Reachability and control of affine hypersurface systems on polytopes
Zhiyun Lin, Mireille E. Broucke · 2007
This paper studies the reachability problem with state constraints; that is, to reach a target without leaving a polytope. First, we provide a conceptual framework for the constrained reachability problem. Then we obtain necessary and sufficient conditions for the problem for affine hypersurface systems. In addition, we provide a geometric characterization of the maximal set of initial states from which the objective can be met. Finally, algorithms on constructing piecewise affine feedback controls that accomplish the objective are presented.