A nonlinear adaptive controller: A comparison between fuzzy logic control and neurocontrol.

*(English)* Zbl 0745.93041
Summary: This paper explores, from a surface-fitting viewpoint, two algorithms which are often applied in the field of intelligent control: fuzzy self- organizing controllers and neural networks. Both methodologies adapt internal model parameters in response to the plant’s input-output mapping. However, while the convergence of single-layer neural networks has been studied in great detail, very few theorems have been proved about self-organizing fuzzy logic controllers. In this paper, it is shown that $B$-splines can provide a framework for choosing the shape of the fuzzy sets. Then the operators chosen to implement the underlying fuzzy logic are examined, showing how they can produce ‘smooth’ control surfaces. It is now possible to make a direct comparison between fuzzy logic controllers and feedforward neural networks, demonstrating that, in a forward-chaining mode, storing the plant’s behaviour in terms of weights or rule confidences is equivalent. Finally, three training rules for the self-organizing fuzzy controller are derived.

##### MSC:

93C40 | Adaptive control systems |

93C42 | Fuzzy control systems |

93C10 | Nonlinear control systems |