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The modes approach is based on Traxler et al. (2001).

The accuracy of the assumed-modes approach is theoretically studied by using the Rayleigh Ritz method that removes the simplifying hypothesis that dry and wet mode shapes are the same.

The nonlinear normal mode approach is used in this analysis.

The complex mode approach is utilized for analyzing efficiently the coupled buffeting response.

The limit of validity of the single-mode approach is also investigated.

A normal mode approach is used to establish the total response.

The complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation.

A backstepping sliding mode approach is applied firstly to compensate the uncertainty which occur in the control system.

A global/local mode approach is employed; the total motions are expressed in terms of global and local motions.

Therefore, a backstepping sliding mode approach is firstly applied, where the backstepping design is to synthesize the controller and the sliding mode term is to compensate disturbances.

In this paper, an adaptive TSK-type CMAC neural control (ATCNC) system via sliding-mode approach is proposed for the chaotic symmetric gyro.