Abstract
This paper presents Coho, a reachability analysis tool for systems modeled by non-linear, ordinary differential equations. Coho represents high-dimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geometry to be exploited while also capturing dependencies in the behaviour of related variables. Reachability is performed by integration where methods from linear programming and linear systems theory are used to bound trajectories emanating from each face of the object. This paper has two contributions: first, we describe the implementation of Coho and, second, we present analysis results obtained by using Coho on several simple models.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Alur, C. Courcoubetis, N. Halbwachs, et al. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995.
Kenneth Arnold and James Gosling. The Java Programming Language. Addison-Wesley, 1996.
R. W. Brockett. Smooth dynamical systems which realize arithmetical and logical operations. In Hendrik Nijmeijer and Johannes M. Schumacher, editors, Three Decades of Mathematical Systems Theory: A Collection of Surveys at the Occasion of the 50th Birthday of J. C. Willems, volume 135 of Lecture Notes in Control and Information Sciences, pages 19–30. Springer, 1989.
Thao Dang and Oded Maler. Reachability analysis via face lifting. In Thomas A. Henzinger and Shankar Sastry, editors, Proceding of the First International Workshop on Hybrid Systems: Computation and Control, pages 96–109, Berkeley, California, April 1998.
Mark R. Greenstreet and Ian Mitchell. Integrating projections. In Thomas A. Henzinger and Shankar Sastry, editors, Proceding of the First International Workshop on Hybrid Systems: Computation and Control, pages 159–174, Berkeley, California, April 1998.
Mark R. Greenstreet. Verifying safety properties of di_erential equations. In Proceedings of the 1996 Conference on Computer Aided Verification, pages 277–287, New Brunswick, NJ, July 1996.
Morris W. Hirsch and Stephen Smale. Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, San Diego, CA, 1974.
Ian Mitchell and Mark Greenstreet. Proving Newtonian arbiters correct, almost surely. In Proceedings of the Third Workshop on Designing Correct Circuits, Båstad, Sweden, September 1996.
Franco P. Preparata and Michael I. Shamos. Computational Geometry: An Introduction. Texts and Monographs in Computer Science. Springer, 1985.
The Mathworks Inc., Natick, Mass. Matlab: High-Performance Numeric Computation and Visualization Software, 1992. http://www.matlab.com.
Claire Tomlin, George Pappas, and Shankar Sastry. Conflict resolution for air traffic management: A case study in multi-agent hybrid systems. Technical Report UCB/ERL M97/33, Electronics Research Laboratory, University of California, Berkeley, 1997. to appear in IEEE Transactions on Automatic Control.
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
Greenstreet, M.R., Mitchell, I. (1999). Reachability Analysis Using Polygonal Projections. 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_12
Download citation
DOI: https://doi.org/10.1007/3-540-48983-5_12
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