Barrier function-based adaptive neuro network sliding mode vibration control for flexible double-clamped beams with input saturation

In this paper, a novel adaptive neuro network nonsingular fast terminal sliding mode control based on barrier Lyapunov functions is proposed for flexible double-clamped beam systems with input saturation and distributed disturbance. First, the Galerkin projection method is employed to reduce the partial differential dynamic equations of the beam into ordinary differential equations. Second, a novel barrier Lyapunov function is employed to design a nonsingular fast terminal sliding mode controller that ensures the closed-loop system is stable with state constraints. In addition, an auxiliary system is proposed to guarantee the stability of the beam system subject to input saturation. Third, an adaptive neural network is used to deal with the possible unknown part of the model parameters. It is proved that the proposed control law can handle input saturation and state constraints simultaneously without knowing the model exactly. Finally, numerical simulations illustrate the effectiveness of the proposed control laws.