Turnpike property of optimal solutions of infinite-horizon variational problems

Given x/sub 0//spl isin/R/sup n/ we study the infinite-horizon problem of minimizing the expression /spl int//sub 0//sup T/ f(x(t), x´(t))dt as T grows to infinity, where a function x: [0,/spl infin/)/spl rarr/R/sup n/ is absolutely continuous and satisfies the initial condition x(0)=x/sub 0/ and f=f(x,u) is an integrand. We study the structure of (f)-weakly optimal solutions and establish the turnpike property for a generic integrand f.