Adaptive neural network control of an arm-string system with actuator fault based on a PDE model

In this paper, an adaptive boundary controller for an undersea detection robot system with actuator failure, unknown disturbance and boundary deflection constraint is proposed. Using Hamilton’s principle, a partial differential equation (PDE) model is established for the detection system, which consists of a rigid arm, a flexible string and a sensor. Considering the actuator failure, a fault-tolerant scheme is proposed to tackle it. To handle the unknown disturbance, we employ radial basis function (RBF) neural networks (NNs) to neutralize the boundary uncertain nonlinear disturbance. The proposed adaptive controller includes a proportional–derivative (PD) feedback structure, a fault-tolerant strategy and a NN control scheme. By choosing an appropriate Lyapunov-Krasovskii function and applying LaSalle’s Invariance Principle, the asymptotic stability of the closed-loop system is rigorously proven. Simulation results validate the proposed controller.