Regularity properties of optimal controls for problems with time-varying state and control constraints

Ilya A. Shvartsman, Richard B. Vinter

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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 Hölder 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.

Original languageEnglish (US)
Pages (from-to)448-474
Number of pages27
JournalNonlinear Analysis, Theory, Methods and Applications
Volume65
Issue number2
DOIs
StatePublished - Jul 15 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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