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Optimality Zone Algorithms for Hybrid Systems: Efficient Algorithms for Optimal Location and Control Computation

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Book cover Hybrid Systems: Computation and Control (HSCC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3927))

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Abstract

A general Hybrid Minimum Principle (HMP) for hybrid optimal control problems (HOCPs) is presented in [1, 2, 3, 4] and in [4, 5], a class of efficient, provably convergent Hybrid Minimum Principle (HMP) algorithms were obtained based upon the HMP. The notion of optimality zones (OZs) ([3, 4]) provides a theoretical framework for the computation of optimal location (i.e. discrete state) schedules for HOCPs (i.e. discrete state sequences with the associated switching times and states). This paper presents the algorithm HMPOZ which fully integrates the prior computation of the OZs into the HMP algorithms class. Summing (a) the computational investment in the construction of the OZs for a given HOCP, and (b) the complexity of (i) the computation of the optimal schedule, (ii) the optimal switching time and optimal switching state sequence, and (iii) the optimal continuous control input, yields a complexity estimate for the algorithm HMPOZ which is linear (i.e. O(L)) in the number of switching times L.

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Author information

Authors and Affiliations

  1. Department of Electrical & Computer Engineering, Centre for Intelligent Machines, McGill University, Montréal, Québec, H3A 2A7, Canada

    Peter E. Caines & M. Shahid Shaikh

Authors
  1. Peter E. Caines
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  2. M. Shahid Shaikh
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Editor information

Editors and Affiliations

  1. Center for Control, Dynamical Systems and Computation, University of California, 93106, Santa Barbara, CA, USA

    João P. Hespanha

  2. SRI International, 333 Ravenswood Ave, Menlo Park, CA, USA

    Ashish Tiwari

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© 2006 Springer-Verlag Berlin Heidelberg

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Caines, P.E., Shaikh, M.S. (2006). Optimality Zone Algorithms for Hybrid Systems: Efficient Algorithms for Optimal Location and Control Computation. In: Hespanha, J.P., Tiwari, A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730637_12

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  • DOI: https://doi.org/10.1007/11730637_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33170-4

  • Online ISBN: 978-3-540-33171-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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