Optimal control problems with mixed and pure state constraints

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

Authors

A. Boccia (Author) Other; Maria do Rosário de Pinho (Author) FEUP; R. B. Vinter (Author) Other

Journal

Title: SIAM Journal on Control and Optimization

Vol. 54 No. 6

Pages: 3061-3083

ISSN: 0363-0129

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 17 Citations

Scopus - 19 Citations

INSPEC

Other information

Authenticus ID: P-00M-7K9

DOI: 10.1137/15m1041845

Abstract (EN): This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both "pure" constraints on the state variable and "mixed" constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of "stratified" necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 23