一些学者注意到，当模糊控制规则的数目增加到足够大时，对被控过程的影响很小甚至没有影响，从而产生了模糊控制器的极限结构理论［32－34］。对于采用线性控制规则的一般模糊控制器，随着控制规则数目的增加，其输出变为输入的线性函数［32］。特别是当控制规则的数目很大时，对于两输入的模糊控制器，其输出近似等于线性PI控制器的输出；对于三输入的模糊控制器，其输出近似等于线性PID控制器的输出。这些结构被一般化到采用多状态变量和多输出模糊集的模糊控制器［33］。若采用任意函数f表达的非线性控制规则，模糊控制器的解析结构则是一个全局的依赖于f的非线性控制器和一个局部的非线性控制器之和，随着控制规则的数目增加到∞，局部非线性控制器也将随之消失［34］。若采用线性控制规则，则随着控制规则的数目增加到∞，全局控制器将变成一个全局近似于线性控制器的多维多值继电控制器［34］。这些结果对于任意模糊逻辑操作、推理方法和解模糊器都适用。极限结构理论说明了模糊控制器的模糊集和模糊规则的数目并非越多越有效，故在实际设计时，要根据具体问题合适地选择模糊集和规则的数目。
Some scholars have noticed that when the number of fuzzy control rules increases enough, it has little or no impact on the controlled process, resulting in the limit structure theory of fuzzy controller [32-34]. For a general fuzzy controller with linear control rules, with the increase of the number of control rules, its output becomes a linear function of the input [32]. Especially when the number of control rules is large, the output of the two input fuzzy controller is approximately equal to that of the linear PI controller; For the three input fuzzy controller, its output is approximately equal to that of the linear PID controller. These structures are generalized to fuzzy controllers using multi state variables and multi output fuzzy sets [33]. If the nonlinear control rules expressed by any function f are adopted, the analytical structure of the fuzzy controller is the sum of a global f-dependent nonlinear controller and a local nonlinear controller. As the number of control rules increases to ∞, the local nonlinear controller will disappear [34]. If linear control rules are adopted, as the number of control rules increases to ∞, the global controller will become a multidimensional multivalued relay controller [34] which is globally similar to the linear controller. These results are applicable to any fuzzy logic operation, reasoning method and defuzzifier. The limit structure theory shows that the more the number of fuzzy sets and fuzzy rules of the fuzzy controller is, the more effective it is. Therefore, in the actual design, the number of fuzzy sets and rules should be appropriately selected according to the specific problems.
客服1