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Theory of Optimal Control Using Bisimulations

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Hybrid Systems: Computation and Control (HSCC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1790))

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Abstract

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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Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA, 94720, USA

    Mireille Broucke, Maria Domenica Di Benedetto & Alberto Sangiovanni-Vincentelli

  2. Dip. di Ingegneria Elettrica, Università di L’Aquila, Poggio di Roio, 67040, L’Aquila, Italy

    Maria Domenica Di Benedetto & Stefano Di Gennaro

Authors
  1. Mireille Broucke
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  2. Maria Domenica Di Benedetto
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  3. Stefano Di Gennaro
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  4. Alberto Sangiovanni-Vincentelli
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Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

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© 2000 Springer-Verlag Berlin Heidelberg

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Broucke, M., Di Benedetto, M.D., Di Gennaro, S., Sangiovanni-Vincentelli, A. (2000). Theory of Optimal Control Using Bisimulations. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_11

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  • DOI: https://doi.org/10.1007/3-540-46430-1_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

  • eBook Packages: Springer Book Archive

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