The broad-learning systems (BLS) with advance control theories have been studied, but found to have two disadvantages: one is that the calculations are too complicated and the other is that the convergence time cannot be guaranteed. In order to mitigate the high computational loading, this study proposes a broad-learning Hermite neural network (BHNN), which has the capability of dynamic mapping and reduces the structural complexity of neural network. Meanwhile, a broad-learning recurrent Hermite neural control (BRHNC) system is proposed while maintaining finite-time stability to speed up the tracking error convergence. The proposed BRHNC system comprises two controllers: a recurrent broad controller that utilizes a BHNN to approximate on-line an ideal finite-time controller and a robust exponential controller that ensures system stability through a Lyapunov function. Meanwhile, the BHNN’s full-tuned parameter learning laws are developed to increase the approximating capacity, learning capacity and accuracy using gradient descent method. Finally, simulation and experimental results show that the BRHNC system has good control, tracking and disturbance rejection properties, while the BRHNC system requires no prior knowledge about the system dynamics.
