Chapter

Hybrid Systems: Computation and Control

Volume 3927 of the series Lecture Notes in Computer Science pp 257-271

Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

  • Antoine GirardAffiliated withDepartment of Electrical and Systems Engineering, University of Pennsylvania
  • , Colas Le GuernicAffiliated withÉcole Normale Supérieure
  • , Oded MalerAffiliated withVERIMAG

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Abstract

This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems.