Normality of Generalized Euler-Lagrange Conditions for State Constrained Optimal Control Problems

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Bettiol, P (Author) Other; Khalil, N (Author) Other; Vinter, RB (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: JOURNAL OF CONVEX ANALYSIS

Vol. 23

Pages: 291-311

ISSN: 0944-6532

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 9 Citations

Other information

Authenticus ID: P-00P-S04

Abstract (EN): We consider state constrained optimal control problems in which the cost to minimize comprises both integral and end-point terms, establishing normality of the generalized Euler-Lagrange condition. Simple examples illustrate that the validity of the Euler-Lagrange condition (and related necessary conditions), in normal form, depends crucially on the interplay between velocity sets, the left end-point constraint set and the state constraint set. We show that this is actually a common feature for general state constrained optimal control problems, in which the state constraint is represented by closed convex sets and the left end-point constraint is a closed set. In these circumstances classical constraint qualifications involving the state constraints and the velocity sets cannot be used alone to guarantee normality of the necessary conditions. A key feature of this paper is to prove that the additional information involving tangent vectors to the left end-point and the state constraint sets can be used to establish normality.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21