Abstract
A simple model for ideal control networks is proposed in this paper. A model for hybrid systems due to Witsenhausen is extended by adding both a discrete output and input. This extended model is used for modeling an ideal network of interactive hybrid systems. An equivalence is established between the network model and the Witsenhausen model. This equivalence allows for simulating complicated systems, and extending different properties of Witsenhausen type systems to control network systems. A simple HVAC application is modeled using the above equivalence.
This research was supported in part by the Army Research Office grant number DAAH04-93-D-0002.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
H. S. Witsenhausen. “A class of hybrid-state continuous time dynamic systems,” IEEE Transactions on Automatic Control, 11(2):161–167, v1966.
R. S. Raji. “Smart networks for control,” IEEE Spectrum, June 1994, p. 49–55.
D. Radford. “Spread-spectrum data leap through ac power wiring,” IEEE Spectrum, November 1996, p. 48–53.
G. Walsh. “On race conditions for networked control systems,” in Proceedings of the 30th CISS,Princeton, NJ, March 1996, p 411–415.
K. Tindell, A. Burns and A.J. Wellings. “Calculating controller area network (CAN) message response times,” Control Eng. Practice, vol. 3, no. 8, p. 1168–1169, 1995.
M. S. Branicky. “Studies in hybrid systems: modeling, analysis, and control,” Ph.D. dissertation, MIT, June 1995.
A. Back, J. Guckenheimer and M. Myers. “A dynamical simulation facility for hybrid systems,” in R. L. Grossman, A. Nerode, A. P. Ravn, H. Rischel et al. Hybrid Systems p. 255–267. Springer-Verlag, New York, 1993.
A. Nerode and W. Kohn. “Models for hybrid systems: Automata, topologies stability.“ In R. L. Grossman, A. Nerode, A. P. Ravn, H. Rischel et al. Hybrid Systems et al., p. 317–356. Springer-Verlag, New York, 1993.
L. Tavernini. “Differential automata and their discrete simulators.“ in Nonlinear analysis, Theory, Methods and Applications, 11(6): 665–683, 1987.
W. S. Wong and R. W. Brockett. “Systems with finite communication bandwidth constraints — Part I: State estimation problems,” in IEEE Transactions on Automatic Control, 42(9): 1294–1299.
R. W. Brockett. “Hybrid models for motion control systems.“ in H.L. Trentelman and J.C. Willems, editors, Essays in Control: Perspectives in the Theory and its Applications, p. 29–53, 1993.
R. W. Brockett. “Dynamical systems and their associated automata.“ in U.Helmke, R. Menniken and J.Saurer, editors, Systems and networks: Mathematical theory and applications. Akademie Verlag, Berlin 1994.
R. L. Grossman, A. Nerode, A. P. Ravn, H. Rischel editors Hybrid systems, volume 736 of Lecture notes in computer science. Springer-Verlag, New York, 1993.
U. Özgüner, H. Goktas, H. Chan. Automotive suspension control through a computer communication network. Vt IEEE Conference on Control Application, 1992.
J. Bräuninger, R. Emig, T. Küttner and A. Löfffe.Controller Area Network for Truck and Bus Application., SAE Transactions, v 99, sect 2, 1990, p 704–714.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bushnell, L., Beldiman, O., Walsh, G. (1998). An equivalence between a control network and a switched hybrid system. In: Henzinger, T.A., Sastry, S. (eds) Hybrid Systems: Computation and Control. HSCC 1998. Lecture Notes in Computer Science, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64358-3_32
Download citation
DOI: https://doi.org/10.1007/3-540-64358-3_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64358-6
Online ISBN: 978-3-540-69754-1
eBook Packages: Springer Book Archive