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International Workshop on Hybrid Systems: Computation and Control

HSCC 2001: Hybrid Systems: Computation and Control pp 418–432Cite as

Validating a Hamilton-Jacobi Approximation to Hybrid System Reachable Sets

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2034))

Abstract

We develop a general framework for solving the hybrid system reachability problem, and indicate how several published techniques fit into this framework. The key unresolved need of any hybrid system reachability algorithm is the computation of continuous reachable sets; consequently, we present new results on techniques for calculating numerical approximations of such sets evolving under general nonlinear dynamics with inputs. Our tool is based on a local level set procedure for boundary propagation in continuous state space, and has been implemented using numerical schemes of varying orders of accuracy. We demonstrate the numerical convergence of these schemes to the viscosity solution of the Hamilton-Jacobi equation, which was shown in earlier work to be the exact representation of the boundary of the reachable set. We then describe and solve a new benchmark example in nonlinear hybrid systems: an auto-lander for a commercial aircraft in which the switching logic and continuous control laws are designed to maximize the safe operating region across the hybrid state space.

Research supported by DARPA under the Software Enabled Control Program (AFRL contract F33615-99-C-3014), by a Frederick E. Terman Faculty Award, and by a graduate fellowship provided by the Délégation Générale pour l’Armement in France.

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Author information

Authors and Affiliations

  1. Scientific Computing and Computational Mathematics Program, Gates 2B, Stanford University, Stanford, CA, 94305, USA

    Ian Mitchell

  2. Department of Aeronautics and Astronautics, Durand 250, Stanford University, Stanford, CA, 94305, USA

    Alexandre M. Bayen & Claire J. Tomlin

Authors
  1. Ian Mitchell
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  2. Alexandre M. Bayen
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  3. Claire J. Tomlin
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Editor information

Editors and Affiliations

  1. Dipartimento di Ingegneria Elettrica, Universitá dell’Aquila, Poggio di Roio, 67040, L’Aquila, Italy

    Maria Domenica Di Benedetto

  2. University of California at Berkeley, Berkeley, CA, 94720

    Alberto Sangiovanni-Vincentelli

  3. PARADES, Via San Pantaleo, 66, 00186, Roma, Italy

    Alberto Sangiovanni-Vincentelli

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© 2001 Springer-Verlag Berlin Heidelberg

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Mitchell, I., Bayen, A.M., Tomlin, C.J. (2001). Validating a Hamilton-Jacobi Approximation to Hybrid System Reachable Sets. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_34

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  • DOI: https://doi.org/10.1007/3-540-45351-2_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41866-5

  • Online ISBN: 978-3-540-45351-2

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