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 |
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Pages (from-to) | 938-948 |
Journal | IEEE Transactions on Automatic Control |
Volume | 51 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2006 |