Synchronization And Control For Chaotic Nonlinear Gyro Systems Using Backstepping Design

Chaotic system,a promising interdisciplinary science,attracts more and more attention.The dynamic behavior of a symmetric gyro with linear-plus-cubic damping,which is subjected to a harmonic excitation,is studied in this dissertation.Gyroscope is attractive and everlasting subjects of dynamics,which has been studied by many researchers.The gyroscope has attributes of great utility to navigation,aeronautical and space engineering.Among these studies,chaos and synchronization in dynamical system have become one of the most important fields.In this dissertation,based on Lyapunov stability theory,chaos synchronization is studied to control chaos effectively by backstepping method are deeply investigated with our designed controller,in which there is no high order-terms.The main contents and contributions of the dissertation are shown as follows:First,we investigate the chaos synchronization of two chaotic gyros using the backstepping approach in this dissertation.Based on the Lyapunov stability theory,we design an advanced controller and verify the stability of the error system.The designed control laws ensure stable controlled and synchronized states for two chaotic nonlinear gyros.Numerical simulations are implemented for illustration and verification of the effectiveness of our controllers.Second,we investigate the chaos synchronization of two uncertain chaotic nonlinear gyros using the adaptive backstepping design.Based on the Lyapunov stability theory,we design an adaptive controller without three order-terms to synchronize the master-slave systems asymptotically.The designed control laws ensure stable synchronized states for two uncertain chaotic gyros in the presence of disturbance.Numerical simulations are given to verify the effectiveness of the proposed adaptive backstepping approach.Finally,in view of the effects of chaos properties,we investigate the problem of gyro chaos control based on the backstepping control method in this dissertation.We design a novel controller without three order terms to stabilize the gyro chaotic systems asymptotically.The designed control laws ensure stable controlled states for gyroscope.Rigorous analysis and numerical simulations are given to verify the effectiveness of the proposed backstepping controller.