Reach control on simplices by piecewise affine feedback

Mireille E. Broucke, Marcus Ganness
2011 Proceedings of the 2011 American Control Conference  
We study the reach control problem for affine systems on simplices, and the focus is on cases when the problem is not solvable by continuous state feedback. We examine from a geometric viewpoint the structural properties of the system which make continuous state feedbacks fail. This structure is encoded by so-called reach control indices, which are defined and developed in the paper. Based on these indices, we propose a subdivision algorithm and associated piecewise affine feedback. The method
more » ... s shown to solve the reach control problem in all remaining cases, assuming it is solvable by open-loop controls.
doi:10.1109/acc.2011.5990740 fatcat:ph5ab2sfsng3hmvl5wuahoaxpy