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Journal of Convex Analysis, Vol. 5, No. 2, pp. 237-248 (1998)
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Turnpike Theorem for Convex Infinite Dimensional Discrete-Time Control Systems

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Alexander J. Zaslavski

Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel, ajzasl@techunix.technion.ac.il

**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

**Full text of the article:**

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