JPH0492901A - Fuzzy controller by neural network - Google Patents

Abstract

PURPOSE:To automatically adjust an antecedent part membership function by constituting the control rule for a consequent part by means of the connection of an intermediate layer and an output layer. CONSTITUTION:Since a system is constituted in such a way that the control rule is decided by the connection of the intermediate layer and the output layer, the identification of control rules and the fine adjustment of antecedent part membership function can automatically be executed by changing connection loads ws, wc, wg and wf by learning. The connection loads ws, wc, wg and wf can be changed based on learning and the control rule and the antecedent part membership function can be identified by applying back propagation. Consequently, the control rule which an expert obtains can automatically be identified by the fuzzy controller.

Description

DETAILED DESCRIPTION OF THE INVENTION OBJECTS OF THE INVENTION [Industrial Field of Application] The present invention relates to a fuzzy controller using fuzzy inference configured by a neural network.

[Conventional technology]

Fuzzy control is being put into practical use as an excellent method for man-machine interfaces that does not require a mathematical model of the controlled object, as it describes control rules that have been acquired through experience by experts in their own verbal form. . However, the control rules that humans acquire do not necessarily involve clear verbal expressions, and are often extremely vague. Moreover, in some cases, it may be done unconsciously. It is difficult to accurately grasp such control rules, and a great deal of effort is required through interviews with experts and subsequent trial and error. Furthermore, adjusting the membership function after constructing a fuzzy controller cannot be done successfully without accurate insight into the controlled object, and requires skill with fuzzy controllers. A method of constructing a fuzzy controller using a neural network has been proposed to solve such problems.

FIG. 8 shows a conventional example of a fuzzy controller using a neural network. This controller is a fuzzy controller with r control rules. This fuzzy controller consists of multiple neural networks.

The neural network 10 corresponds to an antecedent membership function that determines which control rule the inputs X, ~x0 belong to, and outputs the fitness degree 1iA1~□+ of each rule. The other neural networks 11 to 1r correspond to the control rules for the consequent part, and each network has the input/output relationship of the following formula.

y'-fl(x++..., xa)(i-1
,..., r)... (1) fi may be a nonlinear function. Multiply by calculator 21~2n
are the outputs y1-y of the neural network 11-]n
By multiplying ' and the respective fitness degrees μl to μ9′, it is determined whether each control rule for the inputs x1 to Xn has a degree of contribution to the output y. adder 30
calculates the sum of the above results.

FIG. 9 shows another conventional example of a fuzzy controller using a neural network. This conventional example also consists of a plurality of neural networks. neural network 40
is composed of a plurality of sub-networks 41 to 4r called cluster units. Each cluster unit becomes an antecedent member subfunction and extracts the features of the input. Another neural network 50 determines from the output of neural network 40 which control rule the input belongs to. Further, another neural network 60 is composed of sub-networks 61 to 6r having functions equivalent to those of the neural networks 11 to 1n, and is a neural network 5.
The output of the fuzzy controller is created by combining the output of 0 and the output of the subnetworks 61 to 6r.

[Problem to be solved by the invention]

The conventional neural network based fuzzy controller described above consists of multiple neural networks, and the neural network that obtains the antecedent membership function and the neural network that obtains the consequent control rule are configured independently. . Therefore, the neural networks 11 to 1r or 61 to 6r must be made to learn the control rules after the control rules have been clarified in advance using some method. However, as described above, it is difficult to accurately grasp the control rules, and there is a problem in that it requires a great deal of effort.

The present invention has been made to solve the above problems, and uses data on the amount of operation performed by the expert and the output to automatically identify the control rules learned by the expert, and at the same time Our objective is to provide a fuzzy controller that can also automatically adjust the subject membership functions.

[Means to solve the problem]

A fuzzy controller using a first neural network according to the present invention for solving the above problems includes an input layer composed of a plurality of units, and an intermediate layer coupled to the input layer and composed of a plurality of units. and an output layer connected to the intermediate layer and composed of a plurality of units, each unit is not connected within the same layer, and flows from the input layer to the intermediate layer and from the intermediate layer to the output layer. The input layer and the intermediate layer form the antecedent membership function for fuzzy control, and the connection between the intermediate layer and the output layer is used to form the antecedent membership function for fuzzy control. It is characterized in that a subject control rule is configured.

Further, a fuzzy controller using a second neural network according to the present invention for solving the above problems includes: an input layer into which an input signal is input; a layer coupled to the input layer and outputting a predetermined function;
an intermediate layer having at least a layer that outputs an antecedent membership function based on the function, and a layer that outputs an antecedent fitness degree based on the antecedent membership function; It consists of an output layer that outputs the product sum of the antecedent part fitness and the consequent part constant as an inferred value, and each unit is not connected within the same layer, but from the input layer to the middle layer, and from the middle layer to the output layer. It is characterized by being combined by applying a weighting coefficient in one direction.

Preferably, the predetermined function is a sigmoid function f (x)-1/(1+exp(-x)).

[Effect]

In the fuzzy controller configured as above, the antecedent membership function is obtained by combining the input layer and the intermediate layer, and the consequent control rule is obtained by combining the intermediate layer and the output layer. It has become. That is, the antecedent membership function and the consequent control rule can be obtained in one neural network.

Therefore, the back propagation algorithm, which is a learning algorithm of a neural network, can be applied based on the data of the amount of operation and output performed by the expert, so that each weighting coefficient can be automatically determined. As a result, the control rules learned by an expert can be automatically identified based on the weighting coefficients of the connections between the intermediate layer and the output layer, and at the same time, the antecedent membership function can be automatically adjusted.

〔Example〕

Embodiments of the fuzzy controller of the present invention will be described below with reference to the drawings.

This fuzzy controller performs simplified fuzzy inference, in which the consequent is expressed as a constant, the antecedent fitness is multiplied, and the inference value is calculated as the product sum of the antecedent fitness and the consequent constant. use In this way, pack propagation, which is a neural network learning algorithm, can be applied as described later, and the antecedent membership function and control rule can be automatically adjusted.

This reasoning method is expressed as follows in the case of two human forces (x+, X2) and one output (y).

R': If X+ -AlHand X2-
A21then y −f H−(2) y8−Σμ,・f3. μj −A++(X+) ・A21(X2)(j−1,...
・, N) ... (3) Here, "R" is the rule number, A, A2. is a fuzzy variable, f is a constant, y8 is an inference value, μm is antecedent fitness, and N is the number of control rules.

FIG. 1 shows an embodiment of the present fuzzy controller. This controller is a seven-layer neural network of A-G. AJi
are units 71 and 72, and B layer is units 73 to 76.0.
The layer is units 77-84, the D layer is units 85-92,
E layer has units 93 to 98, F layer has units 99 to 10.
7. The G layer consists of a unit 108. The A layer corresponds to the input layer, and the B layer corresponds to the input layer.

The C, D, E, and F layers correspond to the intermediate layer, and the G layer corresponds to the output layer.

Each unit has an input on the left side and an output on the right side. Unit 71, 72, 75, 76.93゜95.96.98
simply distributes the input to the output.

Units 73 and 74 output a constant 1. unit 77
84, 94, 97, and 108 output the sum of inputs. Units 99-107 output the product of the inputs. unit 8
5 to 92, when the input is X, the output f (x) is given by the following formula.

f (x)-1/ (1+exp (-x))...
(4) Equation (4) is called a sigmoid function.

Units 71 and 75. Units 72 and 76 are each coupled by a weighting factor ws. For example, if the output of the unit 71 is 07□, the input 175 of the unit 75 is i 75=WS' 071
・= (5).

Unit 75 and units 77-80 are each coupled with a weighting factor of 1. Unit 76 and Units 81-8
4 are similarly combined with each other with a weighting coefficient of 1. Unit 73 and units 77-80, and unit 74 and units 81-84 are each coupled by a weighting coefficient WC. Units 77-84 and units 85-92 are each coupled with a weighting coefficient of Wg1, and units 85-92 and units 93-98 and units 93-98 and units 99-107 are coupled with a weighting coefficient of 1, respectively, as shown in the figure. ing. However, as an exception, units 87 and 94
．． Units 91 and 97 are each coupled with a weighting coefficient of -1. Units 99 to 107 and unit 108 are coupled by a weighting coefficient wf. Weighting coefficients WS, We
, wg.

wf can be changed by learning. E1ΔE
is the input of the fuzzy controller and ΔU is the output. FIG. 1 is an example of a two-person, one-output, three-antecedent membership function.

First, the input x1 applied to the A layer is normalized by ws. Next, WC, which is a bias, is added to the 0 layer, and the result obtained by multiplying it by wg becomes the input to the D layer. As a result, the position and slope of the center of f (x) are determined by wc and wg, respectively.

The output of the E layer is an antecedent membership function A as shown in FIG. However, the pseudo-trapezoidal membership functions A and 2 can be composed of the sum of two sigmoid functions a and b having different signs, as shown in FIG. Depending on the value of WC, the output may be negative, in which case the output is set to 0. The F layer is a linear unit that receives the product of the outputs of the E layer as input, and its output becomes the antecedent fitness μm. Then, the product-sum or inference value y8 of μ and wf representing the consequent part constant is output from the 0th layer. Based on the above, (2), (3)
Fuzzy inference based on equations is realized.

According to this fuzzy controller, the antecedent membership function is determined by the input layer and the intermediate layer, and the control rule is determined by the connection between the intermediate layer and the output layer, so the connection weight ws
, wc, wg, and wf through learning, it is possible to automatically identify the control rule and fine-tune the antecedent membership function. As a learning algorithm for this purpose, pack propagation expressed by the following delta rule is used. That is, by applying this pack propagation, the control rule and the antecedent membership function can be identified by changing the connection weights ws, wc, wg, and wf based on learning.

(0 layer) δ, I++) = (t, ol (n)
)x f' (l, (n l)...
(6) (B, C, D, F layer) δ, +a)=f” (i, (fi))XΣδ (a
lll, Wl(ll++1... (7) Here, (n) and (n+1) are the nth layer and the n+th layer, respectively.
1 layer, j means the j-th unit, t is the teacher signal of the output layer, i is the input, 0 is the output, f" is the derivative of the output function of the unit, w, "month) is the n-th layer This is the connection load from the Jth unit to the n+1th layer unit.

In the E layer, since multiplication is performed in the F layer, δj3"ゝ-f'(iH'°ゝ)Σ (δ, ("+1)
X (nw, (ffi"' 6 01 "'
10. "' ) 1...(8). Using the results of equations (6), (7), and (8), the joint load is Wz"'(m+1)=lAJ+''')(m)+η°
It is updated as δJ3°ゝ・o, Io−1′ (9). Here, w''13'')(m) is the connection weight obtained by the m-th learning, and η is the learning rate. However, since the initial value of ws varies greatly depending on the input, the learning rate is calculated using the following formula. simplifies configuration.

Wl+”ゝ (m+1)=wI+”’ (m)×(1
+η・δ (a)・o, (a-th)...(1
0) Next, the setting of the initial value of each connection load will be described. First, ws is the reciprocal of the maximum absolute value of the input in the learning data. wc and wg are set so that the membership functions are distributed at equal intervals with respect to the standardized input, as shown in FIG. 7(a). Further, the initial values of wf are all set to 0, and the present controller starts learning from a state without any control rules.

An experimental example of the fuzzy controller of the present invention will be shown below.

The feature of this fuzzy controller is that it is possible to directly identify control rules from the operation pattern of an expert for control objects that are difficult to formulate even though humans can perform precise control. For simplicity, the simulation was performed using a first-order delay system with dead time as the control object.

FIG. 4 shows the system configuration used in the simulation. The time constant and dead time of the controlled object 130 are each 1
It is 00.10. The differentiator 140 calculates the variation ΔE of the error E.
is determined by difference approximation, and the integrator 150 calculates the change Δ of the operation mU.
U is determined using trapezoidal approximation. The limiter 120 limits the input to the controlled object 130 within a range of ±1. Also,
Fuzzy controller 110 in the embodiment of FIG.
The number of units in each layer of , E, and F was increased to create a two-man, one-output cuff membership function. The input of the controller 110 is
The error E between the target value Ya and the output Y and its change ΔE are assumed, the output is the change ΔU of the operation mU, and the sampling time is 1.

The human operation amount is determined in advance so as to obtain a desired response to the target values 0.4, 0.13, and 0.111.

The input waveform of the manipulated variable and the output waveform of the response are shown in FIG. The training data (E, ΔE, ΔU) was created by extracting a total of 135 points of turnout from these input and output waveforms. Furthermore, the sign and order of the data are randomly changed during learning of the neural network so that the neural network learns also for negative target values -0,4°-0,6,-0,8. The initial values of WS are set to the maximum values of 110.8.110.0075 for E and ΔE, respectively, and wc and wg have the antecedent member subfunctions shown in Figure 7 (a
). Each membership function has NB (Negative Big)
, NM (Negative Medium), N
S (Negative small) Z 0
(Zero), P S (Positive
Small) P M (Po5itive Med
ium) and PB (Positive Big). The learning rates were set to 0.1, 0.01, 5, and 0.005 for ws, wc, wg and wf, respectively.

FIG. 6 shows the simulation results after 100 learnings. (a) is a response to a learned target value, and (b) is a response to an unlearned target value. As is clear from this figure, it can be seen that the fuzzy controller of the present invention provides relatively good control even for unlearned target values.

FIG. 7 shows the antecedent membership functions before and after learning. As can be seen from this figure, according to the fuzzy controller of the present invention, fine adjustments corresponding to learning data are automatically performed.

Table 1 is a table showing control rules expressed by wf identified by the present fuzzy controller, and Table 2 is a table showing control rules applied to a conventional fuzzy controller. This table 1.2
As is clear from the above, the control rules identified by the fuzzy controller of the present invention are very similar to the control rules applied to the conventional fuzzy controller that does not use a neural network. Therefore, it can be seen that according to the fuzzy controller of the present invention, control rules learned by an expert can be automatically identified.

Table [Effects of the Invention] As explained above, the present invention applies a neural network to a fuzzy controller, configures an antecedent membership function by an input layer and an intermediate layer, and creates a connection between an intermediate layer and an output layer. Since the control rules of the consequent part are configured, the control rules acquired by the expert can be automatically identified using the amount of operation performed by the expert and the output data, and at the same time, the control rules of the antecedent part membership function can be automatically identified. Adjustments can be made.

[Brief explanation of drawings]

Fig. 1 shows an example of a fuzzy controller using the neural network of the present invention, Fig. 2 shows an antecedent membership function, and Fig. 3 shows a method for constructing a pseudo-trapezoidal membership function. Figure 4 is a configuration diagram of the system used in the simulation, Figure 5 is a diagram showing an example of the amount of operation performed by an expert and the waveform of the output, and Figure 6 is an example of the output waveform of the fuzzy controller. 7 is a diagram showing how the antecedent membership function changes due to learning, and FIGS. 8 and 9 are diagrams showing an example of the configuration of a fuzzy controller using a conventional neural network. 10~1r, 40.41~4r, 50,60°61~
6 "...Neural network, 71-108...
Unit, 110... Fuzzy controller, 120... Limiter, 130... Controlled object, 140... Differentiator, 1
50...integrator

Claims (3)

[Claims] (1) An input layer composed of a plurality of units, an intermediate layer coupled to the input layer and composed of a plurality of units, and an output layer coupled to the intermediate layer and composed of a plurality of units. In a neural network consisting of A fuzzy controller using a neural network, characterized in that an antecedent membership function for fuzzy control is configured, and a consequent control rule for fuzzy control is configured using a connection between an intermediate layer and an output layer. . (2) an input layer to which an input signal is input; a layer coupled to the input layer and outputting a predetermined function;
an intermediate layer having at least a layer that outputs an antecedent membership function based on the function, and a layer that outputs an antecedent fitness degree based on the antecedent membership function; It consists of an output layer that outputs the product sum of the antecedent part fitness and the consequent part constant as an inferred value, and each unit is not connected within the same layer, but from the input layer to the middle layer, and from the middle layer to the output layer. A fuzzy controller using a neural network, which is characterized by being connected by applying a weighting coefficient in one direction. (3) The predetermined function is a sigmoid function f(x)-1/
The fuzzy controller according to claim 2, characterized in that (1+exp(-x)).