Abstract and Applied Analysis
Volume 2003 (2003), Issue 11, Pages 631-650
doi:10.1155/S1085337503210046
A turnpike theorem for continuous-time control systems when the optimal stationary point is not unique
School of Information Technology and Mathematical Sciences (ITMS), University of Ballarat, University Drive, Mount Helen, Ballarat 3353, Victoria, Australia
Received 21 August 2002
Copyright © 2003 Musa A. Mamedov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the turnpike property for the nonconvex optimal control
problems described by the differential inclusion x˙∈a(x). We study the infinite horizon problem of maximizing the functional ∫0Tu(x(t))dt as T grows to infinity. The turnpike theorem is proved for the case when a turnpike set consists of several optimal stationary points.