Well-posedness and Equivalence

In this subtheme of "Hybrid and Switched Systems" we ask ourselves the following questions:

  • Well-posedness: When are hybrid systems well-posed in the sense that they produce (global / infinite / complete) solution trajectories for initial states and inputs of interest and when are these solutions unique?
  • Equivalence: When can we translate certain hybrid model classes into "equivalent" others, where equivalence refers to producing the same dynamical behaviour?

Related Publications

2017

  • Computation of Periodic Solutions in Maximal Monotone Dynamical Systems with Guaranteed Consistency

    2017
    W. P. M. H. Heemels, V. Sessa, F. Vasca, M. K. Camlibel
    Nonlinear Analysis: Hybrid Systems 24, p. 100-114

2015

  • Definitions of incremental stability for hybrid systems (invited paper)

    2015
    R. Postoyan, J.J.B. Biemond, W.P.M.H. Heemels, N. Van De Wouw
    IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan, p. 5544 - 5549

2009

  • Chapter 5: Further switched systems

    2009
    A. Bemporad, M.K. Camlibel, W.P.M.H. Heemels, A. J. van der Schaft, J.M. Schumacher and B. De Schutter
    in "HYCON Handbook of Hybrid Systems Control Theory-Tools-Applications", Cambridge University Press, p. 139-192

  • Chapter 2: Survey of modelling, analysis and control of hybrid systems

    2009
    B. De Schutter, W.P.M.H. Heemels, J. Lunze and C. Prieur
    in "HYCON Handbook of Hybrid Systems Control Theory-Tools-Application", Cambridge University Press, p. 31-55

2004

  • Well-posedness of Hybrid Systems

    2004
    M.K. Camlibel, W.P.M.H. Heemels, A.J. van der Schaft and J.M. Schumacher
    in "Encyclopedia of Life Support Systems (EOLSS)", EOLSS Publishers, Oxford,UK

  • On the controllability of bimodal piecewise linear systems

    2004
    M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
    in "Hybrid Systems: Computation and Control, LNCS", Springer 2993, p. 250-264

2003

  • On solution concepts and well-posedness of linear relay systems

    December, 2003
    A.Y. Pogromsky, W.P.M.H. Heemels and H. Nijmeijer
    Automatica 39(12), p. 2139-2147

  • On the existence and uniqueness of solution trajectories to hybrid dynamical systems

    2003
    W.P.M.H. Heemels, M.K. Camlibel, A.J. van der Schaft and J.M. Schumacher
    in "Nonlinear and Hybrid Control in Automotive Applications", Springer, p. 391-422

  • Modelling, well-posedness, and stability of switched electrical networks

    2003
    W.P.M.H. Heemels, M.K. Camlibel, A.J. van der Schaft and J.M. Schumacher
    in "Hybrid Systems: Computation and Control, Lecture Notes in Computer Science", Springer 2623, p. 249-266

2002

  • On hybrid systems and closed-loop MPC systems

    May, 2002
    A. Bemporad, W.P.M.H. Heemels and B. De Schutter
    IEEE Transactions on Automatic Control 47(5), p. 863-869

  • Note on the equivalence of linear complementarity problems

    2002
    B. De Schutter, W.P.M.H. Heemels and A. Bemporad
    Operations Research Letters 30(4), p. 211-222

  • Solution concepts for hybrid dynamical systems

    2002
    M.K. Camlibel, W.P.M.H. Heemels, A.J. van der Schaft and J.M. Schumacher
    IFAC World Congress 2002, Barcelona, Spain

  • On switched Hamiltonian systems

    2002
    K.M. Gerritsen, A.J. van der Schaft and W.P.M.H. Heemels
    International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2002, South Bend, USA

  • Well-posedness of the complementarity class of hybrid systems

    2002
    W.P.M.H. Heemels, M.K. Camlibel, A.J. van der Schaft and J.M. Schumacher
    IFAC World Congress 2002, Barcelona, Spain

2001

  • Equivalence of hybrid dynamical models

    July, 2001
    W.P.M.H. Heemels, B. De Schutter and A. Bemporad
    Automatica 37(7), p. 1085-1091

  • On well-posedness of relay systems

    2001
    A.Yu. Pogromsky, W.P.M.H. Heemels and H. Nijmeijer
    Nonlinear Control Systems (NOLCOS) 2001, Saint-Petersburg, Russia

  • On hybrid systems and closed-loop MPC systems

    December, 2001
    A. Bemporad, W.P.M.H. Heemels and B. De Schutter
    IEEE Conference on Decision and Control (CDC) 2001, Orlando, USA, p. 1645-1649

  • On the relation between classes of hybrid dynamical models

    December, 2001
    W.P.M.H. Heemels, B. De Schutter and A. Bemporad
    IEEE Conference on Decision and Control (CDC) 2001, Orlando, USA, p. 364-369

2000

  • Projected dynamical systems in a complementarity formalism

    2000
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    Operations Research Letters 27(2), p. 83-91

  • Linear complementarity systems

    2000
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    SIAM Journal on Applied Mathematics 60(4), p. 1234-1269

  • Linear complementarity systems: modelling power and well-posedness

    2000
    W.P.M.H. Heemels, M.K. Camlibel, S. Weiland and J.M. Schumacher
    Workshop on Systems with Time-Domain Constraints 2000, Eindhoven, The Netherlands

  • On dynamics, complementarity and passivity: electrical networks with ideal diodes

    2000
    W.P.M.H. Heemels, M.K. Camlibel and J.M. Schumacher
    Conference on Automation of Mixed Processes: Hybrid Dynamic Systems 2000, Dortmund, Germany

  • From Lipschitzian to non-Lipschitzian characteristics: continuity of behaviors

    December, 2000
    M.K. Camlibel, M.K.K. Cevik, W.P.M.H. Heemels and J.M. Schumacher
    IEEE Conference on Decision and Control (CDC) 2000, Sydney, Australia, p. 4373-4378

  • Well-posedness of a class of linear networks with ideal diodes

    2000
    M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
    International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2000, Perpignan, France

  • A time-stepping method for relay systems

    December, 2000
    W.P.M.H. Heemels, M.K. Camlibel and J.M. Schumacher
    IEEE Conference on Decision and Control (CDC) 2000, Sydney, Australia, p. 4461-4466

  • Continuity of smooth approximations of complementarity systems

    2000
    M.K. Camlibel, M.K.K. Cevik, W.P.M.H. Heemels and J.M. Schumacher
    Workshop on Systems with Time-Domain Constraints 2000, Eindhoven, The Netherlands

1999

  • The Rational Complementarity Problem

    1999
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    Linear Algebra and its Applications 294, p. 93-135

  • Well-posedness of linear complementarity systems

    December, 1999
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    IEEE Conference on Decision and Control (CDC) 1999, Phoenix, USA, p. 3037-3042

  • The nature of solutions to linear passive complementarity systems

    December, 1999
    M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
    IEEE Conference on Decision and Control (CDC) 1999, Phoenix, USA, p. 3043-3042

  • Linear complementarity systems: a study in hybrid systems

    1999
    W.P.M.H. Heemels (supervised by Hans Schumacher, Siep Weiland and Paul van den Bosch)
    Eindhoven University of Technology "PhD Thesis"

1998

  • Complementarity problems in linear complementarity systems

    June, 1998
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    American Control Conference (ACC) 1998, Philadelphia, USA, p. 706-710

  • Mode selection in linear complementarity systems

    1998
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    IFAC Conference on System Structure and Control (SSC) 1998, Nantes, France

  • Dissipative systems and complementarity conditions

    December, 1998
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    IEEE Conference on Decision and Control (CDC) 1998, Tampa, USA, p. 4127-4132

1997

  • Complete description of dynamics in the linear complementary-slackness class of hybrid systems

    December, 1997
    W.P.M.H. Heemels, J.M. Schumacher and S. Weiland
    IEEE Conference on Decision and Control (CDC) 1997, San Diego, USA, p. 1243-1248