15 research outputs found
ARCH-COMP19 Category Report: Continuous and hybrid systems with nonlinear dynamics
We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In this year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmark problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Constrained Polynomial Zonotopes
We introduce constrained polynomial zonotopes, a novel non-convex set
representation that is closed under linear map, Minkowski sum, Cartesian
product, convex hull, intersection, union, and quadratic as well as
higher-order maps. We show that the computational complexity of the
above-mentioned set operations for constrained polynomial zonotopes is at most
polynomial in the representation size. The fact that constrained polynomial
zonotopes are generalizations of zonotopes, polytopes, polynomial zonotopes,
Taylor models, and ellipsoids, further substantiates the relevance of this new
set representation. The conversion from other set representations to
constrained polynomial zonotopes is at most polynomial with respect to the
dimension
Utilizing Dependencies to Obtain Subsets of Reachable Sets
Reachability analysis, in general, is a fundamental method that supports
formally-correct synthesis, robust model predictive control, set-based
observers, fault detection, invariant computation, and conformance checking, to
name but a few. In many of these applications, one requires to compute a
reachable set starting within a previously computed reachable set. While it was
previously required to re-compute the entire reachable set, we demonstrate that
one can leverage the dependencies of states within the previously computed set.
As a result, we almost instantly obtain an over-approximative subset of a
previously computed reachable set by evaluating analytical maps. The advantages
of our novel method are demonstrated for falsification of systems, optimization
over reachable sets, and synthesizing safe maneuver automata. In all of these
applications, the computation time is reduced significantly