Constructing fuzzy controllers with B-spline models

We interpret a type of fuzzy controller as an interpolator of B-spline hypersurfaces. B-spline basis functions of different orders are regarded as a class of membership functions (MFs) with some special properties. These properties lead to several interesting conclusions about fuzzy controllers if such membership functions are employed to specify the linguistic terms of the input variables. We show that by appropriately designing the rule base, Cⁿ-continuity of the output can be achieved (n is the order of the B-spline basis functions). The issues of function approximation and heuristic control using such a fuzzy system are also discussed