Abstract
The paper presents a concept for the reachability analysis of switched continuous systems in which switching only occurs when the continuous state trajectory crosses thresholds defined by a rectangular partitioning of the state space. It combines an existing approach for approximating such systems by rectangular automata with an existing reachability algorithm for this class of hybrid automata. Instead of creating a complete abstraction of the original system by a rectangular automaton first and then analyzing it, in the presented procedure the flow conditions of the visited locations are determinded on-the-fly during the course of the analysis. The algorithm is illustrated with the help of a simple physical example.
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.
Similar content being viewed by others
References
A. Chutinan and B. H. Krogh. Computing polyhedral approximations of dynamic flow pipes. 1998. Submitted to 37th IEEE Conf. on Decision and Control.
T. Dang and O. Maler. Reachability analysis via face lifting. In T.A. Henzinger and S. Sastry, editors, HSCC 98: Hybrid Systems Computation and Control, Lecture Notes in Computer Science 1386, pages 96–109. Springer-Verlag, 1998.
R. Fletcher. Practical Methods of Optimization. J. Wiley and Sons, 1987.
M.R. Greenstreet. Verifying safety properties of differential equations. In R. Alur and T.A. Henzinger, editors, CAV 96: Computer Aided Verification, Lecture Notes in Computer Science 1102, pages 277–287. Springer-Verlag, 1996.
M.R. Greenstreet and I. Mitchell. Integrating projections. In T.A. Henzinger and S. Sastry, editors, HSCC 98: Hybrid Systems Computation and Control, Lecture Notes in Computer Science 1386, pages 159–174. Springer-Verlag, 1998.
T.A. Henzinger, P.-H. Ho, and H. Wong-Toi. Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control, 43(4):540–554, 1998.
T.A. Henzinger, P.W. Kopke, A. Puri, and P. Varaiya. What’s decidable about hybrid automata? In Proceedings of the 27th Annual Symposium on Theory of Computing, pages 373–382. ACM Press, 1995.
S. Kowalewski, O. Stursberg, M. Fritz, H. Graf, I. Hoffmann, J. Preußig, M. Remelhe, S. Simon, and H. Treseler. A case study in tool-aided analysis of discretely controlled continuous systems: The two-tanks problem. In Hybrid Systems V, Lecture Notes in Computer Science. Springer-Verlag, 1998.
J. Preußig, S. Kowalewski, H. Wong-Toi, and T.A. Henzinger. An algorithm for the approximative analysis of rectangular automata. In FTRTFT98: Formal Techniques for Real-time and Fault-tolerant Systems, LNCS. Springer-Verlag, 1998.
O. Stursberg, S. Kowalewski, I. Hoffmann, and J. Preußig. Comparing timed and hybrid automata as approximations of continuous systems. In P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, editors, Hybrid Systems IV, Lecture Notes in Computer Science 1273, pages 361–377. Springer-Verlag, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Preußig, J., Stursberg, O., Kowalewski, S. (1999). Reachability Analysis of a Class of Switched Continuous Systems by Integrating Rectangular Approximation and Rectangular Analysis. In: Vaandrager, F.W., van Schuppen, J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48983-5_20
Download citation
DOI: https://doi.org/10.1007/3-540-48983-5_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65734-7
Online ISBN: 978-3-540-48983-2
eBook Packages: Springer Book Archive