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Theoretical Computer Science
Volume 390, Issue 1, 22 January 2008, Pages 1-26
 
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doi:10.1016/j.tcs.2007.09.025    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2007 Elsevier Ltd All rights reserved.

Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools

Eugene Asarina, E-mail The Corresponding Author, Gordon Paceb, E-mail The Corresponding Author, Gerardo Schneiderc, Corresponding Author Contact Information, E-mail The Corresponding Author and Sergio Yovined, E-mail The Corresponding Author

aLIAFA, Case 7014, 2 pl. Jussieu, 75251 Paris Cedex 5, France bDepartment of Computer Science and AI, University of Malta, Msida, Malta cDepartment of Informatics, University of Oslo, P.O. Box 1080 Blindern, NO-0316 Oslo, Norway dCNRS-VERIMAG, Centre Equation, 2 Ave. Vignate, 38610 Gières, France

Received 21 February 2007; 
revised 13 September 2007; 
accepted 16 September 2007. 
Communicated by B. Durand. 
Available online 23 September 2007.

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Abstract

Polygonal differential inclusion systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. The reachability problem as well as the computation of certain objects of the phase portrait is decidable. In this paper we show how to compute the viability, controllability and invariance kernels, as well as semi-separatrix curves for SPDIs. We also present the tool SPeeDI+, which implements a reachability algorithm and computes phase portraits of SPDIs.

Keywords: Hybrid systems; Differential inclusions; Verification; Phase portrait


 
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