A comparison of control problems for timed and hybrid systems

Franck Cassez, Thomas A. Henzinger, Jean François Raskin

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

56 Citations (Scopus)


In the literature, we find several formulations of the control problem for timed and hybrid systems.We argue that formulations where a controller can cause an action at any point in dense (rational or real) time are problematic, by presenting an example where the controller must act faster and faster, yet causes no Zeno effects (say, the control actions are at times (formula presented). Such a controller is, of course, not implementable in software. Such controllers are avoided by formulations where the controller can cause actions only at discrete (integer) points in time. While the resulting control problem is wellunderstood if the time unit, or “sampling rate” of the controller, is fixed a priori, we define a novel, stronger formulation: the discrete-time control problem with unknown sampling rate asks if a sampling controller exists for some sampling rate. We prove that this problem is undecidable even in the special case of timed automata.

Original languageEnglish
Title of host publicationHybrid Systems: Computation and Control
Subtitle of host publication5th International Workshop, HSCC 2002, Proceedings
EditorsC Tomlin, M Greenstreet
Place of PublicationBerlin; Heidelberg
PublisherSpringer, Springer Nature
Number of pages15
ISBN (Print)354043321X, 9783540433217
Publication statusPublished - 2002
Externally publishedYes
Event5th International Workshop on Hybrid Systems: Computation and Control, HSCC 2002 - Stanford, United States
Duration: 25 Mar 200227 Mar 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)03029743
ISSN (Electronic)16113349


Other5th International Workshop on Hybrid Systems: Computation and Control, HSCC 2002
Country/TerritoryUnited States


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