Research On The Monotonicity Of Fuzzy Control Algorithm

Intelligent fuzzy control theory significantly lags behind the development of its techniques at present. An important factor is that the properties of the fuzzy control methods themselves need deep studying. For a monotone inertia system, the monotonicity of a control algorithm is naturally requested, which is important in analyzing the stability of the monotone inertial fuzzy control system. Based on the concept of monotone rule-base, the monotonicity of the fuzzy control algorithm is discussed in detail with direct analysis methods. For the Mamdani fuzzy control algorithm of one dimension, we use the inference operator "max-min " . under the condition more than two rules being excited, as long as the number of excited rules is less than two, and the output fuzzy sets of the rules in the rule-base are fuzzy numbers in the shape of bending isosceles triangle, the one dimensional Mamdani fuzzy control algorithm is monotonic. For the two dimensional algorithm under the inference operator "max-product" , research shows that two dimensional Mamdani fuzzy control algorithm based on monotone rule-base may not be monotonic, but is rough monotonic. if the output fuzzy sets of the rules in the rule-base are bending isosceles triangles. Rough monotone means that the monotonicity of the algorithm holds if the distance between the two input states is far enough. From the practical point, a sufficient condition for the monotonicity of the two dimensional fuzzy control algorithm is presented. The influence of the input fuzzy sets used in the rule-base on the monotonicity of the control algorithm is discussed. Research shows that the influence of the grading fuzzy numbers of the input universe on the output ofthe control algorithm is only in relation to the relatively "fat" or "thin" of theadjoining fuzzy numbers.