port Hamiltonian systems , 2005, IEEE Transactions on Automatic Control.

[70]  Denis Dochain,et al.  Burning magneto-hydrodynamics plasmas model: A port-based modelling approach , 2017 .

[71]  Bernhard Maschke,et al.  A structured control model for the thermo-magneto-hydrodynamics of plasmas in tokamaks , 2016 .

[72]  A. Schaft,et al.  Hamiltonian formulation of planar beams , 2003 .

[73]  F. Couenne,et al.  Distributed port-Hamiltonian modelling for irreversible processes , 2017 .

[74]  Laurent Lefèvre,et al.  Geometric discretization for a plasma control model , 2013 .

[75]  Françoise Couenne,et al.  Infinite Dimensional Port Hamiltonian Representation of Chemical Reactors , 2012 .

[76]  Laurent Lefèvre,et al.  Parabolic matching of hyperbolic system using Control by Interconnection , 2017 .

[77]  Joachim Deutscher,et al.  Stability and passivity preserving Petrov-Galerkin approximation of linear infinite-dimensional systems , 2012, Autom..

[78]  P. Kotyczka.  Finite Volume Structure-Preserving Discretization of 1D Distributed-Parameter Port-Hamiltonian Systems , 2016 .

[79]  Bernhard Maschke,et al.  Port-based modelling of mass transport phenomena , 2009 .

[80]  Alessandro Macchelli,et al.  A Stability Analysis Based on Dissipativity of Linear and Nonlinear Repetitive Control , 2019, IFAC-PapersOnLine.

[81]  Jacquelien M. A. Scherpen,et al.  Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems , 2012, Autom..

[82]  Ramkrishna Pasumarthy,et al.  A Finite Dimensional Approximation of the shallow water Equations: The port-Hamiltonian Approach , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[83]  Alessandro Macchelli,et al.  Asymptotic Stabilisation of Distributed Port-Hamiltonian Systems by Boundary Energy-Shaping Control , 2015 .

[84]  Lumped Approximation of Transmission Line with an Alternative Geometric Discretization , 2004 .

[85]  Hans Zwart,et al.  Well-posedness of infinite-dimensional linear systems with nonlinear feedback , 2019, Syst. Control. Lett..

[86]  Laurent Lefèvre,et al.  Control by interconnection and energy shaping methods of port Hamiltonian models - Application to the shallow water equations , 2009, 2009 European Control Conference (ECC).

[87]  Mónika Polner,et al.  A Hamiltonian vorticity–dilatation formulation of the compressible Euler equations , 2013 .

[89]  Robert Altmann,et al.  A port-Hamiltonian formulation of the Navier-Stokes equations for reactive flows , 2017, Syst. Control. Lett..

[90]  Noboru Sakamoto,et al.  Optimality of Passivity-Based Controls for Distributed Port-Hamiltonian Systems , 2013, NOLCOS.

[91]  Hans Zwart,et al.  Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control , 2017, Autom..

[92]  L. Lefévre,et al.  Distributed and backstepping boundary controls for port-Hamiltonian systems with symmetries , 2017 .

[93]  Kurt Schlacher,et al.  Port-Hamiltonian modelling and energy-based control of the Timoshenko beam , 2011 .

[94]  Bernhard Maschke,et al.  Port hamiltonian systems extended to irreversible systems : The example of the heat conduction , 2004 .

[95]  A. Schaft,et al.  Hamiltonian formulation of distributed-parameter systems with boundary energy flow , 2002 .

[96]  Denis Matignon,et al.  Port-Hamiltonian formulation and symplectic discretization of plate models Part I: Mindlin model for thick plates , 2018, Applied Mathematical Modelling.