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In this paper, a hybrid deep learning neural network controller (HDLNNC) for nonlinear systems is proposed. The proposed controller structure consists of a multi-layer feed-forward neural network, which can be trained based on the hybrid deep learning. The Lyapunov stability criterion is used to develop an adaptive learning rate due to the learning rate of the updating parameters plays a worthy role in achieving the stability of a system. To show the robustness of the proposed controller and its performance, several tests such as disturbance signals and parameter variations are carried on a numerical example. In this concern, the practical implementation of the proposed HDLNNC is executed on a real system. The results indicate that the proposed controller is able to improve the system performance compared with other existing controllers.

Hybrid deep learning controller for nonlinear systems based on adaptive learning rates