Reachability and control synthesis for piecewise-affine hybrid systems on simplices

L.C.G.J.M. Habets, P.J. Collins, J.H. Schuppen, van

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    Abstract

    In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices. The construction is based on the solution to the control-to-facet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit algorithm using only linear algebra and reach-set computations for automata; no numerical integration is required. The method is conservative, in that it may fail to find a control law where one exists, but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewise-affine hybrid systems is undecidable.
    Original languageEnglish
    Pages (from-to)938-948
    JournalIEEE Transactions on Automatic Control
    Volume51
    Issue number6
    DOIs
    Publication statusPublished - 2006

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