Hierarchical fuzzy control of multivariable systems via semi-tensor product method

A new kind of scheme is proposed to obtain hierarchical fuzzy control of multivariable systems. It is based on algebraic fuzzy reasoning equations of fuzzy system using semi-tensor product framework recently described. First, the bi-decomposition of multivariable fuzzy systems is considered, and some new results are obtained. Using these results, the algorithm of hierarchical fuzzy systems realization is developed such that one can easily design the middle layers of the hierarchical structure. The resulting hierarchical system is totally equivalent to the conventional single layer fuzzy logic system. At last, an example is given to demonstrate that the algorithm is effective and feasible.