Neuro-Fuzzy Controller

Neuro-fuzzy modeling has been known as a powerful tool ([1]-[14]) which can facilitate the effective development of models by combining information from different sources, such as empirical models, heuristics and data. Neuro-fuzzy models describe systems by means of fuzzy if–then rules represented in a network structure, to which learning algorithms known from the area of artificial neural networks can be applied.

A neuro-fuzzy controller is a knowledge-based system characterized by a set of rules, which model the relationship among control input and output. The reasoning process is defined by means of the employed aggregation operators, the fuzzy connectives and the inference method. The fuzzy knowledge base contains the definition of fuzzy sets stored in the fuzzy database and a collection of fuzzy rules, which constitute the fuzzy rule base. Fuzzy cooperative coevolution, and symbiotic evolution, t

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

cooperative coevolution, and symbiotic evolution, t adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

adaptive evolutionary algorithms (SAEAs) are based.

rules are defined by their antecedents and consequents, which relate an observed input state to a desired output. Two typical types of neuro-fuzzy controllers are Mamdani-type and TSK-type neuro-fuzzy controllers.

For Mamdani-type neuro-fuzzy controllers ([1]), the minimum fuzzy implication is used in fuzzy reasoning. The neuro-fuzzy controllers employ the inference method proposed by Mamdani in which the consequence parts are defined by fuzzy sets. A Mamdani-type fuzzy rule has the form:

IF x₁ is A_1j (m_1j , σσσσ1j ) and x₂ is A_2j(m_2j , σσσσ2j )…and x_n is A_nj (m_nj , σσσσnj)

THEN y’ is B_j (m_j ,σσσσj ) (2.1) where m , and_ij σ_ij represent a Gaussian membership function with mean and deviation with

ith dimension and jth rule node. The consequences Bj of jth rule is aggregated into one fuzzy set for the output variable y^’. The crisp output is obtained through defuzzification, which calculates the centroid of the output fuzzy set.

Besides the more common fuzzy inference method proposed by Mamdani, Takagi, Sugeno and Kang introduced a modified inference scheme ([5]). The first two parts of the fuzzy inference process, fuzzifier the inputs and applying the fuzzy operator are exactly the same. A Takagi-Sugeno-Kang (TSK) type fuzzy model employs different implication and aggregation methods than the standard Mamdani’s type. For TSK-type neuro-fuzzy controllers ([5]), the consequence of each rule is a function input variable. The general adopted function is a linear combination of input variables plus a constant term. A TSK-type fuzzy rule has the form:

IF x₁ is A_1j (m_1j , σσσσ1j ) and x₂ is A_2j(m_2j , σσσσ2j )…and x_n is A_nj (m_nj , σσσσnj )

THEN y’=w0j+w1jx1+…+wnjxn (2.2) where w_0j represents the first parameter of a linear combination of input variables with jth rule node and wij represents the ith parameter of a linear combination of ith input variable.Since

. The crisp output is obtained through defuzzificat calculates the centroid of the output fuzzy set.

Besides the more common fuzzy inference method prop calculates the centroid of the output fuzzy set.

. The crisp output is obtained through defuzzificat . The crisp output is obtained through defuzzificat calculates the centroid of the output fuzzy set.

Besides the more common fuzzy inference method prop Besides the more common fuzzy inference method prop calculates the centroid of the output fuzzy set.

calculates the centroid of the output fuzzy set.

. The crisp output is obtained through defuzzificat . The crisp output is obtained through defuzzificat . The crisp output is obtained through defuzzificat

Besides the more common fuzzy inference method prop Besides the more common fuzzy inference method prop

the consequence of a rule is crisp, the defuzzification step becomes obsolete in the TSK inference scheme. Instead, the model output is computed as the weighted average of the crisp rule outputs, which is computationally less expensive then calculating the center of gravity.

Recently, there are many researchers ([5], [35], and [44]) to show that using a TSK-type neuro-fuzzy controller achieves superior performance in network size and learning accuracy than that of Mamdani-type neuro-fuzzy controllers. According to this reason, in this dissertation, a TSK-type neuro-fuzzy controller (TNFC) is adopted to perform various dynamic problems. Therefore, the proposed SAEAs are used to tune free parameters of a TNFC.

The structure of a TNFC is shown in Fig. 2.1, where n and R are, respectively, the number of input dimensions and the number of rules. It is a five-layer network structure. The functions of the nodes in each layer are described as follows:

Layer 1 (Input Node): No function is performed in this layer. The node only transmits input values to layer 2.

Layer 2 (Membership Function Node): Nodes in this layer correspond to one linguistic label of the input variables in layer1; that is, the membership value specifying the degree to which an input value belongs to a fuzzy set ([3]-[4]) is calculated in this layer. In this dissertation, the Gaussian membership function is adopted in this layer. Therefore, for an external inputx , _i the following Gaussian membership function is used:

[ ]

functions of the nodes in each layer are described

No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on functions of the nodes in each layer are described

No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on No function is performed in this layer. The node on

function of the jth term of the ith input variablex . _i

Layer 3 (Rule Node): The output of each node in this layer is determined by the fuzzy AND operation. Here, the product operation is utilized to determine the firing strength of each rule.

The function of each rule is

⁼

∏

i ij

j u

u ^{(3) (2)} (2.5)

Layer 4 (Consequent Node): Nodes in this layer are called consequent nodes. The input to a node in layer 4 is the output derived from layer 3, and the other inputs are the input variables from layer 1 as depicted in Fig. 2.1. The function of a node in this layer is

where the summation is over all the inputs and where w are the corresponding parameters _ij of the consequent part.

Layer 5 (Output Node): Each node in this layer corresponds to single output variable. The node integrates all the actions recommended by layers 3 and 4 and acts as a defuzzifier with

∑

where R is the number of fuzzy rule.

Each node in this layer corresponds to single outpu

node integrates all the actions recommended by layers 3 and 4 and acts as a defuzzifier with

∑

^{R (4)}

Each node in this layer corresponds to single outpu Each node in this layer corresponds to single outpu Each node in this layer corresponds to single outpu node integrates all the actions recommended by laye

Each node in this layer corresponds to single outpu node integrates all the actions recommended by laye

Each node in this layer corresponds to single outpu node integrates all the actions recommended by laye

Each node in this layer corresponds to single outpu node integrates all the actions recommended by laye

node integrates all the actions recommended by laye

Each node in this layer corresponds to single outpu Each node in this layer corresponds to single outpu node integrates all the actions recommended by laye

node integrates all the actions recommended by laye

Each node in this layer corresponds to single outpu Each node in this layer corresponds to single outpu Each node in this layer corresponds to single outpu Each node in this layer corresponds to single outpu node integrates all the actions recommended by laye

node integrates all the actions recommended by laye

Each node in this layer corresponds to single outpu node integrates all the actions recommended by laye

̋_˄ ̋_˅

Figure 2. 1: Structure of the TSK-type neuro-fuzzy controller.

在文檔中 以改良安全性增強式學習為基礎的自我適應進化演算法應用於模糊類神經控制器設計之研究 (頁 28-32)