Combining mathematical model and heuristics into controllers: an adaptive fuzzy control approach

In this paper, we propose a general framework to combine mathematical model and heuristics into nonlinear adaptive controller design, where the heuristics are in the form of fuzzy IF-THEN rules. We consider the case where the following three pieces of information are available: 1) an approximate model of the nonlinear system under control; 2) a collection of fuzzy IF-THEN rules describing the error between the approximate model and the real system; and 3) fuzzy control rules describing recommended control actions under various conditions. Our approach combines these three pieces of information into an adaptive fuzzy controller. Specifically, the first two pieces of information are used to construct an estimated model of the system and a controller is designed based on this estimated model. The third piece of information is used to construct another controller. The final controller is a weighted average of these two controllers. We develop an adaptive law for adjusting the free parameters in the controller such that the closed-loop system follows a desired trajectory