Autoregressive self-tuning feedback control of the Hénon map

This paper describes a method based on self-feedback for controlling both chaotic and nonchaotic forms of the H\'enon map with and without additive Gaussian white noise. We describe a nonlinear self-tuning controller that makes use of a feedback reference signal and a linear autoregressive formulation for the gain. This controller is effective at stabilizing the map to a variety of fixed point or period-two orbits. We contrast our approach with the method of Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] which has been used to control some chaotic processes and recently, some nonchaotic, stochastic ones.