Kybernetika 51 no. 1, 4-19, 2015

A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics

Masayasu Suzuki and Noboru SakamotoDOI: 10.14736/kyb-2015-1-0004

Abstract:

In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control inputs. This work is a new attempt to systematically design a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability.

Keywords:

symbolic dynamics, global stability, chaos control

Classification:

37B10, 74H65, 93D15

paper.pdf

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