The route of the vehicle

Sugeno fuzzy inference algorithm for optimizing

Determination of the control method

PROBLEM STATEMENT AND PRELIMINARIES

There are a lot of methods to control, therefor in choosing a method of control is the success of the system, it is necessary to take into account all the requirements for the project management. As is known to control strictly nonlinear [1], based on what was selected fuzzy control theory.

It is known that there is a plurality of fuzzy control systems or decision-making, such as Mamdani [5, 6], Sugeno [6-8], Takagi [9], Takagi - Sugeno [9, 10], Takagi - Sugeno - Kang [9, 10].

To solve the problem of automatically optimizes of the route of the car, no need to use sophisticated algorithms such as TSC [10], but cannot be used as a simple algorithm as an algorithm Mamdani [7], for many reasons, one of which is the requirement for output parameter fuzzy inference algorithm, here we have linear process not just the decision making. Therefor in this article we will focus on the choice of algorithm Sugeno [10].

It is needed to work in specific road map for simplicity that use the one show in (Figure-3) that moves upon it a car to be adjusted on the basis of fuzzy logic algorithm using Sugeno fuzzy inference.

The Sugeno fuzzy inference has four inputs and one output. We define the module inputs Sugeno like the following:

§ Start-Stop state for the route (ST);

§ Coefficient of congestion along the selected route (KP);

§ The proportion of fuel to the final goal of the route (TK);

§ The number of gas stations, taking into accounts all possible paths to the final goal (AP).

Output parameters of the algorithm:

§ The optimal path to the final goal, depending on the ratio of the amount of fuel in the car and for the number of petrol stations (OP).

Define the levels of factors and parameter (possible values) is shown in Table-1.

Table-1. The levels of factors and parameters.

Variable	Fuzzy value	numeric value
ST	Small Average High	[1-3] [2-5] [4-8]
KP	Low Average High	[0-0.25] [0.2-0.5] [0.4-0.75]
TK	Low Average High	[0-0.33] [0.2-0.66] [0.5-1]
AP	Small Average High	[1-3] [2-4] [3-5]

Fuzzy decision algorithm Sugeno decision-making system is shown in Figure-4.

Figure-4. Fuzzy decision algorithm Sugeno management system roadmap.

Sugeno FIS was proposed to develop a systematic approach to generate fuzzy rules from a given input-output data. The Sugeno FIS architecture used in this paper for the choice the optimal way to the final goal of a vehicle is shown in Figure-3. The rule base for Sugeno FIS is given by:

§ if (ST is S₁₁) and (KP is S₂₁) and (TK is S₃₁) and (AP is S₄₁) then Z1 = r₁ (ST, KP, TK, AP);

§ if (ST is S₁₂) and (KP is S₂₁) and (TK is S₃₁) and (AP is S₄₁) then Z1 = r₁ (ST, KP, TK, AP);

§ if (ST is S₁₃) and (KP is S₂₁) and (TK is S₃₁) and (AP is S₄₁) then Z1 = r₁ (ST, KP, TK, AP);

§ if (ST is S₁₁) and (KP is S₂₂) and (TK is S₃₁) and (AP is S₄₁) then Z1 = r₁ (ST, KP, TK, AP);

§ if (ST is S₁₂) and (KP is S₂₃) and (TK is S₃₁) and (AP is S₄₁) then Z1 = r₁ (ST, KP, TK, AP);

§ if (ST is S₁₃) and (KP is S₂₄) and (TK is S₃₁) and (AP is S₄₁) then Z1 = r₁ (ST, KP, TK, AP);

with

Z_k = r_k (ST, KP, TK, AP) k = 1,...,38

where: S_ij, Z_k, and r_k represent the jth membership functions of the ith input, the output of the k_th rule, and the kth output membership functions, respectively.

As shown in Figure-4, the Sugeno FIS structure consists of five layers: fuzzy layer, product layer, normalized layer, de-fuzzy layer, and summation layer. The operating mechanism of the layers for Sugeno FIS can be described as follows:

Layer-1:

In this layer, the crisp input values are converted to the fuzzy values by the input membership functions. In this paper, the following generalized bell for the inputs is used:

Generalized bell membership functions for (i =1…4), (j =1, 2, 3), (x = ST or x = KP or x = TK or x = AP):

where a_ij, b_ij and c_ij, are the premise parameters that characterize the shapes of the input membership functions.

Layer-2:

In this layer, the weighting factor of each rule is computed. The weighting factor of each rule, which is expressed as ω_k, is determined by evaluating the membership expressions in the antecedent of the rule. This is accomplished by first converting the input values to fuzzy membership values by using the input membership functions in the layer_1 and then applying the «and» operator to these membership values. The «and» operator corresponds to the multiplication of input membership values. Hence, the weighting factors of the rules are computed as follows:

ω₁ = S ₁₁ (ST) S ₂₁ (KP) S ₃₁ (TK) S ₄₁ (AP)

ω₂ = S ₁₂ (ST) S ₂₁ (KP) S ₃₁ (TK) S ₄₁ (AP)

ω₃ = S ₁₃ (ST) S ₂₁ (KP) S ₃₁ (TK) S ₄₁ (AP)

ω₄ = S ₁₁ (ST) S ₂₂ (KP) S ₃₁ (TK) S ₄₁ (AP)

.

.

.

ω₃₇ = S ₁₃₇ (ST) S ₂₃₇ (KP) S ₃₁ (TK) S ₄₁ (AP)

ω₃₈ = S ₁₃₈ (ST) S ₂₃₂ (KP) S ₃₁ (TK) S ₄₁ (AP)

Layer-3:

The normalized weighting factor of each rule, is computed by using

Layer-4:

In this layer, the output rules can be written as:

k = 1,...,38

where p_k are the consequent parameters that characterize the shapes of the output membership functions. Here, the types of the output membership functions (r_k) are linear.

Layer-5:

Each rule is weighted by own normalized weighting factor and the output of the FIS is calculated by summing of all rule outputs:

The Sugeno FIS used in this paper contains a total of 304 fitting parameters, of which 34 (3Ч3+3Ч4+2Ч2+3Ч3=34) are the premise parameters and 270 (5Ч54=270) are the consequent parameters.

Дата добавления: 2015-07-02