Adaptive control of the singularly perturbed chaotic systems based on the scale time estimation by keeping chaotic property

TL;DR

This paper introduces an adaptive control method for stabilizing singularly perturbed chaotic systems by maintaining their chaotic properties, utilizing slow scale time estimation to improve ecological system management without constant intervention.

Contribution

It proposes a novel adaptive control approach based on slow time scale estimation and Poincare map control, preserving chaos in singularly perturbed systems.

Findings

Control strategy maintains chaos in ecological systems.

Reduces need for continuous control actions.

Enables online Lyapunov exponent calculation.

Abstract

In this paper, a new approach to the problem of stabilizing a chaotic system is presented. In this regard, stabilization is done by sustaining chaotic properties of the system. Sustaining the chaotic properties has been mentioned to be of importance in some areas such as biological systems. The problem of stabilizing a chaotic singularly perturbed system will be addressed and a solution will be proposed based on the OGY (Ott, Grebogi and Yorke) methodology. For the OGY control, Poincare section of the system is defined on its slow manifold. The multi-time scale property of the singularly perturbed system is exploited to control the Poincare map with the slow scale time. Slow scale time is adaptively estimated using a parameter estimation technique. Control with slow time scale circumvents the need to observe the states. With this strategy, the system remains chaotic and chaos identification is possible with online calculation of lyapunov exponents. Using this strategy on ecological system improves their control in three aspects. First that for ecological systems sustaining the dynamical property is important to survival of them. Second it removes the necessity of insertion of control action in each sample time. And third it introduces the sufficient time for census.