Theory of Optimal Control Using Bisimulations

  • Mireille Broucke
  • Maria Domenica Di Benedetto
  • Stefano Di Gennaro
  • Alberto Sangiovanni-Vincentelli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1790)


We consider the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal control problem: to synthesize optimal enabling conditions for switching between locations in which the control is constant. An algorithmic solution is obtained by translating the hybrid automaton to a finite automaton using a bisimulation and formulating a dynamic programming problem with extra conditions to ensure non-Zenoness of trajectories. We show that the discrete value function converges to the viscosity solution of the Hamilton-Jacobi-Bellman equation as a discretization parameter tends to zero.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Mireille Broucke
    • 1
  • Maria Domenica Di Benedetto
    • 1
    • 2
  • Stefano Di Gennaro
    • 2
  • Alberto Sangiovanni-Vincentelli
    • 1
  1. 1.Dept. of Electrical Engineering and Computer SciencesUniversity of California at BerkeleyUSA
  2. 2.Dip. di Ingegneria ElettricaUniversità di L’AquilaL’AquilaItaly

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