Abstract
This paper addresses the question of extending the usual approximation and sampling theory of continuous signals and systems to those encompassing discontinuities, such as found in modern complex control systems (mode switches for instance). We provide some evidence that the Skorokhod topology is a good candidate for dealing with those cases in a uniform manner by showing that, in the boolean case, Skorokhod uniformly continuous signals are exactly the signals with uniform bounded variability.
This work has been partially supported by Esprit R&D project Crisys EP 25514 and by Airbus-Verimag contracts 2001-2002
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Chutinan and B.H. Krogh. Computing approximating automata for a class of hybrid systems. Mathematical and Computer Modeling of Dynamical Systems, 6:30–50, March 2000. Special Issue on Discrete Event Models of Continuous Systems.
P. Billingsley. Convergence of probability measures. John Wiley & Sons, 1999.
M.S. Branicky. Topology of hybrid systems. In 32nd Conference on Decision and Control, pages 2309–2311. IEEE, 1993.
P. Caspi. Embedded control: from asynchrony to synchrony and back. In T. Hen-zinger and Ch. Kirsch, editors, First International Wokshop on Embedded Software, volume 2211 of Lecture Notes in Computer Science, 2001.
P. Caspi and R. Salem. Threshold and bounded-delay voting in critical control systems. In Mathai Joseph, editor, Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 1926 of Lecture Notes in Computer Science, pages 68–81, September 2000.
E. Asarin, O. Maler, and A. Pnueli. On discretization of delays in timed automata and digital circuits. In R. deSimone and D. Sangiorgi, editors, Concur’98, volume 1466 of Lecture Notes in Computer Science, pages 470–484. Springer, 1998.
J. Ouaknine. Digitisation and full abstraction for dense-time model checking. In TAC AS 02, volume 2280 of Lecture Notes In Computer Science, pages 37–51. Springer, 2002.
H. Kopetz. Real-Time Systems Design Principles for Distributed Embedded Applications. Kluwer, 1997.
M. Broucke. Regularity of solutions and homotopic equivalence for hybrid systems. In Proceedings of the 37th IEEE Conference on Decision and Control, volume 4, pages 4283–4288, 1998.
R. Alur, T.A. Henzinger, G. Lafferriere, and G.J. Pappas. Discrete abstractions of hybrid systems. Proceedings of the IEEE, 88:971–984, 2000.
J.H. Wensley, L. Lamport, J. Goldberg, M.W. Green, K.N. Lewitt, P.M. Melliar-Smith, R.E Shostak, and Ch.B. Weinstock. SIFT: Design and analysis of a fault-tolerant computer for aircraft control. Proceedings of the IEEE, 66(10):1240–1255, 1978.
W. Kohn and A. Nerode. Models for hybrid systems: automata, topologies, controllability and observability. In Hybrid Systems, volume 732 of Lecture Notes in Computer Science. Springer, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Caspi, P., Benveniste, A. (2002). Toward an Approximation Theory for Computerised Control. In: Sangiovanni-Vincentelli, A., Sifakis, J. (eds) Embedded Software. EMSOFT 2002. Lecture Notes in Computer Science, vol 2491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45828-X_22
Download citation
DOI: https://doi.org/10.1007/3-540-45828-X_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44307-0
Online ISBN: 978-3-540-45828-9
eBook Packages: Springer Book Archive