Publications

Michael Clerx and Pieter Collins. Reducing run-times of excitable cell models by replacing computationally expensive functions with splines. To appear in Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems, 2014.

Pieter Collins. Input-output representations for verifying safety properties. To appear in Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems, 2014.

Johanna Nellen, Erika Abraham, Xin Chen, and Pieter Collins. Counterexample generation for hybrid automata. In Proceedings of the Second International Workshop on Formal Techniques for Safety-Critical Systems, 2013.

Luca Benvenuti, Davide Bresolin, Pieter Collins, Alberto Ferrari, Luca Geretti, and Tiziano Villa. Assume-guarantee verification of nonlinear hybrid systems with Ariadne. Int. J. Robust Nonlinear Control, 2012.

L.C.G.J.M. Habets, P.J. Collins, and J.H. van Schuppen. Control to facet by piecewise-affine output feedback. IEEE Trans. Automatic Control, 57(11):2831–2843, 2012.

Milahi Marin, Andrea Benigni, Hakima Lakhdar, Antonello Monti, and Pieter Collins. Towards the implementation of a parallel real-time simulator for DSP cluster. In Proceedings of the 2012 International Simulation Multi-Conference, 2012.

Pieter Collins, Davide Bresolin, Luca Geretti, and Tiziano Villa. Computing the evolution of hybrid systems using rigorous function calculus. In Proceedings of the 4th IFAC Conference on Analysis and Design of Hybrid Systems, 2012.

Luca Benvenuti, Davide Bresolin, Pieter Collins, Alberto Ferrari, Luca Geretti, and Tiziano Villa. Ariadne: Dominance checking of nonlinear hybrid automata using reachability analysis. In Proceedings of the 6th International Workshop on Reachability Problems, volume 7550 of Lecture Notes in Computer Science, pages 79–91, 2012.

Philippe Uyttendaele, Frank Thuijsman, Pieter Collins, Ralf Peeters, Gijs Schoenmakers, and Ronald Westra. Evolutionary games and periodic fitness. Dyn. Games Appl., 2(3):335–345, 2012.

Pieter Collins. Computable probability theory and stochastic processes. In Proceedings of the Ninth International Conference on Computability and Complexity in Analysis, 2012.

Pieter Collins and Ivan S. Zapreev. Computable semantics for CTL* on discrete-time and continuous-space dynamic systems. Int. J. Found. Comput. Sci., 22(4):801–821, 2011.

Lorenzo Sella and Pieter Collins. Computation of symbolic dynamics for two-dimensional piecewise-affine maps. Discrete Contin. Dyn. S. (B), 15(3):739–767, 2011.

Pieter Collins. Semantics and computability of the evolution of hybrid systems. SIAM J. Control Optim., 49(2):890–925, 2011.

Alexandre Goldsztejn, Wayne Hayes, and Pieter Collins. Tinkerbell is chaotic. SIAM J. Appl. Dynam. Sys., 10(4):1480–1501, 2011.

Pieter Collins, Milad Niqui, and Nathalie Revol. A validated real function calculus. Math. Comput. Sci., 5:437–467, 2011.

Pieter Collins, Luc C.G.J.M. Habets, Jan H. van Schuppen, Ivana Cerna, Jana Fabrikova, and David Safranek. Abstraction of biochemical reaction systems on polytopes. In Proceedings of the 18th IFAC World Congress, 2011.

Lorenzo Sella and Pieter Collins. Computation of symbolic dynamics for one-dimensional maps. J. Comput. Applied Math., 234:418–436, 2010.

  1. Zivanovic and P. Collins. Numerical solutions to noisy systems. In Proceedings of the 49th IEEE Conference on Decision and Control, pages 798 –803, 2010.

Pieter J. Collins, Milad Niqui, and Nathalie Revol. A Taylor function calculus for hybrid system analysis: Validation in Coq (extended abstract). In Proceedings of the Third International Workshop on Numerical Software Verification, 2010.

Pieter Collins and Daniel Gra ̧ca. Effective computability of solutions of differential inclusions–the ten thousand monkeys approach. J. Univ. Comput. Sci., 15(6):1162–1185, 2009.

Pieter J. Collins, Luc C.G.J.M. Habets, Mihaly Petreczky, and Jan H. van Schuppen. Control of piecewise-affine hybrid systems – Extended abstract. In A. Giua, C. Mahulea, M. Silva, and J. Zaytoon, editors, 3rd IFAC Conference on Analysis and Design of Hybrid Systems, pages 234–237, 2009.

Mihaly Petreczky, Dirk A. van Beek, Jacobus E. Rooda, Pieter Collins, and Jan H. van Schuppen. Sampled-data control of hybrid systems with discrete inputs and outputs. In A. Giua, C. Mahulea, M. Silva, and J. Zaytoon, editors, 3rd IFAC Conference on Analysis and Design of Hybrid Systems, pages 334–339, 2009.

D.A. van Beek, P. Collins, D.E. Nadales Agut, J.E. Rooda, and R.R.H. Schiffelers. New concepts in the abstract format of the Compositional Interchange Format. In A. Giua, C. Mahulea, M. Silva, and J. Zaytoon, editors, 3rd IFAC Conference on Analysis and Design of Hybrid Systems, 2009.

Pieter Collins. A computable type theory for control systems. In Proceedings of the 48th IEEE Conference on Decision and Control, 2009.

Pieter Collins and Ivan Zapreev. Computable CTL* for discrete-time and continuous-space dynamic systems. In Oliver Bournez and Igor Potapov, editors, Reachability Problems, volume 5797 of Lecture Notes in Computer Science, pages 107–119. Springer, 2009.

Pieter Collins. Computability of homology for compact absolute neighbourhood retracts. In Proceedings of the Sixth International Conference on Computability and Complexity in Analysis, 2009.

Pieter Collins. Controllability and falsification of hybrid systems. In Proceedings of the European Control Conference, 2009.

Pieter Collins. Computable types for dynamic systems. In Proceedings of the Fifth Conference on Computability in Europe, 2009.

Pieter Collins and Ivan S. Zapreev. Computable CTL for discrete-time and continuous-space dynamic systems. In Proceedings of the Fifth Conference on Computability in Europe, 2009.

Pieter Collins. Chaotic dynamics in hybrid systems. Nonlinear Dyn. Syst. Theory, 8(2):169–194, 2008.

C.M. Lee, P.J. Collins, B. Krauskopf, and H.M. Osinga. Tangency bifurcations of global Poincare maps. SIAM J. Appl. Dyn. Syst., 7(3):712–754, 2008.

Pieter Collins and Alexandre Goldszteijn. The reach-and-evolve algorithm for reachability analysis of nonlinear dynamical systems. In Vesa Halava and Igor Potapov, editors, Proceedings of the Workshop on Reachability Problems, Liverpool, . Electronic Notes in Theoretical Computer Science, pages 83–97, 2008.

Pieter Collins. Computability and representations of the zero set. In Vasco Brattka and Klaus Weihrauch, editors, Proceedings of the 5th International Conference on Computability and Complexity in Analysis, Electronic Notes in Theoretical Computer Science, pages 45–51, 2008.

Pieter Collins and Daniel Graça. Effective computability of solutions of ordinary differential equations – the thousand monkeys approach. In Proceedings of the 5th International Conference on Computability and Complexity in Analysis, Electronic Notes in Theoretical Computer Science, pages 53–64, 2008.

Lorenzo Sella and Pieter Collins. Symbolic dynamics for a piecewise-affine system with hysteresis. In Proceedings of the 18th International Symposium on the Mathematical Theory of Networks and Systems, Blacksburg, Virginia, 2008.

Pieter Collins. Computability of controllers for discrete-time semicontinuous systems. In Proceedings of the 18th International Symposium on the Mathematical Theory of Networks and Systems, Blacksburg, Virginia, 2008.

Pieter Collins, Luc Habets, and Jan H. van Schuppen. Control-to-facet by piecewise- affine output feedback. In Proceedings of the 18th International Symposium on the Mathematical Theory of Networks and Systems, Blacksburg, Virginia, 2008.

Luca Benvenuti, Davide Bresolin, Alberto Casagrande, Pieter Collins, Alberto Ferrari, Emanuele Mazzi, Alberto Sangiovanni-Vincentelli, and Tiziano Villa. Reachability computation for hybrid systems with ariadne. In Proceedings of the 17th IFAC World Congress, 2008.

Lorenzo Sella and Pieter Collins. Discrete dynamics of two-dimensional nonlinear hybrid automata. In Magnus Egerstedt and Bud Mishra, editors, Proceedings of the 11th International Workshop on Hybrid Systems: Computation and Control, St. Louis, 2008, volume 4981 of Lecture Notes in Computer Science, pages 486–499. Springer, 2008.

Pieter Collins. Optimal semicomputable approximations to reachable and invariant sets. Theory Comput. Syst., 41(1):33–48, 2007.

Pieter Collins. Universal trellises. J. Knot Theory Ramifications, 16(4):471–487, 2007.

Lorenzo Sella and Pieter Collins. Stability analysis of switched-linear hybrid systems. In Proceedings of the European Control Conference 2007, Kos, Greece, 2-5 July 2007, 2007.

Pieter Collins. Effective computation for nonlinear systems. In S. Barry Cooper, Benedikt Löwe, and Andrea Sorbi, editors, Computation and Logic in the Real World, Proceedings of the Third Conference on Computability in Europe, Siena, Italy, 18-23 June 2007, volume 4497 of Lecture Notes in Computer Science, pages 169–178. Springer, 2007.

Pieter Collins, Luc Habets, Anton Kuut, Margreet Nool, Mihaly Petreczky, and Jan H. van Schuppen. ConPAHS – a software package for control of piecewise-affine hybrid systems. In Proceedings of the 2006 IEEE Conference on Computer Aided Control Systems Design, Munich, Germany, October 4-6, 2006, pages 76–81, 2006.

  1. C. G. J. M. Habets, P. J. Collins, and J. H. van Schuppen. Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Trans. Automat. Control, 51(6):938–948, 2006.

Pieter Collins. Generalised hybrid trajectory spaces. In Proceedings of the 17th International Symposium on the Mathematical Theory of Networks and Systems, Kyoto, pages 2101–2109, 2006.

Andrea Balluchi, Alberto Casagrande, Pieter Collins, Alberto Ferrari, Tiziano Villa, and Alberto L. Sangiovanni-Vincentelli. Ariadne: a framework for reachability analysis of hybrid automata. In Proceedings of the 17th International Symposium on the Mathematical Theory of Networks and Systems, pages 1269–1267, 2006.

Pieter Collins and John Lygeros. Computability of finite-time reachable sets for hybrid systems. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, pages 4688–4693, New York, 2005.

Pieter Collins. On the computability of reachable and invariant sets. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, pages 4187–4192, New York, 2005.

Pieter Collins. Entropy-minimising models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits. Dyn. Syst., 20(4):369–400, 2005.

Pieter Collins. Continuity and computability of reachable sets. Theor. Comput. Sci., 341:162–195, 2005.

Pieter Collins. Forcing relations for homoclinic orbits of the Smale horseshoe map. Experiment. Math., 14(1):75–86, 2005.

Eugene Asarin and Pieter Collins. Noisy turing machines. In Proceedings of the 32nd International Colloquium on Automata, Languages and Programming, pages 1031–1042, 2005.

Pieter Collins and Bernd Krauskopf. Chaotic lasers: manifolds, bifurcations and symbolic dynamics. In Proceedings of Equadiff 2003, Singapore, 2005. World Scientific.

Pieter Collins. Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits. Dyn. Syst., 19(1):1–39, 2004.

Pieter Collins and Jan H. van Schuppen. Observability of hybrid systems and Turing machines. In Proceedings of the 43rd IEEE Conference on Decision and Control, New York, 2004.

Pieter Collins and Jan H. van Schuppen. Observability of piecewise-affine hybrid systems. In Hybrid Systems: Computation and Control, number 2993 in Lecture Notes in Computer Science, pages 265–279, 2004.

Pieter Collins. A trajectory-space approach to hybrid systems. In Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, Leuven, 2004.

Pieter Collins and Bernd Krauskopf. Entropy and bifurcations in a chaotic laser. Phys. Rev. E (3), 66(5):056201, 8, 2002.

Pieter Collins. Symbolic dynamics from homoclinic tangles. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 12(3):605–617, 2002.

Pieter Collins. Relative periodic point theory. Topology Appl., 115(1):97–114, 2001.

Pieter Collins. Dynamics forced by surface trellises. In Geometry and topology in dynamics (Winston-Salem, NC, 1998/San Antonio, TX, 1999), volume 246 of Contemp. Math., pages 65–86. Amer. Math. Soc., Providence, RI, 1999.