Anti-Synchronization Of MIMO Affine Chaotic Systems Based On Differential Geometry Theory

The exact feedback linearization method based on differential geometry theory has been widely concerned in the field of the chaos control and synchronization.Especially,there are perfect applications in the case of the single input and single output(SISO),but there is few in the case of the multiple inputs and multiple outputs(MIMO).In this paper,the anti-synchronization between identical structure chaotic systems in the case of the MIMO is investigated by the feedback linearization based on the differential geometry method.In the first chapter,the mathematical basics and concepts for the differential geometry are briefed,then the relative order,the coordinate transformation,the basic necessary &sufficient condition of the full-state feedback linearization for the solvability of the affine MIMO nonlinear system are summarized in detail.In the second chapter,several literatures are introduced in which the current research status for the anti-synchronization control and applications in the differential geometry method can be seen.In the third chapter,after the principle of the anti-synchronization control in the case of the MIMO is demonstrated,which including the determination of the output function,calculation of vector relative order,the nonlinear coordinate transformation and the full-state feedback linearization,the controller is designed combined with the outer loop control which depended on the optimal control principle of the quadratic performance index.The Lorenz system,Rossler system and Chen system are taken as examples to verify the effectiveness of the proposed scheme.