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

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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.

This work was partially supported by the European Community projects IST-2001-33520 CC (Control and Computation) and IST-2003-507219 PROSYD (Property-based System Design) as well as by the project CalCel of région Rhône-Alpes.