Motor-Transmission Drive System: a Benchmark Example for Safety Verification

Abstract

This paper introduces the Motor-Transmission Drive System as a benchmark example for the safety analysis of hybrid systems. In particular, we illustrate the problem of checking the gear meshing duration and the impact impulse (both of which we refer to as safety) of the Motor-Transmission Drive System. We aim to provide a complete problem description to which different verification tools or approaches for safety analysis can be applied and compared. For this reason, we first elaborate on a hybrid automaton (HA) model of the Motor-Transmission Drive System to describe the gear meshing process with uncertain initial states, and then we specify the safety property of interest. Next, we clarify the characteristic phenomena exhibited by the benchmark which make the verification problem hard to solve. Finally, we show some simulation results to illustrate the influences of the initial states on the safety property. This benchmark example can help the researchers and engineers to find appropriate methods for safety verification of this kind of hybrid system.

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

“…• Gearbox benchmark from [16]: This benchmark has the smallest number of continuous state variables, but the reachable set does not converge to a steady state and the reachable set for one point in time might intersect multiple guards at once.…”

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

“…• Gearbox benchmark from [17]: This benchmark has the smallest number of continuous state variables, but the reachable set does not converge to a steady state and the reachable set for one point in time might intersect multiple guards at once.…”

“…With four continuous state variables, the gearbox benchmark has a relatively low number of continuous state variables. The challenging aspect of this benchmark is that the solution heavily depends on the initial state as already pointed out in [17]. For some initial continuous states, the target region is reached without any discrete transition, while for other initial states, several discrete transitions are required.…”

ARCH-COMP17 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics

“…The challenging aspect of this benchmark is that the solution heavily depends on the initial state as already pointed out in [11]. For some initial continuous states, the target region is reached without any discrete transition, while for other initial states, several discrete transitions are required.…”

“…Less continuous state variables are considered in the platooning benchmark [8], but one can arbitrarily switch between two discrete states: a normal operation mode and a communication-failure mode. Finally, the gearbox benchmark in [11] has the smallest number of continuous state variables, but the reachable set does not contract to a steady state and the reachable set for one point in time might intersect multiple guards at once. Next, let us briefly discuss some specificities of each benchmark problem.…”