Hermite broad-learning recurrent neural control with adaptive learning rate for nonlinear systems

Abstract

Although conventional control systems are simple and widely used, they may not be effective for complex and uncertain systems. This study proposes a Hermite broad-learning recurrent neural network (HBRNN) to address such challenges. The HBRNN has a wide network structure and incorporates an internal feedback loop that enables fast learning and dynamic mapping. Furthermore, a Hermite broad-learning recurrent neural control (HBRNC) with the HBRNN as the main controller is proposed. All the network parameters of the HBRNN are updated online according to parameter learning laws through the gradient descent approach. To prevent network parameter overtraining of the HBRNN, an adaptive learning rate (ALR) is established using a discrete-type Lyapunov function to determine the least upper bound for the learning rate. The ALR can dynamically adjust the learning rates within specified ranges during the training process, thus achieving an appropriate balance between convergence speed and system stability. Finally, the HBRNC system with ALR is applied to a chaotic circuit and a reaction wheel pendulum, and its effectiveness is validated through simulation and experimentation.