Rough Neural Network and Adaptive Feedback Linearization Control Based on Lyapunov Function

In this manuscript, rough neural network and adaptive feedback linearization control based on Lyapunov function is studied. The assumed system in this study is a system that contains both linear and nonlinear terms. The considered controller in this paper is adaptive feedback linearization, in which the adaptation laws of the weights are found as a result of the stability proof in the sense of Lyapunov. Although feedback linearization has a strong potential to eliminate the nonlinear term of the system, its weakness is the requirement of an exact model of the process. Due to the fact that the identification of almost all of the nonlinear systems is an arduous task, by using the broad-appeal neural network, this problem has been facilitated. Since the most prominent problem of any identification is uncertainty, the rough strategy is aimed to decrease the uncertainties of the identification. So, they have designed based on rough neurons. A rough neuron is regarded as a pair of neurons called lower boundary neuron and upper boundary neuron. Rough neuron approach, allows the use of interval computing in neural networks. Therefore, it can be considered as a new theory in designing neural networks. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made.