Optimal Programs on Infinite Horizon 1
Alexander J. Zaslavski · SIAM Journal on Control and Optimization · 1995
We consider the limit behavior, as $N \to \infty $, of the expression $\sum _{i = 0}^{N - 1} v(x_i ,x_{i + 1} )$ for programs $\{ x_i \} _{i = 0}^\infty $ in a compact metric space K where v is a real-valued function defined on $K \times K$. We study the structure of $(v)$-good programs and establish the existence of a $G_\delta $ set F in ${\bf C}(K \times K)$ such that, for each $u \in F$, all $(u)$-good programs have the same limit points set and also, for every $x \in K$, there exists a $(u)$-optimal program $\{ x_i \} _{i = 0}^\infty $ satisfying $x_0 = x$.