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

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3 Author(s)
Habets, L.C.G.J.M. ; Dept. of Math. & Comput. Sci., Technische Univ. Eindhoven, Netherlands ; Collins, P.J. ; van Schuppen, J.H.

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:51 ,  Issue: 6 )