State Space Reconstruction Using Extended State Observers to Control Chaos in a Nonlinear Pendulum

Chaos control may be understood as the use of tiny perturbations for the stabilization of unstable periodic orbits embedded in a chaotic attractor. Since chaos may occur in many natural processes, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter allows this kind of behavior to be desirable in different applications. In general, it is not necessary to have a mathematical model to achieve the control goal since all control parameters may be resolved from time series analysis. Therefore, state space reconstruction is an important task related to chaos control. This contribution analyzes chaos control performed using a semi-continuous method based on OGY approach and proposes the use of extended state observers in order to perform state space reconstruction. The use of extended state observers allows a direct application of the control method. Comparing with the delay coordinates method, extended state observers avoids the calculation of parametric changes related to delayed Poincaré sections that influence the system dynamics. The proposed procedure is applied in the control of chaos in a nonlinear pendulum, showing that it may be used to control chaos in mechanical systems.