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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
verfasst von : Thao Dang, David Salinas
Erschienen in: Computer Aided Verification
Verlag: Springer Berlin Heidelberg
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This paper is concerned with the problem of computing the image of a set by a polynomial function. Such image computations constitute a crucial component in typical tools for set-based analysis of hybrid systems and embedded software with polynomial dynamics, which found applications in various engineering domains. One typical example is the computation of all states reachable from a given set in one step by a continuous dynamics described by a differential or difference equation. We propose a new algorithm for over-approximating such images based on the Bernstein expansion of polynomial functions. The images are stored using template polyhedra. Using a prototype implementation, the performance of the algorithm was demonstrated on two practical systems as well as a number of randomly generated examples.