Flow* 1.2: More Effective to Play with Hybrid Systems

Abstract

This paper gives a brief overview of the new features introduced in the latest version of the tool Flow*. We mainly describe the new efficient scheme for integrating linear ODEs. We show that it can efficiently handle the challenging benchmarks on which, to the best of our knowledge, only SpaceEx works. Moreover, it is also possible to extend the method to deal with unbounded initial sets. A comparison between Flow* 1.2 and SpaceEx on those benchmarks is given. Besides, we also investigate the scalability of Flow* 1.2 based on our non-linear line circuit benchmarks.

CommonRoad-Reach: A Toolbox for Reachability Analysis of Automated Vehicles

“…Existing toolboxes are either not capable of excluding time-varying forbidden states [23]- [26], [28], or are based on inherently inefficient Hamilton-Jacobi-Bellmann solvers [29]- [32]. Despite the aforementioned applications of reachable sets in recent works, a toolbox implementing those methods is not publicly available.…”

“…2) Existing toolboxes for reachability analysis: Recently, several publicly available toolboxes for reachability analysis have been developed. Tools such as Flow* [23] and SpaceEx [24] offer efficient C++ implementations of set representations and reachability algorithms for linear [24] and nonlinear [23] hybrid systems. Although C++-based tools have good performance, their compilation overhead makes them difficult to use for prototyping.…”

A Multi-Step Approach to Accelerate the Computation of Reachable Sets for Road Vehicles

“…can be computed with standard tools for reachability analysis; a non-exhaustive list is given by Flow* [24], SpaceEx [25], C2E2 [26], JuliaReach [27], and CORA [28].…”

Interval Reachability Analysis using Second-Order Sensitivity

“…The second class considers a simpler set representation in the form of (multi-dimensional) intervals, using methods based on differential inequalities (Scott and Barton, 2013), Taylor models (Chen et al, 2012), growth bounds (Reissig et al, 2016) or monotonicity . Due to the simpler set representation, these methods tend to offer better efficiency and scalability at the cost of the accuracy of the over-approximations, and are thus particularly used in the field of abstraction-based control synthesis (see e.g.…”

“…Indeed, the sampling in our third step can be used to tune the desired tradeoff between the computational complexity and the conservativeness of the over-approximation. Compared to methods relying on Taylor models such as Chen et al (2012) which usually require a decomposition of the time range to reduce the accumulation of errors, the proposed approach relying on mixed-monotonicity does not have this problem and all over-approximations can be computed in a single time step.…”