STABILIZING HIGHER PERIODIC ORBITS OF CHAOTIC DISCRETE-TIME MAPS

Abstract

This paper presents two controller design methods for stabilizing higher periodic orbits of chaotic, discrete-time systems: transformation to the controller canonical form and multiparameter control. Each method is based on the locally linearized system representation. Accordingly, each method explicitly addresses the problem of control of a linear time-varying system and therefore produces a time-varying controller. The freedom in the design of the time-varying controller is used to optimize the properties of the closed loop system. The controller design methods are applied to the Hénon map and the Ikeda map for stabilizing orbits of periods 7, 11, 13, and 31, respectively. The issue of measurement noise is also considered.