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
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Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-bounded Projection-based Controllers
2023
W.P.M.H. Heemels, A. Tanwani
IEEE Conference on Decision and Control (CDC) 2023, Singapore "ieee Control Systems Letters [joint with CDC]", p. 1590-1595
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Hybrid Systems with Continuous-Time Inputs: Subtleties in Solution Concepts and Existence Results
2021
W.P.M.H. Heemels, P. Bernard, K. Scheres, R. Postoyan, R.G. Sanfelice
IEEE Conference on Decision and Control (CDC) 2021, Austin (Texas), USA, p. 5368-5373
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Extended Projected Dynamical Systems with Applications to Hybrid
Integrator-Gain System
December, 2019
B. Sharif, M.F. Heertjes, W.P.M.H. Heemels
IEEE Conference on Decision and Control (CDC) 2019, Nice, France, p. 5773-5778
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Consistency of a time-stepping method for a class of piecewise-linear networks
2002
Camlibel, M.K., Heemels, W.P.M.H., Schumacher, J.M.,
IEEE Transactions on Circuits and Systems 49(3), p. 349-357
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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
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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
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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
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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
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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
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Equivalence of hybrid dynamical models
July, 2001
W.P.M.H. Heemels, B. De Schutter and A. Bemporad
Automatica 37(7), p. 1085-1091
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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"
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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
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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
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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
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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