Minimal Solutions for Discrete-Time Control Systems in Metric Spaces

Abstract

In this work we study the structure of minimal solutions for an autonomous discrete-time control system in a metric space X determined by a continuous function . A sequence is called (v)-minimal if for each pair of integers and each sequence satisfying , the inequality is valid. We consider a space of functions equipped with a natural complete metric and show that for a generic function v there exists a (v)-minimal sequence.

Keywords:

• Complete metric space
• Generic property
• Good sequence
• Minimal sequence
• 1991 Mathematics Subject Classifications: 49J99