Algorithmic analysis of nonlinear hybrid systems

  • Thomas A. Henzinger
  • Pei -Hsin Ho
Session 7: Invited Titorial
Part of the Lecture Notes in Computer Science book series (LNCS, volume 939)


Hybrid systems model discrete programs that are embedded in continuous environments. Model-checking tools are available for the analysis of linear hybrid systems, whose continuous variables are bounded by piecewise-linear trajectories. Most embedded programs, however, operate in nonlinear environments. We present, analyze, and apply two algorithms for translating nonlinear hybrid systems into linear hybrid systems.

The clock translation replaces nonlinear variables by clock variables; the rate translation approximates nonlinear variables by piecewise-linear envelopes. Both translations are sound for reachability; that is, if we establish a safety property of the translated linear system, we may conclude that the original nonlinear system satisfies the property. The clock translation is also complete for reachability; that is, the original system and the translated system satisfy the same safety properties. The two translations apply to incomparable classes of nonlinear hybrid systems. From the clock translation we obtain a new decidability result for hybrid systems.

With the help of Hytech, a symbolic model checker for linear hybrid systems, we automatically verify a nonlinear railroad gate control program using the clock translation, and a nonlinear temperature control program using the rate translation.


Hybrid System Safety Property Label Transition System Action Predicate Rate Translation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Thomas A. Henzinger
    • 1
  • Pei -Hsin Ho
    • 1
  1. 1.Computer Science DepartmentCornell UniversityIthaca

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