On the regularity of optimal controls for state constrained problems

Ilya A. Shvartsman, Richard B. Vinter

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper we summarize new results on the regularity of optimal controls for dynamic optimization problems with functional inequality constraints, a control constraint expressed in terms of a general closed convex set 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 non-time varying. 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 circumstance, however, a weaker regularity property (Holder continuity with Holder index 1/2) 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.

Original languageEnglish (US)
Title of host publication2004 43rd IEEE Conference on Decision and Control (CDC)
Pages2285-2290
Number of pages6
DOIs
StatePublished - Dec 1 2004
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume3
ISSN (Print)0191-2216

Other

Other2004 43rd IEEE Conference on Decision and Control (CDC)
CountryBahamas
CityNassau
Period12/14/0412/17/04

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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    Shvartsman, I. A., & Vinter, R. B. (2004). On the regularity of optimal controls for state constrained problems. In 2004 43rd IEEE Conference on Decision and Control (CDC) (pp. 2285-2290). [WeB13.5] (Proceedings of the IEEE Conference on Decision and Control; Vol. 3). https://doi.org/10.1109/CDC.2004.1428729