An adaptive backstepping fuzzy sliding mode control is proposed to approximate the unknown system dynamics for a cantilever beam in this paper. The adaptive backstepping fuzzy sliding mode control is developed by combining the backstepping method with adaptive fuzzy strategy, where backstepping design approach is used to drive the trajectory tracking errors to converge to zero rapidly with global asymptotic stability and fuzzy logic system is designed to approximate the unknown nonlinear function in the adaptive backstepping fuzzy sliding mode control. The proposed backstepping controllers can ensure proper tracking of the reference trajectory, and impose a desired dynamic behavior, giving robustness and insensitivity to parameter variations. Numerical simulation for cantilever beam is investigated to verify the effectiveness of the proposed adaptive backstepping fuzzy sliding mode control scheme and demonstrate the satisfactory vibration suppression performance.

An adaptive sliding mode controller using radial basis function (RBF) network is proposed to approximate the unknown system dynamics for cantilever beam. Neural network controller is designed to approximate the unknown system model. In the presence of unknown model uncertainties and external disturbances, sliding mode controller is employed to compensate for such system nonlinearities and improve the tracking performance. Online neural network (NN) weight tuning algorithms are designed based on Lyapunov stability theory, which can guarantee bounded tracking errors as well as bounded NN weights. Numerical simulation for cantilever beam is investigated to verify the effectiveness of the proposed adaptive neural control scheme and demonstrate the satisfactory vibration suppression performance.

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