Investigation of regularity conditions in optimal control problems with geometric mixed constraints

Author(s)

Arutyunov, A. V. ^{[1, 2]} ; Karamzin, D. Yu. ^{[3, 4]} ; Pereira, F. L. ^[5] ; Silva, G. N. ^[3]

Affiliation

^[1] Peoples Friendship Univ Russia, Fac Nat Sci, Moscow - Russia

^[2] Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow - Russia

^[3] Univ Estadual Paulista, UNESP, Dept Appl Math, Sao Jose Do Rio Preto - Brazil

^[4] Russian Acad Sci, Dorodnicyn Comp Ctr, Moscow - Russia

^[5] Univ Porto, Fac Engn, P-4100 Oporto - Portugal

• Document type: Journal article
• Source: OPTIMIZATION; v. 65, n. 1, p. 185-206, JAN 2 2016.
• Web of Science Citations: 2

Abstract

We investigate regularity conditions in optimal control problems with mixed constraints of a general geometric type, in which a closed non-convex constraint set appears. A closely related question to this issue concerns the derivation of necessary optimality conditions under some regularity conditions on the constraints. By imposing strong and weak regularity condition on the constraints, we provide necessary optimality conditions in the form of Pontryagin maximum principle for the control problem with mixed constraints. The optimality conditions obtained here turn out to be more general than earlier results even in the case when the constraint set is convex. The proofs of our main results are based on a series of technical lemmas which are gathered in the Appendix. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC