---
_id: '4565'
abstract:
- lang: eng
  text: "In the literature, we find several formulations of the control\r\nproblem
    for timed and hybrid systems. We argue that formulations where\r\na controller
    can cause an action at any point in dense (rational or real)\r\ntime are problematic,
    by presenting an example where the controller\r\nmust act faster and faster, yet
    causes no Zeno effects (say, the control\r\nactions are at times 0, 1/2, 1, 1
    1/4, 2, 2 1/8, 3, 3 1/16 ,...). Such a controller is,\r\nof 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 well- understood 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."
acknowledgement: "Partially supported by the FNRS, Belgium, under grant 1.5.096.01.\r\nPartially
  supported by the DARPA SEC grant F33615-C-98-3614, the AFOSR MURI grant F49620-00-1-0327,
  the NSF Theory grant CCR-9988172, and the MARCO GSRC grant 98-DT-660.\r\nPartially
  supported by a “Crédit aux chercheurs” from the Belgian National Fund for Scientific
  Research."
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Franck
  full_name: Cassez, Franck
  last_name: Cassez
- first_name: Thomas A
  full_name: Henzinger, Thomas A
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
- first_name: Jean
  full_name: Raskin, Jean
  last_name: Raskin
citation:
  ama: 'Cassez F, Henzinger TA, Raskin J. A comparison of control problems for timed
    and hybrid systems. In: <i>Proceedings of the 5th International Workshop on Hybrid
    Systems: Computation and Control</i>. Vol 2289. Springer; 2002:134-148. doi:<a
    href="https://doi.org/10.1007/3-540-45873-5_13">10.1007/3-540-45873-5_13</a>'
  apa: 'Cassez, F., Henzinger, T. A., &#38; Raskin, J. (2002). A comparison of control
    problems for timed and hybrid systems. In <i>Proceedings of the 5th International
    Workshop on Hybrid Systems: Computation and Control</i> (Vol. 2289, pp. 134–148).
    Stanford, CA, USA: Springer. <a href="https://doi.org/10.1007/3-540-45873-5_13">https://doi.org/10.1007/3-540-45873-5_13</a>'
  chicago: 'Cassez, Franck, Thomas A Henzinger, and Jean Raskin. “A Comparison of
    Control Problems for Timed and Hybrid Systems.” In <i>Proceedings of the 5th International
    Workshop on Hybrid Systems: Computation and Control</i>, 2289:134–48. Springer,
    2002. <a href="https://doi.org/10.1007/3-540-45873-5_13">https://doi.org/10.1007/3-540-45873-5_13</a>.'
  ieee: 'F. Cassez, T. A. Henzinger, and J. Raskin, “A comparison of control problems
    for timed and hybrid systems,” in <i>Proceedings of the 5th International Workshop
    on Hybrid Systems: Computation and Control</i>, Stanford, CA, USA, 2002, vol.
    2289, pp. 134–148.'
  ista: 'Cassez F, Henzinger TA, Raskin J. 2002. A comparison of control problems
    for timed and hybrid systems. Proceedings of the 5th International Workshop on
    Hybrid Systems: Computation and Control. HSCC: Hybrid Systems - Computation and
    Control, LNCS, vol. 2289, 134–148.'
  mla: 'Cassez, Franck, et al. “A Comparison of Control Problems for Timed and Hybrid
    Systems.” <i>Proceedings of the 5th International Workshop on Hybrid Systems:
    Computation and Control</i>, vol. 2289, Springer, 2002, pp. 134–48, doi:<a href="https://doi.org/10.1007/3-540-45873-5_13">10.1007/3-540-45873-5_13</a>.'
  short: 'F. Cassez, T.A. Henzinger, J. Raskin, in:, Proceedings of the 5th International
    Workshop on Hybrid Systems: Computation and Control, Springer, 2002, pp. 134–148.'
conference:
  end_date: 2002-03-27
  location: Stanford, CA, USA
  name: 'HSCC: Hybrid Systems - Computation and Control'
  start_date: 2002-03-25
date_created: 2018-12-11T12:09:30Z
date_published: 2002-03-14T00:00:00Z
date_updated: 2023-06-02T10:29:10Z
day: '14'
doi: 10.1007/3-540-45873-5_13
extern: '1'
intvolume: '      2289'
language:
- iso: eng
month: '03'
oa_version: None
page: 134 - 148
publication: 'Proceedings of the 5th International Workshop on Hybrid Systems: Computation
  and Control'
publication_identifier:
  isbn:
  - '9783540433217'
publication_status: published
publisher: Springer
publist_id: '144'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A comparison of control problems for timed and hybrid systems
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 2289
year: '2002'
...