Computationally advantageous and stable hierarchical fuzzy systems for active suspension

A new type of hierarchical fuzzy system (HFS), namely, Hierarchical Classifying-Type Fuzzy System (HCTFS), is developed and proposed in the paper. While the HCTFS enjoys the full benefits of a traditional HFS, one of which is to suppress the effects of the unwanted phenomenon, “the curse of dimensionality,” it also offers one great advantage that all rule strengths are preserved when passing through subsystem layers. To demonstrate the potential of the HCTFS, computational complexity analysis will be conducted on the complete rule-base models of a conventional fuzzy system and the HCTFS. Furthermore, a methodology of stability analysis is proposed incorporating the use of the the HCTFS, providing the reader with another option of hierarchical fuzzy controller design upon stability concerns. To verify and conclude our proposal, a mathematical example and simulations are provided. In our simulated example, the the HCTFS controller incorporating the proposed stability analysis technique are applied to the active suspension system. The results obtained from the active suspension system are then discussed and compared with the results of the ideal and passive suspension systems.