IJPAM: Volume 7, No. 3 (2003)

TURNPIKE PROPERTY FOR INFINITE DIMENSIONAL
CONVEX DISCRETE-TIME CONTROL SYSTEMS
IN A BANACH SPACE

Alexander J. Zaslavski
Department of Mathematics
Technion - Israel Institute of Technology
Haifa, 32000, ISRAEL
e-mail: ajzasltx.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 $n$. This result is a generalization of the main result of Zaslavski [Journal of Convex Analysis, 5 (1998), 237-248], which was established for convex uniformly continuous functions.

Received: April 27, 2003

AMS Subject Classification: 49J99

Key Words and Phrases: Banach space, convex function, generic function, turnpike property

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 7
Issue: 3