Verification of periodically controlled hybrid systems: Application to an autonomous vehicle

Tichakorn Wongpiromsarn, Sayan Mitra, Andrew Lamperski, Richard M. Murray

Research output: Contribution to journalArticlepeer-review


This article introduces Periodically Controlled Hybrid Automata (PCHA) for modular specification of embedded control systems. In a PCHA, control actions that change the control input to the plant occur roughly periodically, while other actions that update the state of the controller may occur in the interim. Such actions could model, for example, sensor updates and information received from higher-level planning modules that change the set point of the controller. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariant properties of PCHAs is presented. For PCHAs with polynomial continuous vector fields, it is possible to check these conditions automatically using, for example, quantifier elimination or sum of squares decomposition. We examine the feasibility of this automatic approach on a small example. The proposed technique is also used to manually verify safety and progress properties of a fairly complex planner-controller subsystem of an autonomous ground vehicle. Geometric properties of planner-generated paths are derived which guarantee that such paths can be safely followed by the controller.

Original languageEnglish (US)
Article number53
JournalTransactions on Embedded Computing Systems
Issue numberSUPPL. 2
StatePublished - Aug 2012


  • Embedded systems
  • Invariants

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture


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