A purely adaptive controller to synchronize and control chaotic systems

Following the work presented by the author in a previous paper, a model reference adaptive controller is proposed to control or synchronize chaotic systems. This is achieved by exploiting the boundedness of chaotic evolutions. The synthesis is carried out in two stages. Firstly, an adaptive controller containing a fixed gain linear action is presented and applied to the control of a Lorenz system. Then, when the linear term of the error equation is characterized by a Hurwitz matrix, the control law is further simplified to a purely discontinuous action whose amplitude is adaptively estimated. Finally, numerical results are presented for the case in which this simpler controller is used to synchronize two models of the Chua circuit, characterized by a Hurwitz linear matrix.