École Nationale Supérieure de
Techniques Avancées

Abstract

In the context of a constrained control-system, the set of sustainable thresholds is a set valued-map that describe the thresholds that can be satisfied for a certain amount of time, given an initial condition. This work's aim is to analyse the sensitivity of the set of sustainable thresholds in the case of discrete time control problems, with state and control constraints. In this regard, semicontinuity and Lipschitz continuity of this set-valued map are proved under hypotheses on the dynamics and the constraints. Then, considerations on the Hausdorff distance between two sets of sustainable thresholds are presented, as well as some results about projection on such a set. Finally, an algorithm that approximates the projection is exposed.