Shvartsman, Ilya (Univ. of Bath), Vinter, Richard B. (Imperial Coll.)

On Regularity of Optimal Controls for State Constrained Problems

Scheduled for presentation during the Regular Session "Convex Optimization I" (ThP12), Thursday, July 27, 2006, 16:35−17:00, Room 104b

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

In this paper we report new results on the regularity of optimal controls for dynamic optimization problems with functional inequality state constraints, a convex time-dependent control constraint and a coercive cost function. Recently it has been shown that the linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition, that requires linear independence merely with respect to non-negative weighting parameters, provided the control constraint set is independent of the time variable. We show that, if the control constraint set, regarded as a time dependent multifunction, is merely Lipschitz continuous with respect to the time variable, then optimal controls can fail to be Lipschitz continuous. In these circumstances, however, a weaker H"older continuity-like regularity property can be established. On the other hand, Lipschitz continuity of optimal controls is guaranteed for time varying control sets under a positive linear independence hypothesis, when the control constraint sets are described, at each time, by a finite collection of functional inequalities.