# Discrete-time control for rectangular hybrid automata

Henzinger TA, Kopke P. 1997. Discrete-time control for rectangular hybrid automata. Proceedings of the 24th International Colloquium on Automata, Languages and Programming. ICALP: Automata, Languages and Programming, LNCS, vol. 1256, 582–593.

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Author

Henzinger, Thomas A

^{ISTA}^{}; Kopke, PeterSeries Title

LNCS

Abstract

Rectangular hybrid automata model digital control programs of analog plant environments. We study rectangular hybrid automata where the plant state evolves continuously in real-numbered time, and the controller samples the plant state and changes the control state discretely, only at the integer points in time. We prove that rectangular hybrid automata have finite bisimilarity quotients when all control transitions happen at integer times, even if the constraints on the derivatives of the variables vary between control states. This is sharply in contrast with the conventional model where control transitions may happen at any real time, and already the reachability problem is undecidable. Based on the finite bisimilarity quotients, we give an exponential algorithm for the symbolic sampling-controller synthesis of rectangular automata. We show our algorithm to be optimal by proving the problem to be EXPTIME-hard. We also show that rectangular automata form a maximal class of systems for which the sampling-controller synthesis problem can be solved algorithmically.

Publishing Year

Date Published

1997-01-01

Proceedings Title

Proceedings of the 24th International Colloquium on Automata, Languages and Programming

Acknowledgement

This research was supported in part by the ONR YIP award N00014-95-1-0520, by the NSF CAREER award CCR-9501708, by the NSF grant CCR-9504469, by the AFOSR contract F49620-93-1-0056, by the ARO MURI contract DAAH-04-96-1-0341, by the ARO contract DAAL03-91-C-0027 through the MSI at Cornell University, by the ARPA grant NAG2-892, and by the SRC contract 95-DC-324.036.

Volume

1256

Page

582 - 593

Conference

ICALP: Automata, Languages and Programming

Conference Location

Bologna, Italy

Conference Date

1997-07-07 – 1997-07-11

ISBN

IST-REx-ID

### Cite this

Henzinger TA, Kopke P. Discrete-time control for rectangular hybrid automata. In:

*Proceedings of the 24th International Colloquium on Automata, Languages and Programming*. Vol 1256. Springer; 1997:582-593. doi:10.1007/3-540-63165-8_213Henzinger, T. A., & Kopke, P. (1997). Discrete-time control for rectangular hybrid automata. In

*Proceedings of the 24th International Colloquium on Automata, Languages and Programming*(Vol. 1256, pp. 582–593). Bologna, Italy: Springer. https://doi.org/10.1007/3-540-63165-8_213Henzinger, Thomas A, and Peter Kopke. “Discrete-Time Control for Rectangular Hybrid Automata.” In

*Proceedings of the 24th International Colloquium on Automata, Languages and Programming*, 1256:582–93. Springer, 1997. https://doi.org/10.1007/3-540-63165-8_213.T. A. Henzinger and P. Kopke, “Discrete-time control for rectangular hybrid automata,” in

*Proceedings of the 24th International Colloquium on Automata, Languages and Programming*, Bologna, Italy, 1997, vol. 1256, pp. 582–593.Henzinger, Thomas A., and Peter Kopke. “Discrete-Time Control for Rectangular Hybrid Automata.”

*Proceedings of the 24th International Colloquium on Automata, Languages and Programming*, vol. 1256, Springer, 1997, pp. 582–93, doi:10.1007/3-540-63165-8_213.