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

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

doi:10.1109/TAC.2006.876952

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

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

Center for Analysis, Scientific Computing and Applications

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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 language	English
Pages (from-to)	938-948
Journal	IEEE Transactions on Automatic Control
Volume	51
Issue number	6
DOIs	https://doi.org/10.1109/TAC.2006.876952
Publication status	Published - 2006

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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.",

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

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