A simplex architecture for hybrid systems using barrier certificates

Junxing Yang, Md Ariful Islam, Abhishek Murthy, Scott A. Smolka, Scott D. Stoller

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


This paper shows how to use Barrier Certificates (BaCs) to design Simplex Architectures for hybrid systems. The Simplex architecture entails switching control of a plant over to a provably safe Baseline Controller when a safety violation is imminent under the control of an unverified Advanced Controller. A key step of determining the switching condition is identifying a recoverable region, where the Baseline Controller guarantees recovery and keeps the plant invariably safe. BaCs, which are Lyapunov-like proofs of safety, are used to identify a recoverable region. At each time step, the switching logic samples the state of the plant and uses bounded-time reachability analysis to conservatively check whether any states outside the zero-level set of the BaCs, which therefore might be non-recoverable, are reachable in one decision period under control of the Advanced Controller. If so, failover is initiated. Our approach of using BaCs to identify recoverable states is computationally cheaper and potentially more accurate (less conservative) than existing approaches based on state-space exploration. We apply our technique to two hybrid systems: a water tank pump and a stop-sign-obeying controller for a car.

Original languageEnglish
Title of host publicationComputer Safety, Reliability, and Security - 36th International Conference, SAFECOMP 2017, Proceedings
EditorsFriedemann Bitsch, Stefano Tonetta, Erwin Schoitsch
Number of pages15
ISBN (Print)9783319662657
StatePublished - 2017
Event36th International Conference on Computer Safety, Reliability, and Security, SAFECOMP 2017 - Trento, Italy
Duration: Sep 13 2017Sep 15 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10488 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference36th International Conference on Computer Safety, Reliability, and Security, SAFECOMP 2017


  • Barrier certificates
  • Hybrid systems
  • Reachability
  • Simplex architecture
  • Switching logic


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