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We study the reach control problem for affine systems on simplices, and thefocus is on cases when it is known that the problem is not solvable bycontinuous state feedback. We examine from a geometric viewpoint the structuralproperties of the system which make continuous state feedbacks fail. Thisstructure is encoded by so-called reach control indices, which are defined anddeveloped in the paper. Based on these indices, we propose a subdivisionalgorithm and associated piecewise affine feedback. The method is shown tosolve the reach control problem in all remaining cases, assuming it is solvableby open-loop controls.

Reach Control on Simplices by Piecewise Affine Feedback