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Formal Methods in System Design

, Volume 50, Issue 1, pp 1–38 | Cite as

Reachability computation for polynomial dynamical systems

  • Tommaso DreossiEmail author
  • Thao Dang
  • Carla Piazza
Article

Abstract

This paper is concerned with the problem of computing the bounded time reachable set of a polynomial discrete-time dynamical system. The problem is well-known for being difficult when nonlinear systems are considered. In this regard, we propose three reachability methods that differ in the set representation. The proposed algorithms adopt boxes, parallelotopes, and parallelotope bundles to construct flowpipes that contain the actual reachable sets. The latter is a new data structure for the symbolic representation of polytopes. Our methods exploit the Bernstein expansion of polynomials to bound the images of sets. The scalability and precision of the presented methods are analyzed on a number of dynamical systems, in comparison with other existing approaches.

Keywords

Reachability Polynomial dynamical systems Bernstein coefficients 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Verimag, Centre EquationGièresFrance
  3. 3.University of UdineUdineItaly

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