智能控制智能控制智能控制 (29).pdf

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1、Sugeno(TSK)Fuzzy ModelsIntroductionTakagi,Sugeno and Kang The rules of the fuzzy system are defined by IF-then rules.If-then rulesIf x is A and y is B then Z=f(x,y)Z=f(x,y):a crisp function in the consequent.f(x,y):a polynomial?;but it can be any?.?-order sugeno fuzzy model:f(x,y)is a?order polynomi

2、al.zeroorder sugeno fuzzy model：f(x,y)is a constant.Property A special case of Mamdani model,in which each rules consequent is specified by a fuzzy single(or a pre-defuzzifiedconsequent)A special case of Tsukamoto fuzzy model,in which each rules consequent is specified by an MF of a step function ce

3、nter at the constant.Functionally,equivalent to a Radial Basis Function network under certain minor constraints.Overall OutputThe output is a weighted average:,(,),(,(,()(,),ikikA Bm i kA Biiix yyzyfxfxxywwwhere wiis the firing strength of the i-th output.Double summation over all i(x MFs)and all k(

4、y MFs).Summation over all i(fuzzy rules).VisualizationExample 1-1001000.51XMembership Gradessmall medium large(a)Crisp Antecedent MFs-1001002468XY(b)Crisp I/O Curve-1001000.51XMembership Gradessmall medium large(c)Fuzzy Antecedent MFs-1001002468XY(d)Fuzzy I/O Curve If x is small then y=0.1x+6.4 If x

5、 is medium then y=0.5x+5 If x is large then y=x 2Fuzzy Rule Set VS Nonfuzzy Rules Set Example 2 If x is small and y is small then z=x+y+1 If x is small and y is large then z=y+5 If x is large and y is small then z=x+3 If x is large and y is large then z=x+y+2-50500.51XMembership GradesSmallLarge-50500.51YMembership GradesSmallLarge-505-5050510XYZSummary Sugeno(TSK)Fuzzy Models Rules Property Overall output An example