Efficient representation and computation of reachable sets for hybrid systems

  • Authors:

  • Olaf Stursberg;Bruce H. Krogh

  • Affiliations:

  • Process Control Laboratory, CT-AST, University of Dortmund, Dortmund, Germany and Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
  • Year:
  • 2003

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Abstract

Computing reachable sets is an essential step in most analysis and synthesis techniques for hybrid systems. The representation of these sets has a deciding impact on the computational complexity and thus the applicability of these techniques. This paper presents a new approach for approximating reachable sets using oriented rectangular hulls (ORHs), the orientations of which are determined by singular value decompositions of sample covariance matrices for sets of reachable states. The orientations keep the over-approximation of the reachable sets small in most cases with a complexity of low polynomial order with respect to the dimension of the continuous state space. We show how the use of ORHs can improve the efficiency of reachable set computation significantly for hybrid systems with nonlinear continuous dynamics.