The Reachability Problem for Uncertain Hybrid Systems Revisited: A Viability Theory Perspective

  • Yan Gao
  • John Lygeros
  • Marc Quincapoix
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)


We revisit the problem of designing controllers to meet safety specifications for hybrid systems, whose evolution is affected by both control and disturbance inputs. The problem is formulated as a dynamic game and an appropriate notion of hybrid strategy for the control inputs is developed. The design of hybrid strategies to meet safety specifications is based on an iteration of alternating discrete and continuous safety calculations. We show that, under certain assumptions, the iteration converges to a fixed point, which turns out to be the maximal set of states for which the safety specifications can be met. The continuous part of the calculation relies on the computation of the set of winning states for one player in a two player, two target, pursuit evasion differential game. We develop a characterization of these winning states using methods from non-smooth analysis and viability theory.


Hybrid System Control Input Hybrid Strategy Dynamic Game Discrete Transition 
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 2006

Authors and Affiliations

  • Yan Gao
    • 1
  • John Lygeros
    • 2
  • Marc Quincapoix
    • 3
  1. 1.School of ManagementUniversity of Shanghai for Science and TechnologyShanghaiChina
  2. 2.Department of Electrical EngineeringUniversity of Patras, RioPatrasGreece
  3. 3.Laboratoire de MathematiquesUniversité de Bretagne OccidentaleBrestFrance

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