Continuous Petri Nets and Transition Systems

In many systems, the values of finitely many parameters can be influenced in a continuous way by controls acting with possibly varying strength over intervals of time. For this, we present general models of continuous Petri nets and of continuous transition systems with situation-dependent concurrency. With a suitable concept of morphisms, we obtain a categorial adjunction between these two models, and often even a coreflection. This shows that the concept of regions is also applicable in this continuous setting. Finally, we prove that our categories of continuous Petri nets and of continuous automata with concurrency have products and conditional coproducts.

[1]  René David,et al.  Continuous and Hybrid Petri Nets , 1998, J. Circuits Syst. Comput..

[2]  Mogens Nielsen,et al.  Models for Concurrency , 1992 .

[3]  E. Dubois,et al.  Continuous Petri net with maximal speeds depending on time , 1994, Proceedings of the Fourth International Conference on Computer Integrated Manufacturing and Automation Technology.

[4]  Manfred Droste.  Concurrent Automata and Domains , 1992, Int. J. Found. Comput. Sci..

[5]  René David,et al.  Petri nets for modeling of dynamic systems: A survey , 1994, Autom..

[6]  Grzegorz Rozenberg,et al.  Elementary Transition Systems , 1990, Theor. Comput. Sci..

[7]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[8]  Madhavan Mukund.  Petri Nets and Step Transition Systems , 1992, Int. J. Found. Comput. Sci..

[9]  Philippe Darondeau,et al.  Theory of Regions , 1996, Petri Nets.

[10]  Manfred Droste,et al.  Petri nets and automata with concurrency relations—an adjunction , 1993 .

[11]  Manfred Droste,et al.  From Petri Nets to Automata with Concurrency , 2002, Appl. Categorical Struct..

[12]  Manuel Silva Suárez,et al.  Autonomous Continuous P/T Systems , 1999, ICATPN.

[13]  Isabel Demongodin,et al.  Differential Petri nets: representing continuous systems in a discrete-event world , 1998 .