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Abstract and Applied Analysis
Volume 2003 (2003), Issue 11, Pages 631-650

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 Hindawi Publishing Corporation. 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.


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.