Reachability and Control Synthesis for Piecewise-Affine Hybrid Systems on Simplices
Luc C. G. J. M. Habets, Pieter J. Collins, Jan H. van Schuppen · IEEE Transactions on Automatic Control · 2006
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.