Reach Control on Simplices By Piecewise Affine Feedback

This thesis provides a deep study of the Reach Control Problem (RCP) for affine systems defined on simplices. Necessary conditions for solvability of the problem by open loop control are presented, improving upon the results in the literature which are for continuous state feedback only. So-called reach control indices are introduced and developed which inform on the structural properties of the system which cause continuous state feedbacks to fail. A novel synthesis method is presented consisting of a subdivision algorithm based on these indices and an associated piecewise affine feedback. The method is shown to solve RCP for all cases in the literature where continuous state feedback fails, provided it is solvable by open loop control. Textbook examples of existing synthesis methods for RCP are provided. The motivation for studying RCP and its relevance to complex control specifications is illustrated using a biomedical application.