Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion

  • Thao Dang
  • David Salinas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5643)


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.


Hybrid System Polynomial System Multivariate Polynomial Polynomial Optimization Polynomial Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Thao Dang
    • 1
  • David Salinas
    • 1
  1. 1.VerimagGièresFrance

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