Reachability Analysis of Hybrid Systems Using Symbolic Orthogonal Projections

ABSTRACT. This paper deals with reachability analysis of hybrid systems with continuous dynamics described by linear differential inclusions and arbitrary linear maps for discrete updates. The invariants, guards, and sets of reachable states are given as convex polyhedra. Our reachability algorithm is based on a novel representation class for convex polyhedra, the symbolic orthogonal projections (sops), on which various geometric operations, including convex hulls, Minkowski sums, linear maps, and intersections, can be performed efficiently and exactly. The capability to represent intersections of convex polyhedra exactly is superior to support function-based approaches like the LGG-algorithm of Le Guernic and Girard.

Accompanied by some simple examples, we address the problem of the monotonic growth of the exact representation and propose a combination of our reachability algorithm with the LGG-algorithm. This results in an efficient method of better accuracy than the LGG-algorithm and its productive implementation in SpaceEx.