A hybrid parallel decomposed interval type-2 fuzzy-Jordan neural network for controlling uncertain ball-and-beam systems

Abstract This paper introduces a parallel intelligent control architecture that integrates a decomposed interval type-2 fuzzy neural network with a Jordan recurrent neural network for regulating the ball-and-beam system. In the proposed design, the interval type-2 fuzzy component is decomposed into multiple sublayers to better characterize uncertainty and mitigate rule interaction, while the Jordan network operates in parallel to provide dynamic compensation through recurrent feedback. Adaptation laws are formulated to enable online learning and ensure stable operation under parameter variations. The effectiveness of the proposed controller is validated through comprehensive simulations and real-time experiments. Quantitative results show that the proposed method achieves lower tracking errors than existing approaches, reducing the RMSE by approximately 26% compared with IT2FNN and by about 22% compared with T2FCMAC, as summarized in table 1. These results confirm that the parallel decomposed interval type-2 fuzzy–Jordan network provides a robust and practical solution for intelligent control of nonlinear systems.