Synchronization of Underactuated Unknown Heavy Symmetric Chaotic Gyroscopes via Optimal Gaussian Radial Basis Adaptive Variable Structure Control

This brief proposes modified projective synchronization (MPS) methods for underactuated unknown heavy symmetric chaotic gyroscope systems via optimal Gaussian radial basis adaptive variable structure control. Chaotic gyroscope systems are considered as underactuated systems where a control input is designed to synchronize the two degree of freedoms interactions. Until now, no investigation of this subject with one control input has been presented. The importance of obtaining synchronization objectives is specified when the dynamics of gyroscope system are unknown. In this brief, using the neural variable structure control technique, a control law is established that guarantees the MPS of underactuated unknown chaotic gyros. In the neural variable structure control, Gaussian radial basis functions are utilized to estimate online the system dynamic functions. Adaptation laws of the online estimator are derived in the sense of the Lyapunov function. Moreover, online and offline optimizers are applied to optimize the energy of the control signal. The proposed solution is generalized to chaos control of the mentioned gyroscopes. Numerical simulations are presented to verify the proposed synchronization methods.