Optimal control problems with mixed constraints

• Type: Article in International Scientific Journal
• Date: 2010

Authors

Francis Clarke (Author) Other; Maria do Rosário de Pinho (Author) FEUP

Journal

Title: SIAM Journal on Control and Optimization

Vol. 48 No. 7

Pages: 4500-4524

ISSN: 0363-0129

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 56 Citations

Scopus - 63 Citations

COMPENDEX

INSPEC

Scientific classification

FOS: Engineering and technology > Electrical engineering, Electronic engineering, Information engineering

Other information

Authenticus ID: P-003-CV1

DOI: 10.1137/090757642

Abstract (EN): We develop necessary conditions of broad applicability for optimal control problems in which the state and control are subject to mixed constraints. We unify, subsume, and significantly extend most of the results on this subject, notably in the three special cases that comprise the bulk of the literature: calculus of variations, differential-algebraic systems, and mixed constraints specified by equalities and inequalities. Our approach also provides a new and unified calibrated formulation of the appropriate constraint qualifications, and shows how to extend them to nonsmooth data. Other features include a very weak hypothesis concerning the type of local minimum, nonrestrictive hypotheses on the data, and stronger conclusions, notably as regards the maximum (or Weierstrass) condition. The necessary conditions are stratified, in the sense that they are asserted on precisely the domain upon which the hypotheses (and the optimality) are assumed to hold. This leads to local, intermediate, and global versions of the necessary conditions, according to how the hypotheses are formulated.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 25