How Fuzzy Control can Bene t from Classical Control Theory : The Fuzzy State

Fuzzy control is more than just an alternative to classical control theory. As a core principle, fuzzy control provides the designer with an easy-to-use framework for incorporating expert knowledge, and it acknowledges the fact that, in the real world, everything is a matter of degree. While it is easy to design a fuzzy controller with only a few input variables, the designer encounters diiculties when the number of input variables of the controller increases, since the size of the rule set can grow exponentially. Even though classical control theory has been applied very successfully , its major drawback is that it requires a lot of mathematical insights. But classical control theory has developed the notion of the state controller, which grows only linearly in the number of input variables. Also, the concept of the state controller allows for an easy design process. This paper shows how the notion of the state controller can be transferred to fuzzy control without using any of the typical mathematical issues, such as diierential equations or Laplace transformation. This transfer proposes a new design principle that has the following advantages: (1) instead of having to keep the number of inputs small, it is easy to consider as many input variables as seem useful, (2) the number of parameters, needed to specify all rules grows only linearly in the number n of input variables, and (3) the controller behaves more robust with respect to disturbances abound in the real world.