Adaptive critic-based quaternion neuro-fuzzy controller design with application to chaos control

Neuro-fuzzy control structures despite all of the advantages from both neural networks features and fuzzy inference engines always get in trouble due to a large number of fuzzy rules which is because of the high order of the system or the large number of divisions considered for each input. In this paper, a new adaptive neuro-fuzzy controller is proposed based on the quaternion numbers, and thus the mentioned problem of large rule numbers is solved by using the quaternion back propagation concept. Furthermore, utilizing reinforcement learning which assesses output value produced by a critic is another strength of the proposed method. Finally, in order to show the superiority and effectiveness of the proposed controller in comparison with conventional neuro-fuzzy ones, a complex and challenging chaos control problem which is a chaotic spinning disk control is provided.