Research Interests

Topological dynamics

• Fixed-point theories of Lefschetz and Nielsen
• Conley index theory
• Homo/heteroclinic tangles and trellises
• Forcing relations of horseshoe orbits

Control theory

• Foundations of hybrid systems theory
• Observability and realisation of (piecewise-affine) hybrid systems
• Verification of nonlinear hybrid automata

Computability

• Computable analysis and topology
• Computable semantics for systems and logics
• Rigorous computations for nonlinear systems

Research Grants

Job Openings

Software

• Ariadne -- Reachability analysis of hybrid systems, including a library for set-based computation. Latest internal release (0.4.4)
• Tangle -- Computations on tangles and braids. (Version 0.3.5)
• TBLAS -- Templated BLAS routines in C++. (Development version 0.4.1)
• TLAPACK -- Templated LAPACK routines for general matrices in C++. (Development version 0.4.1)

Publications

Journals

• Pieter Collins and Daniel Graca. "Effective computability of solutions of differential inclusions --- the ten thousand monkeys approach". J. Univ. Comput. Sci. 15(6) 1162--1185, 2009.
• Clare Lee, Pieter Collins, Bernd Krauskopf and Hinke Osinga"Tangency bifurcations of global Poincaré maps". SIAM J. Appl. Dyn. Syst. 7(3), 71200754, 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.
• Luc C. G. J. M. Habets, Pieter Collins and Jan 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, "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". Experimental Math. 14(1), 75--86, 2005.
• Pieter Collins, "Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits". Dyn. Syst. 19(1), 1--39, 2004.
• Pieter Collins and Bernd Krauskopf, "Entropy and bifurcations in a chaotic laser". Phys. Rev. E 66(5), 056201, 2002.
• Pieter Collins, "Symbolic Dynamics from Homoclinic Tangles". Intern. J. Bifur. Chaos 12(3), 605--617, 2002.
• Pieter Collins, "Relative periodic point theory". Topology Appl. 115(1), 97--114, 2001.

Invited contributions

• Pieter Collins, "Chaotic Dynamics in Hybrid Systems", Nonlinear Dynamics and Systems Theory 8(2), 169--194, 2008.

Conference proceedings

• Pieter Collins. "A computable type theory for control systems". To appear in Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, 2009.
• Pieter Collins and Ivan Zapreev. "Computable CTL* for discrete-time and continuous-space dynamic systems". In Proceedings of the 3rd Workshop on Reachability Problems, Lecture Notes in Computer Science 5797, 107--119, 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 Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems, Zaragoza 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 Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems, Zaragoza 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 Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems, Zaragoza 2009.
• Pieter Collins, "Controllability and Falsification of Hybrid Systems". Proceedings of the European Control Conference, Budapest, August 2009.
• Pieter Collins, "Computability of Homology for Compact Absolute Neighbourhood Retracts". Proceedings of the Sixth International Conference on Computability and Complexity in Analysis, Ljubljana, August 2009.
• Pieter Collins and Alexandre Goldsztejn, "The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems". Proceedings of the 2nd Workshop on Reachability Problems, Liverpool, July 2008. Electronic Notes in Theoretical Computer Science 223, 87--102, 2008.
• Pieter Collins, "Computability and Representations of the Zero Set". Proceedings of the Fifth International Conference on Computability and Complexity in Analysis, Hagen, August 2008. Electronic Notes in Theoretical Computer Science 221, 37--43, 2008.
• Pieter Collins and Daniel S. Graça, "Effective Computability of Solutions of Ordinary Differential Equations The Thousand Monkeys Approach". Proceedings of the Fifth International Conference on Computability and Complexity in Analysis, Hagen, August 2008. Electronic Notes in Theoretical Computer Science 221, 103--114, 2008.
• Pieter Collins, Luc Habets and Jan H. van Schuppen, "Control-to-facet by piecewise-affine output feedback". Proceedings of the 18th International Symposium on the Mathematical Theory of Networks and Systems, Blacksburg, Virginia, July 2008.
• Pieter Collins, "Computability of controllers for discrete-time semicontinuous systems". Proceedings of the 18th International Symposium on the Mathematical Theory of Networks and Systems, Blacksburg, Virginia, July 2008.
• Lorenzo Sella and Pieter Collins, "Symbolic Dynamics for a Piecewise-Affine System with Hysteresis". Proceedings of the 18th International Symposium on the Mathematical Theory of Networks and Systems, Blacksburg, Virginia, July 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", Proceedings of the 17th IFAC World Congress, 2008.
• Lorenzo Sella and Pieter Collins, "Discrete Dynamics of Two-Dimensional Nonlinear Hybrid Automata". Proceedings of the 11th International Conference on Hybrid Systems: Computation and Control, Springer-Verlag, 2008.
• Pieter Collins, "Effective computation for nonlinear systems", Computation and Logic in the Real World, Lecture Notes in Computer Science 4497, 169--178, Springer-Verlag, 2007.
• Lorenzo Sella and Pieter Collins, "Stability Analysis of Switched-Linear Hybrid Systems". Proceedings of the European Control Conference 2007, Kos, Greece, July 2-5, 2007.
• Pieter Collins, Luc C.G.J.M. Habets, Anton Kuut, Margreet Nool, Mihaly Petreczky and Jan H. van Schuppen, "ConPAHS - A software package for control of piecewise-affine hybrid systems". Proceedings of the IEEE International Symposium on Computer-Aided Control System Design, 2006.
• Pieter Collins, "Generalised Hybrid Trajectory Spaces". Proceedings of the 17th International Symposium on the Mathematical Theory of Networks and Systems, Kyoto, Japan, July 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". Proceedings of the 17th International Symposium on the Mathematical Theory of Networks and Systems, Kyoto, Japan, July 2006.
• Pieter Collins and John Lygeros, "Computability of finite-time reachable sets for hybrid systems". Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference, Sevilla, 2005.
• Pieter Collins, "On the Computability of Reachable and Invariant Sets". Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference, Sevilla, 2005.
• Eugene Asarin and Pieter Collins, "Noisy Turing machines". Proceedings of the International Colloquium on Automata, Languages and Programming, Lisbon, 2005.
• Pieter Collins and Jan H. van Schuppen, "Observability of Hybrid Systems and Turing Machines". Proceedings of the 43rd IEEE Conference on Decision and Contol, Paradise Island, Bahamas, 2004.
• Pieter Collins, "A trajectory-space approach to hybrid systems". Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, Katholiek Univ. Leuven, Belgium, August 2004.
• Pieter Collins and Jan H. van Schuppen, "Observability of Piecewise-Affine Hybrid Systems". Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 2623, Springer-Verlag, 2004.
• Pieter Collins and Bernd Krauskopf, "Chaotic lasers: manifolds, bifurcations and symbolic dynamics", Proceedings of Equadiff 2003, World Scientific.
• Pieter Collins, "Dynamics Forced by Surface Trellises". Geometry and topology in dynamics, Contemp. Math. 246, 1999.

Other

• Pieter Collins, "Dynamics of Surface Maps with Homoclinic and Heteroclinic Tangles". Ph.D. Thesis, University of California, Berkeley, 1999
• Pieter Collins, "Hybrid trajectory spaces". CWI Research Report MAS-R0501, ISSN 1386-3703, 2005.
• Pieter Collins, "Semantics and Computability of the Evolution of Hybrid Systems". CWI Research Report MAS-R0801, ISSN 1386-3703, 2008.

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