Breaking Dense Structures: Proving Stability of Densely Structured Hybrid Systems

Abstraction and refinement is widely used in software development. Such techniques are valuable since they allow to handle even more complex systems. One key point is the ability to decompose a large system into subsystems, analyze those subsystems and deduce properties of the larger system. As cyber-physical systems tend to become more and more complex, such techniques become more appealing. In 2009, Oehlerking and Theel presented a (de-)composition technique for hybrid systems. This technique is graph-based and constructs a Lyapunov function for hybrid systems having a complex discrete state space. The technique consists of (1) decomposing the underlying graph of the hybrid system into subgraphs, (2) computing multiple local Lyapunov functions for the subgraphs, and finally (3) composing the local Lyapunov functions into a piecewise Lyapunov function. A Lyapunov function can serve multiple purposes, e.g., it certifies stability or termination of a system or allows to construct invariant sets, which in turn may be used to certify safety and security. In this paper, we propose an improvement to the decomposing technique, which relaxes the graph structure before applying the decomposition technique. Our relaxation significantly reduces the connectivity of the graph by exploiting super-dense switching. The relaxation makes the decomposition technique more efficient on one hand and on the other allows to decompose a wider range of graph structures.Comment: In Proceedings ESSS 2015, arXiv:1506.0325

The Degree of Masking Fault Tolerance vs. Temporal Redundancy

Abstract-Self-stabilizing systems, intended to run for a long time, commonly have to cope with transient faults during their mission. We model the behavior of a distributed self-stabilizing system under such a fault model as a Markov chain. Adding fault detection to a self-correcting non-masking fault tolerant system is required to progress from non-masking systems towards their masking fault tolerant functional equivalents. We introduce a novel measure, called limiting window availability (LWA) and apply it on self-stabilizing systems in order to quantify the probability of (masked) stabilization against the time that is needed for stabilization. We show how to calculate LWA based on Markov chains: first, by a straightforward Markov chain modeling and second, by using a suitable abstraction resulting in a space-reduced Markov chain. The proposed abstraction can in particular be applied to spot fault tolerance bottlenecks in the system design

Integration of the End Cap TEC+ of the CMS Silicon Strip Tracker

The silicon strip tracker of the CMS experiment has been completed and inserted into the CMS detector in late 2007. The largest sub-system of the tracker is its end cap system, comprising two large end caps (TEC) each containing 3200 silicon strip modules. To ease construction, the end caps feature a modular design: groups of about 20 silicon modules are placed on sub-assemblies called petals and these self-contained elements are then mounted into the TEC support structures. Each end cap consists of 144 petals, and the insertion of these petals into the end cap structure is referred to as TEC integration. The two end caps were integrated independently in Aachen (TEC+) and at CERN (TEC--). This note deals with the integration of TEC+, describing procedures for end cap integration and for quality control during testing of integrated sections of the end cap and presenting results from the testing

Reception Test of Petals for the End Cap TEC+ of the CMS Silicon Strip Tracker

The silicon strip tracker of the CMS experiment has been completed and was inserted into the CMS detector in late 2007. The largest sub system of the tracker are its end caps, comprising two large end caps (TEC) each containing 3200 silicon strip modules. To ease construction, the end caps feature a modular design: groups of about 20 silicon modules are placed on sub-assemblies called petals and these self-contained elements are then mounted onto the TEC support structures. Each end cap consists of 144 such petals, which were built and fully qualified by several institutes across Europe. Fro