Adaptive neural network control of a flexible string system with non-symmetric dead-zone and output constraint

This study is concerned with adaptive neural network control for a vibrating flexible string system under the influence of non-symmetric input dead-zone, output constraint and system uncertainties. First, the backstepping method is incorporated into the context of boundary control scheme and the barrier Lyapunov function is exploited to ensure the output constraints are never transgressed. Subsequently, an adaptive neural network control is developed to globally stabilize the string system and compensate for the effect of the input dead-zone. Besides, the online updating laws are introduced to compensate for the uncertainties of the system and the σ-modification is adopted to adjust the robustness of the system. Under the proposed control, the bounded stability of the closed-loop system is proven based on Lyapunov functions without simplifying or discretizing the infinite-dimensional dynamics. Finally, simulation results are presented for control performance verification.