Journal of Convex Analysis, Vol. 5, No. 2, pp. 237-248 (1998)

Turnpike Theorem for Convex Infinite Dimensional Discrete-Time Control Systems

Alexander J. Zaslavski

Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel,

Abstract: In this work we study the structure of "approximate" solutions for an infinite dimensional discrete-time optimal control problem determined by a convex function $v: K \times K \to R^1$, where $K$ is a convex closed bounded subset of a Banach space. We show that for a generic function $v$ there exists $y_v \in K$ such that each "approximate" optimal solution $\{x_i\}_{i=0}^n$ $\subset K$ is a contained in a small neighborhood of $y_v$ for all $i \in \{N,\dots, n-N\}$, where $N$ is a constant which depends on the neighborhood and does not depend on $n$.

Keywords: Turnpike property, Banach space, convex function, generic function

Classification (MSC2000): 49J99

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