This thesis studies the Reach Control Problem (RCP) for affine systems defined on simplices. The thesis focuses on cases when it is known that the problem is not solvable by continuous state feedback. Previous work has proposed (discontinuous) piecewise affine feedback to resolve the gap between solvability by open-loop controls and solvability by feedbacks. The first results on solvability by time-varying feedback are presented. Time-varying feedback has the advantage to be more robust to measurement errors circumventing problems of discontinuous controllers. The results are theoretically appealing in light of the strong analogies with the theory of stabilization for linear control systems. 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 are provided. The motivation for studying RCP and its relevance to complex control specifications is illustrated using a material transfer system.

This thesis studies the Reach Control Problem (RCP) for affine systems defined on simplices. The thesis focuses on cases when it is known that the problem is not solvable by continuous state feedback. Previous work has proposed (discontinuous) piecewise affine feedback to resolve the gap between solvability by open-loop controls and solvability by feedbacks. The first results on solvability by time-varying feedback are presented. Time-varying feedback has the advantage to be more robust to measurement errors circumventing problems of discontinuous controllers. The results are theoretically appealing in light of the strong analogies with the theory of stabilization for linear control systems. 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 are provided. The motivation for studying RCP and its relevance to complex control specifications is illustrated using a material transfer system.