Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Abstract

Abstract.A promising technique for the formal verification of embedded and cyber-physical systems is flow-pipe construction, which creates a sequence of regions covering all reachable states over time. Flow-pipe construction methods can check whether specifications are met for all states, rather than just testing using a finite and incomplete set of simulation traces. A fundamental challenge when using flow-pipe construction on high-dimensional systems is the cost of geometric operations, such as intersection and convex hull. We address this challenge by showing that it is often possible to remove the need to perform high-dimensional geometric operations by combining two model transformations, direct time-triggered conversion and dynamics scaling. Further, we prove the overapproximation error in the conversion can be made arbitrarily small. Finally, we show that our transformation-based approach enables the analysis of a drivetrain system with up to 51 dimensions.

Reachability Analysis of Large Linear Systems With Uncertain Inputs in the Krylov Subspace

“…In particular, when using zonotopes, support functions, or the combination thereof, one can efficiently compute systems with more than 100 continuous state variables. Recently, a new technique has been proposed which combines simulation results by using the superposition principle to represent reachable states via generalized star sets [15,25]. Although this technique can compute large systems, it cannot consider uncertain time-varying inputs and requires a formally verified solver for linear systems.…”

“…At the time the approach in [37] was proposed, tools for reachability analysis had an exponential complexity as well, so that overall the computation time could be significantly reduced. However, modern tools such as SpaceEx [29], Flow* [18], HyLAA [15], XSpeed [36], or CORA [2] have a polynomial complexity, as demonstrated in [3], and thus would most certainly outperform the technique proposed in [37], even without any order reduction. The same authors later combined reachability analysis with Krylov subspace approximation methods [38].…”

ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics

“…The powertrain benchmark is an extensible benchmark for hybrid systems with linear continuous dynamics taken from [5,Sec. 6] and [8,Sec. 4].…”

ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics

“…The powertrain benchmark is an extensible benchmark for hybrid systems with linear continuous dynamics taken from [5, Sec. 6] and [8,Sec. 4].…”

“…As soon as the gears are close enough, the gear is considered meshed. The model includes a monitor state that checks whether the gears are meshed or free and is available in SpaceEx format 8 and as a Simulink model 9 . Once the monitor reaches the state meshed, it stays there indefinitely.…”