Deep learning controller for nonlinear system based on Lyapunov stability criterion

Abstract

For the current paper, the technique of feed-forward neural network deep learning controller (FFNNDLC) for the nonlinear systems is proposed. The FFNNDLC combines the features of the multilayer feed-forward neural network (FFNN) and restricted Boltzmann machine (RBM). The RBM is a very important part for the deep learning controller, and it is applied in order to initialize a multilayer FFNN by performing unsupervised pretraining, where all the weights are equally zero. The weight laws for the proposed network are developed by Lyapunov stability method. The proposed controller is mainly compared with FFNN controller (FFNNC) and other controllers, where all the weights values for all the designed controllers are equally zero. The proposed FFNNDLC is able to respond the effect of the system uncertainties and external disturbances compared with other existing schemes as shown in simulation results section. To show the ability of the proposed controller to deal with a real system, it is implemented practically using an ARDUNIO DUE kit microcontroller for controlling an electromechanical system. It is proved that the proposed FFNNDLC is faster than other FFNNCs in which the parameters are learned using the backpropagation method. Besides, it is able to deal with the changes in both the disturbance and the system parameters.