State space reconstruction applied to a multiparameter chaos control method

Abstract

The idea of the chaos control is the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The OGY method achieves system stabilization by using small perturbations promoted in the neighborhood of the desired orbit when the trajectory crosses a Poincare section. A generalization of this method considers multiple actuations of parameters and sections, known as semi-continuous multiparameter method. This paper investigates the state space reconstruction applied to this general method, allowing chaotic behavior control of systems with non-observable states using multiple control parameters from time series analysis, avoiding the use of governing equations. As an application of the proposed multiparameter general formulation it is presented an uncoupled approach where the control parameters do not influence the system dynamics when they are not active. This method is applied to control chaos in a nonlinear pendulum using delay coordinates to perform state space reconstruction. Results show that the proposed procedure can be applied together with delay coordinates providing UPO stabilization.