模糊联想记忆FUZZYASSOCIATIVEMEMMORIESⅡ

1、模糊联想记忆FUZZY ASSOCIATIVE MEMMORIESPresented by Yang BaishengE.E. Dept.Xidian UniversityOUTLINEwFuzzy Hebb FAMs（续） 6.Binary Input-Output FAMs 7. Multiantecedent FAM Rules 8. Adaptive Decompositional InferencewAdaptive FAMs (Product-Space Clustering in FAM Cells) 1.Adaptive FAM-Rule Generation 2.Adapti

2、ve BIOFAM Clustering 3.Adaptive BIOFAM Example: Inverted PendulumBinary Input-Output FAMsBIOFAMs map system-variable to control, classification, or other output data.For example: A BIOFAM maps traffic densities to screen (and red) light durations. In inverted-pendulum example, the system maps the sy

3、stem-variable ( ) to control data ( ).dvvd,fMultiantecedent FAM Rules (多前提FAM规则)1.Consider the FAM rule: “IF X is A, THEN C is Z,” or for short. 2.The rule is “IF X is A AND Y is B, THEN C is Z,” or for short.CTAACM);,(CBA),( CAWhat to do?Multiantecedent FAM Rules (多条件FAM规则)2 Single-antecedent FAMs:

4、Multiantecedent FAM Rules:),(BCACMBMABAFACMAACCBCACCBCMBBCCTBBCM),( CB),( CACTAACM);,(CBADefuzzify it to yield the exact output.Multiantecedent FAM Rules Suppose we present the exact inputs , to the single-FAM-rule system that stores(A,B;C).We present the unit bit vectors and to as nonfuzzy set inpu

5、ts.Thenix),(),(jYiXjiIIFyxFBCjYACiXMIMICbCajiCbaji),min(jyFiXIjYIFProperty of Hebb MatrixMultiantecedent FAM RuleswRepresenting with its membership function wFor all in :z)(),min(zmbaCjiZCmCBIOFAM prescriptionMultiantecedent FAM RulesAlso, We can get the FAM rules:),;,(DCBA),(CBICAIyxFTjYTiXjiCbCaji

6、Cbaji),min()(),min(zmbaCjiIF we encode : and with correlation-product encoding, decompositional inference gives the BIOFAM version of correlation-product inference:),(CA),( CBCorrelation-Product EncodingAdaptive Decompositional InferencewLet define an arbitrary neural-network system that maps fuzzy

7、subset of to fuzzy subsets of . can define a different neural-network. qnXIIN:)()(),(BNANBAFYXBACCCqpYIIN:AXCZThe neural-network change with time.Adaptive FAMs(Product-Space Clustering in FAM Cells)wAdaptive FAM-Rule GenerationwAdaptive BIOFAM ClusteringwAdaptive BIOFAM Example: Inverted PendulumAda

8、ptive FAM-Rule GenerationLet denote quantization vectors in the input-output product space .We count the number of quantizing vectors in each FAM cell . ijkkkijij1521kkkijFkmm,1kpnII Adaptive BIOFAM Clustering Through neural-network learning algorithm, learn to distribute input-output data in the in

9、put-output product space. Data clusters reflect FAM rules, such as the steady-state FAM rule ”IF is ZE AND is ZE, THEN is ZE.”f确定状态变量（条件变量）和控制变量 （结论变量）收集相应 的 训练样本(大量的有代表性的)根据训练样本的分布区间，划分为相应的模糊数，并赋于模糊语言量。自适应DCLAVQ对样本聚类。统计落在每 个可能单元中的突触矢量个数，计算每个规则的权值据区间划分进行规则合并 产生规则库，建立FAM系统BIOFAM聚类提取规则的过程Inverted Pend

10、ulum1、确定状态变量和控制变量 状态变量：摆线与垂直方向的 夹角 摆线的运动角速度 控制变量：马达作用于摆线的力 2、训练样本 在这里我是利用MATLAB工具包里的倒立摆模型生成了 1000个倒立摆轨迹样本作为训练样本。45,45s150,150fMembership Function-40-200204000.20.40.60.81-150 -100 -50050100 15000.20.40.60.81-10-5051000.20.40.60.81fFAM Bank & Synaptic Histogram02040600100200300400FAM Rules00),(),

11、(),();,(iBCACBCACaAMBMABAFMCBMCAMCBAmnnnmiiimmACcacacacacacacacacacacacaCAM21212221212111FAM Rulesw去模糊 按照质心法解模糊得马达作用力为-2.18。（20，-30）PS，NS ZEPS，ZE NS（0.83，0.31）（0.83，0.22） 0.31)(FmFZE)(FmFNS 0.22CbaCbCaBAFjiji),min(),(仿真演示系统小车轨迹scopeFAM RulesFAM RulesREFERENCEw基于FAM模糊控制器的研究中南大学 蔡自兴，文敦伟 2003.08w单级倒立摆的模糊控制及仿真山东师范大学 赵 莉 2004.09w二级倒