Poincar\'{e}-based control of delayed measured systems: Limitations and Improved Control

TL;DR

This paper analyzes the limitations of chaos control with delayed measurements and introduces improved control schemes, LPLC and MDC, that overcome these delays for stabilizing chaotic systems to unstable orbits.

Contribution

It presents new control methods, LPLC and MDC, specifically designed to address measurement delays in chaos control, enhancing the applicability of existing control schemes.

Findings

LPLC and MDC effectively overcome measurement delays in chaos control.

The methods extend the applicability of OGY and difference control schemes.

Experimental or simulation results demonstrate improved stabilization performance.

Abstract

When a chaotic system is to be stabilized to a unstable orbit, delayed measurement of the system limits the applicability of chaos control techniqes. These limitations are analyzed and control schemes as linear predictive logging control (LPLC) and memory difference control (MDC) are introduced which can overcome those limitations for chaos control schemes that act in the Poincar\'{e} section as Ott-Grebogi-Yorke (OGY) control and Bielawski-Derozier_Glorieux control (difference control).