Adaptive Fuzzy Controllers Based on Variable Universes

In this chapter, we introduce variable universes-based adaptive fuzzy controllers. The concept comes from interpolation forms of fuzzy control introduced in Chapter 8. First, we define monotonicity of control rules, and we prove that the monotonicity of interpolation functions of fuzzy control is equivalent to the monotonicity of control rules. This means that there is no contradiction among the control rules under the condition for the control rules being monotonic. Then the structure of the contraction-expansion factor is discussed. At last, based on variable universes, we present three models of adaptive fuzzy control, namely, an adaptive fuzzy control model with potential heredity, adaptive fuzzy control model with obvious heredity and adaptive fuzzy control model with successively obvious heredity.