Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers

This paper illustrates the control of chaos using a fuzzy estimating system based on batch training and recursive least square methods for a continuous time dynamic system. The fuzzy estimator system is trained on both Ott–Geobogi–Yorke (OGY) control algorithm and Pyragas’s delayed feedback control algorithm. The system, considered as a case study, is a Bonhoeffer–van der Pol (BVP) oscillator. It is found that the implemented fuzzy control system constructed on OGY algorithm results in smaller control transient response than that of the OGY control algorithm itself. The transient response of Pyragas fuzzy control does not show a significant improvement in compare to the Pyragas control itself. In general the proposed control techniques show very effective low cost energy behavior in chaos control in compare to conventional non-linear control methods. Also the robustness of controlled system against random disturbances increases when the fuzzy estimation of OGY or Pyragas controller is used as a chaos controller.