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This paper presents a novel approach for designing adaptive controller of nonlinear dynamical systems based on an improved quasi-ARX neural network prediction model. The improved quasi-ARX neural network prediction model has two parts: the linear part is used for stability and the nonlinear part is used to satisfy accuracy requirement. Then, we can obtain a linear controller and a nonlinear controller based on the characteristic of the improved quasi-ARX neural network prediction model. A fuzzy switching algorithm is designed between the two controllers. Theory analysis and simulations are given to show the effectiveness of the proposed method both on stability and accuracy.