JP2000347708A - Method and apparatus for controlling dynamic system using neural network and storage medium storing control program for dynamic system using neural network - Google Patents

Abstract

(57) [Summary] (with correction) [PROBLEMS] To provide a control method of a dynamic system by a neural network that can imitate the operation of a reference system that can generate a control target trajectory. SOLUTION: When K data of a set of m-dimensional output trajectories, which are outputs of motion of a dynamic system, are designated, data of K control target trajectories is converted into time of an internal state based on an n-dimensional dynamic system. Under the evolution mechanism and the output mechanism of the dynamic system, create an interconnected neural network and affine mapping that realizes the dynamic characteristic of the reference system that can be generated, and Create and control a layered neural network for converting an n-dimensional state vector to an r-dimensional state vector, which changes the dynamics characteristics of an engine system composed of a coupled neural network and an affine map to mimic the affine neural vector field For this purpose, an r-dimensional control signal to be input to the dynamic system at each time is created.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for controlling a dynamic system using a neural network, and a storage medium storing a control program for a dynamic system using a neural network. In the control method, when a target output of the motion of the dynamic system is designated for the dynamic system to be controlled, a control signal is generated, and the control signal is input to the dynamic system. The present invention relates to a method and an apparatus for controlling a dynamic system using a neural network, which enables the system to achieve a target output of a designated motion, and a storage medium storing a control program for a dynamic system using a neural network.

[0002]

2. Description of the Related Art Numerous control methods have been established for linear dynamic systems. As shown in well-known literature, for example, Chapter 8 “Control Theory” of the Dictionary of Modern Mathematical Sciences (Osaka Books), for a linear dynamic system, the controllability of the system and the Judgment methods for observability, stability, etc., and system state estimation methods using observers, Kalman filters, etc. have been established.Also, regarding the optimal control method, the optimal regulator configuration method and optimal servo configuration by Kalman have been established. The law has been established.

[0003]

However, many real dynamic systems, such as robots and voice systems, are non-linear systems. The method established as the linear system theory is effective to some extent for local analysis and control of nonlinear systems, but is not effective for global analysis and control thereof. Therefore, establishment of a control method for a nonlinear dynamic system is an important issue.

For a nonlinear dynamic system with n internal state variables, r control input variables, and m output variables,
Given the dynamic characteristics and output mechanism of this dynamic system,
As a control target of this dynamic system, the initial internal state n
When K data of a set of m-dimensional output trajectories, which are the output of the motion of this dynamic system at time [0, T], at the time [0, T], are specified, the dynamic system generates For each n-dimensional vector of the initial internal state, each specified m-dimensional output start is set as the output of the motion,
The challenge is to generate an r-dimensional control signal to be input to this dynamic system.

[0005] By the way, various real problems require that dynamic systems function autonomously with minimal supervision. Therefore, this dynamic system can not only achieve the specified control target trajectory as described above, but also convert the control target trajectory to the time evolution of the internal state based on the n-dimensional dynamical system and the output of this dynamic system. It is required to be the same as the operation of the reference system, which can occur under the mechanism. Therefore, it is an issue to generate an r-dimensional control signal to be input to the dynamic system so that the operation of the dynamic system mimics the operation of the norm.

The present invention has been made in view of the above points, and an operation of the dynamic system can generate such a control target trajectory with respect to a control target trajectory designated as a non-linear dynamic system. An object of the present invention is to provide a method and an apparatus for controlling a dynamic system using a neural network by a nonlinear dynamic system capable of imitating the operation of such a reference system, and a storage medium storing a control program for the dynamic system using a neural network. I do.

[0007]

FIG. 1 is a diagram for explaining the principle of the present invention. The present invention (Claim 1) provides a method for controlling a dynamic system using a neural network for performing motion control of a dynamic system including a robot.
For a dynamic system having n internal state variables, r control input variables, and m output variables, the dynamic characteristics and output mechanism of the dynamic system are given, and the control target of the dynamic system is When K data of a set of an n-dimensional vector of the initial internal state and an m-dimensional output trajectory which is the output of the motion of the dynamic system at time [0, T] with respect to the n-dimensional vector is designated (step 1) ), Realizing the power characteristics of the reference system that can generate the data of the K control target trajectories under the time evolution of the internal state based on the n-dimensional dynamical system and the output mechanism of the dynamic system. Then, an affine mapping is created with the interconnected neural net (step 2), and the dynamic characteristics of the dynamic system to be controlled are determined using the dynamic characteristics of the engine system composed of the interconnected neural network and the affine mapping. A layered neural network for transforming an n-dimensional state vector into an r-dimensional state vector, which is changed to imitate a fin neural vector field, is created (step 3). A layered neural net generated from the internal state of the system is created (step 4), and the dynamic state is controlled at each time from the internal state of the dynamic system to be controlled at each time by using the layered neural network. An r-dimensional control signal to be input to the system is created (Step 5).

FIG. 2 is a block diagram showing the principle of the present invention. The present invention (claim 2) is a control system of a dynamic system using a neural network for performing motion control of a dynamic system including a robot, wherein n internal state variables, r control input variables, and m For a dynamic system with three output variables, the dynamic characteristics of the dynamic system and the output mechanism inputs, and the initial internal state n
Dimensional vector and time [0,
T], input means 1 for designating K data of a set of m-dimensional output trajectories, which is the output of the motion of the dynamic system at T], and data of the K control target trajectories input by the input means 1 are converted into n-dimensional data. An affine neurodynamic system that creates an interconnected neural network and an affine mapping that realizes the time evolution of internal states based on a dynamical system and the dynamics of the reference system that can be generated under the output mechanism of the dynamical system Parameter changing means 2 and changing the dynamic characteristics of the dynamic system to be controlled so as to mimic the affine neural vector field of the dynamic characteristics of the reference system constituted by the interconnected neural network and the affine mapping, n A layered neural network for transforming a dimensional state vector into an r-dimensional state vector is created, and an r-dimensional signal input to the dynamic system is
Layered neural network creating means 3 for creating a layered neural network generated from the internal state of the dynamic system;
Using the layered neural network created by the layered neural network creating means 3, an r-dimensional control signal to be input to the dynamic system at each time for control based on the internal state of the dynamic system to be controlled at each time. And a control signal generating means 4 for generating

According to a third aspect of the present invention, there is provided a storage medium storing a control program for a dynamic system using a neural network for performing motion control of a dynamic system including a robot, wherein n internal state variables and For a dynamic system having r control input variables and m output variables, the dynamic characteristics and output mechanism of the dynamic system are given, and the initial internal state n When K data of a set of a dimensional vector and an m-dimensional output trajectory, which is the output of the motion of the dynamic system at time [0, T] with respect to the n-dimensional vector, are designated, the K control target trajectories of the K control target trajectories are specified. Data is obtained by using an interconnected neural network and an affinity network to realize the time evolution of internal states based on an n-dimensional dynamical system and the power characteristics of a reference system that can be generated under the output mechanism of the dynamic system. Affinity neurodynamic system parameter creation process for mapping and dynamic characteristics of the dynamic system to be controlled mimicking the affine neural vector field of the dynamic characteristics of the reference system composed of interconnected neural networks and affine mapping A layered neural network for converting an n-dimensional state vector into an r-dimensional state vector, and generating an r-dimensional signal to be input to the dynamic system from an internal state of the dynamic system. Using a layered neural network creation process for creating a net and a layered neural network created by the layered neural network creation process, the internal state at each time of the dynamic system to be controlled is determined at each time for control. Control signal creation process for creating an r-dimensional control signal for input to a dynamic system Having.

As described above, according to the present invention, the parameter creation means of the affine neurodynamic system uses the dynamics of the reference system to be imitated by the dynamic system to be controlled based on the data of the designated control target trajectory. The properties are constructed using an interconnected neural network and an affine map. Therefore, a model of the dynamic characteristics of the reference system, which is generally nonlinear, is obtained, and control based on the reference system for making the dynamic system function autonomously is possible.

[0011] Further, the layered neural network creating means includes:
To match the dynamic characteristic of the dynamic system to be controlled with the model of the dynamic characteristic of the reference system created by the parameter creating means of the affine neurodynamic system,
We are constructing a layered neural network that changes the dynamic characteristics of this dynamic system. Therefore, it is possible to match the dynamic characteristic of the dynamic system of the control target that is nonlinear with the model of the dynamic characteristic of the reference system that is generally nonlinear.

On the other hand, the control signal creation means uses the layered neural network created by the layered neural network creation means to convert the internal state at each time of the dynamic system to be controlled at each time as a control signal. Feedback to the strategic system. Therefore, this dynamic system can function autonomously and imitate the operation of the reference system, and the dynamic trajectory, which is the object of the present invention, is designated as the nonlinear dynamic system and the control target trajectory designated. Control of a non-linear dynamic system can be realized, in which the system can mimic the operation of a reference system that can generate such a control target trajectory.

[0013]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 3 shows the configuration of the dynamic system of the present invention, FIG. 4 shows the operation of the dynamic system of the present invention, and FIG. 5 shows the configuration of the control system of the dynamic system of the present invention. For the dynamic system as shown in FIG. 3 of the present invention, means for generating a control signal to be input to the dynamic system is provided so that the operation of the dynamic system is the same as the operation of the exemplary system as shown in FIG. To provide.

As shown in FIG. 5, the dynamic system using a neural network according to the present invention comprises a dynamic system 30, a neural network learning unit 10, and a control signal creation unit 20. As shown in FIG. 5, by inputting the control signal created by the control signal creation unit 20 to the dynamic system 30 to be controlled, the operation of the dynamic system 30 to be controlled mimics the operation of the reference system. Is achieved.

First, the dynamic system 30 to be controlled and the control target will be described in detail, and then the control signal creation unit 20 and the neural network learning unit 10 of the present invention will be described in detail. 1. Dynamic System and Control Target: (1) Dynamic System 30: First, a dynamic system to be controlled in the present invention will be described. This dynamic system 30, n-number of internal state variables _{x = (x 1, ...,} x n) and r pieces of control input variables _{u = (u 1, ...,} u r) has, n from n + r-dimensional space It has a mapping v = f (x, u) to a dimensional space as a dynamic characteristic of the system, and has a mapping y = h (x) from an n-dimensional space to an m-dimensional space as an output mechanism of the system. Here, the number n of internal state variables, the number r of control input edits, the dynamic characteristics f (x, u) of the system, and the output mechanism h of the system
(X) is known, and the internal state at any time t can be observed.

Next, the operation of the dynamic system to be controlled in the present invention at time [0, T] will be described.
As shown in FIG. 3, the dynamic system 30 to be controlled is
Is an n-dimensional vector x ⁰ = (x ⁰ ₁ ,..., X ⁰ _n ) is input as an initial state of the dynamic system, and an r-dimensional signal u (t) = (u ₁ (t) _,. (T)), t∈
When [0, T] is input as a control signal of the dynamic system, the internal state x (t) = (x ₁ (t),..., X _n (t)) at time t is represented by the dynamics

[0017]

(Equation 1)

The output mechanism of the system y =
Under h (x), y (t) = h (x (t)), t∈ [0, T], and an m-dimensional trajectory y (t) = (y ₁ (t),..., y _m (t )), T∈
[0, T] is output.

An example of a dynamic system to be controlled in the present invention will be described. FIG. 6 is an example of a dynamic system to be controlled according to the present invention, and is a schematic diagram showing a two-joint robot arm moving in an XY plane. Here, the X axis is the horizontal direction, the Y axis is the vertical direction, gravity moves in the negative direction of the Y axis, and g ₀ is the gravitational acceleration. Also,
m ₁ and m ₂ are the masses of link 1 and link 2, respectively, L
₁ and L ₂ are link 1, link length, L _g1 ,
L _g2 is the distance from joint 1 and joint 2 to the center of mass of link 1 and link 2, respectively, I ₁ and I ₂ are the moments of inertia of link 1 and link 2 around the axis of joint 1 and joint 2, respectively. theta _1, theta _2, respectively, the joint 1, the joint 2 displacement, ^theta. _1, ^theta. _2, respectively a joint 1, the speed of displacement of the joint 2, tau _1, tau _2, respectively, the joint 1, joint 2 is the joint driving force.

At this time, n = 4, r = 2, m = 2, x = (x ₁ , x ₂ , x ₃ , x ₄ ), u = (u ₁ ,
u ₂ ) and y = (y ₁ , y ₂ ) are respectively x ₁ = θ ₁ , x ₂ = θ ₂ , x ₃ = θ ₁ ,
x ₄ = θ ₂ , u ₁ = τ ₁ , u ₂ = τ ₂ y ₁ is the X coordinate of the tip of the robot arm, and y ₂ is the Y coordinate of the tip of the robot arm. Further, the dynamic system characteristics v = f (x, u) and v = (v ₁ , v ₂ , v ₃ , v ₄ ) of the system are as follows.

[0021]

(Equation 2)

## EQU1 ## Further, the output mechanism of the system y = h (x), y = (y 1, y 2) _{is, y 1 = L 1 cos (} x 1) + L 2 cos (x 1 + x 2), y 2 = L 1 sin (X ₁ ) + L ₂ sin (x ₁ + x ₂ ).

(2) Control target: The control target in the present invention is to make the operation of the dynamic system as shown in FIG. 3 the same as the operation of the reference system as shown in FIG. 4 at time [0, T]. That is. First, the operation of the reference system at time [0, T] will be described. Then, data specified in the control of the dynamic system will be described, and a technique required in this case and a measure in the present invention will be described.

First, the operation of the reference system at time [0, T] will be described. The reference system, as shown in FIG. 4, inputs n to the dynamic system 30 to be controlled.
Dimensional vector _{^{x 0 = (x 1 0,}} ..., x n 0) When is input as an initial state, dynamics [Phi is n-dimensional trajectory x (t) = Φ (t , x 0), generates a control Output mechanism y of the target dynamic system
Under h (x), y (t ) = h (x (t)), and t∈ [0, T], m-dimensional trajectory _{y (t) = (y 1} (t), ..., y m ( t)), t∈
[0, T] is output.

Next, data specified when controlling the dynamic system 30 shown in FIG. 3 will be described. In the present invention, as shown in FIG. 4, K initial states x ^k = (x ₁ ^k , .., X _n ^k ), (k = 1,.
K) and output trajectories when they are input to the reference system y ^k (t) = (y ₁ ^k (t),..., Y _m ^k (t)), t
∈ [0, T], (k = 1,..., K) are specified when controlling the dynamic system.

Therefore, data (x ^k , y ^k (t)), t∈ [0, T], (k
= 1,..., K), a technique for estimating the dynamical system Φ in the reference system is required. FIG. 7 is a block diagram of a model of the reference system according to the present invention. In the reference system to be imitated by the dynamic system in FIG. This is an example of a model of a reference system constructed as a system. In the present invention, as shown in FIG. 7, a method of modeling a dynamical system Φ in a reference system as an affine neurodynamical system using an interconnected neural network is used. In the present invention, the affine neurodynamic system that models the dynamic system Φ in the reference system is acquired by the parameter creation unit 12 of the affine neurodynamic system in the layered neural network learning unit 10 illustrated in FIG.

2. Control signal creation unit 20: In the control signal creation unit 20 of the present invention, the neural network learning unit 10
In the three-layer neural network u = g _W (x) with n input units, r output units, and W parameters learned by the above, the internal state of the dynamic system at each time t x (t) = (x ₁ (T),..., X _n (t)) and outputs u (t) = g _W (x (t)) = (u ₁ (t) _,.
(T)) as a control signal at each time t.
Feedback to

3. Neural network learning unit 10: The neural network learning unit 10 is executed using a computer system. As shown in FIG. 8, the neural network learning unit 1
At 0, the dynamic characteristics of the dynamic system 30 to be controlled v = f (x, u), its output mechanism y = h (x), and the initial state which is data specified when controlling the dynamic system 30 And a set of target trajectories (x ^k , y ^k (t)), t∈ [0, T], (k =
,..., K) are input to the computer system, and the parameter creation unit 12 for the affine neurodynamic system calculates the parameters μ = (w, A, b) of the affine neurodynamic system, and the input control. Dynamic property v = f (x, u) of the target dynamic system and constructed affine neural vector field

[0029]

(Equation 3)

The parameter w of the three-layer neural network having n input units and r output units is calculated by the layered neural network creating unit 13, and the parameter is calculated when the number of input units is n and the number of output units is r. Constructs and outputs a three-layer neural network u = g _W (x) of _W.

Hereinafter, each part will be described in detail. Affine neurodynamic system parameter creation unit 12: In the affine neurodynamic system parameter creation unit 12, the Φ model of the n-dimensional dynamic system in the reference system shown in FIG.
An affine neurodynamic system is constructed by using an interconnected neural network having n visible units and n _H hidden units and an affine mapping from n-dimensional space to r-dimensional space. Specifically, the number of hidden units n _H , the parameters w = (w _ij ), (i = 1,..., N + n _H , j = 0, 1, 1, of the interconnected neural network)
, N + n _H ), Affine mapping parameters A = (A _ij ), (i = 1,..., N _H , j = 1,.
n), b = (b ₁ ,..., b _nH ).

First, a parameter w having n visible units and n _H hidden units at time [0, T].
The operation of the mutual connection neural network will be described. The state of such an interconnected neural network at time t is n
+ N _H dimensional vector z (t) = (z ₁ (t),..., Z _{n + nH} (t)), and such an interconnected neural network has an n + n _H dimensional vector z ⁰ = (z ⁰ ₁ ,..., Z ⁰ _{n + nH} ) is input as the initial state,

[0033]

(Equation 4)

The state is updated according to the following equation, and the n-dimensional trajectory z _V (t) = (z ₁ (t),..., Z _n (t), t}
[0, T] is output. Next, the operation of the affine mapping in which the parameters are (A, b) will be described. Such an affine map is n
When the dimension vector z _V = ((z _v ) ₁ ,..., (Z _v ) _n is input, the n _H dimension vector z _H = ((z _H ) ₁ ,..., Z _H = A _zV + b. and outputs a (z _{H) nH).}

Next,

[0036]

(Equation 5)

With respect to w and (A, b) having the following relationship, an affine neurodynamic system μ = (w, A, b) based on an interconnected neural network of parameters w and an affine mapping with parameters (A, b) The operation at time [0, T] in b) will be described. Affine neurodynamic system μ = (w, A,
b), when an n-dimensional vector x = (x ₁ ,..., x _n ) is input as an initial state, an affine mapping with parameters (A, b) becomes an n + n _H- dimensional vector z ⁰ = (z ⁰ ₁₎ , ..., z ⁰ _{n + nH} )

[0038]

(Equation 6)

And this n + n _H- dimensional vector is
The parameters are initially input to the interconnected neural network of w, and the interconnected neural network
-Dimensional trajectory z _V (t) = (z ₁ (t),..., Z _n (t)), t∈
[0, T] is output.

Next, n in the reference system shown in FIG.
The model of the three-dimensional dynamical system Φ is converted into a set of initial state and target trajectory, which is known input / output data of the reference system (x ^k = (x ₁ ^k ,... X _n ^k ); y ^k (t) ² = Y ₁
^{k (t), ..., y} m k (t))), t∈ [0, T],
(K = 1,..., K) and the output mechanism of the dynamic system to be controlled y = h (x) = (h ₁ (x),..., H _m (x)), the affine neurodynamic system μ = A calculation method constructed as (w, A, b) will be described.

First, an allowable error ε and a learning rate η are set.

[0042]

(Equation 7)

Is calculated and stored. In the case of the two-joint robot arm shown in FIG.

[0044]

(Equation 8)

Is as follows. Then, the number of hidden units n _H is determined, and the following operation is performed. n _H is sequentially increased from n _H = 0 for the first time, and the following operation is repeated until the error E becomes equal to or less than ε. Step 101) w _ij , w _i0 , w _{in + c} , A _cj , b _c (i, j = 1,...,
n, c = 1,..., n _H )

[0046]

(Equation 9)

Calculate and save. Step 102) First, data x ^k = (x ₁ ^k ,..., X _n ^k ), (k = 1,..., K) of the designated initial state is converted to a parameter value μ = (w, A, b). Input to the affine neurodynamic system and output x ^k (t) = (x ₁ ^k (t),..., X _n ^k (t)),
Save t∈ [0, T]. Next, the error

[0048]

(Equation 10)

Is calculated. If E ≦ ε, the process ends. If E ≧ ε, the process proceeds to the next step. Step 103) The parameter value μ = (w, A, b) of the affine neurodynamic system is updated as follows, and
Return to 2.

[0050]

[Equation 11]

However,

[0052]

(Equation 12)

And

[0054]

(Equation 13)

And p ^k (t) = (p ₁ ^k (t),..., P _n ^k (t), t}
[0, T], (k = 1, ..., K) is

[0056]

[Equation 14]

Is calculated. However,

[0058]

(Equation 15)

Is as follows. Affiliation obtained by the above operation
The parameter μ = (w, A, b) of the neurodynamic
The input is made to the neural network creating unit 13. Layered Neural Network Creation Unit 13: Layered Neural Network
In the packet creation unit 13, n units and an intermediate layer
To n _pTanh units and r units in the output layer
That is, a layered neural network with weight parameter W = u = g_W(X) is prepared and the number of intermediate units is n_pAnd weight parameter w
Acquired by learning.

Hereinafter, the layered neural network u = g
The learning method of _W (x) will be described. First, to set the allowable error epsilon _W, S number of n-dimensional data ^{_{q s = (q 1 s,}} ..., q n s), (s = 1, ..., S) to generate randomly. Next, for the input affine neurodynamic system parameter μ = (w, A, b), the affine neural vector field, which is the dynamic characteristic of the reference system to be imitated by the dynamic system to be controlled,

[0061]

(Equation 16)

Is calculated. However,

[0063]

[Equation 17]

Is as follows. Then, the error E _W,

[0065]

(Equation 18)

Then, the layered neural network u = g _W (x) is learned so that the error E _W is equal to or smaller than ε _W. This type of learning of a layered neural network is well known, and therefore detailed description is omitted. Then, the layered neural network u = g _W (x) for which learning has been completed is output.

A disk device connected to a computer used as a control device by constructing the above operation as a program, a floppy disk or a CD-ROM
The present invention can be easily realized by storing the program in a portable storage medium such as the above, and installing it when implementing the present invention. It should be noted that the present invention is not limited to the above example,
Various modifications and applications are possible within the scope of the claims.

[0068]

As described above, the present invention provides a non-linear dynamic system having n internal variables, r control input variables, and m output variables, and a desired trajectory output of the motion for the initial internal state. When specified, a model of the reference system that generates the specified control target trajectory can be constructed, and the input of the non-linear dynamic system such that the operation of the non-linear dynamic system can mimic the operation of the reference system. Since the dimension control signal can be generated, there is an effect that control that the nonlinear dynamic system imitates the operation of the reference system can be realized.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining the principle of the present invention.

FIG. 2 is a principle configuration diagram of the present invention.

FIG. 3 is a block diagram of a dynamic system to be controlled in the present invention.

FIG. 4 is a block diagram of a reference system to be imitated by the dynamic system of the present invention.

FIG. 5 is a block diagram of control of a dynamic system according to the present invention.

FIG. 6 is an example of a dynamic system to be controlled by the present invention.

FIG. 7 is a block diagram of a model of a reference system according to the present invention.

FIG. 8 is a detailed diagram of a neural network learning unit in the control of the dynamic system according to the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Input means 2 Parameter creation means of affine neurodynamic system 3 Layered neural network creation means 4 Control signal creation means 10 Neural network learning unit 11 Input unit 12 Parameter creation unit of affine neurodynamic system 13 Layered neural network creation unit 20 Control signal creation Part 30 Dynamic system

Claims (3)

[Claims] 1. A method for controlling a dynamic system using a neural network for controlling motion of a dynamic system including a robot, comprising: n internal state variables, r control input variables, and m output variables. For the dynamic system, the dynamic characteristics and output mechanism of the dynamic system are given, and as a control target of the dynamic system, the n-dimensional vector of the initial internal state and the time [0, T When K data of a set of m-dimensional output trajectories, which are the outputs of the motions of the dynamic system, are designated, the data of the K control target trajectories is converted into the time of the internal state based on the n-dimensional dynamic system. Under the evolution and output mechanism of the dynamic system, create an interconnected neural network and affine mapping to realize the dynamic characteristics of the reference system that can be generated, A layered neural of the transformation from an n-dimensional state vector to an r-dimensional state vector that changes properties to mimic the affine neural vector field of the dynamics properties of the engine system composed of an interconnected neural network and the affine mapping Creating a layered neural network for generating an r-dimensional signal to be input to the dynamic system from an internal state of the dynamic system; and using the layered neural network, A method for controlling a dynamic system by a neural network, wherein an r-dimensional control signal to be input to the dynamic system at each time for control is created from the internal state at each time. 2. A control system for a dynamic system using a neural network for performing motion control of a dynamic system including a robot, wherein n internal state variables, r control input variables, and m output variables. , The dynamic characteristics and output mechanism of the dynamic system are input, and as a control target of the dynamic system, an n-dimensional vector of the initial internal state and a time [0 , T], input means for designating K data of a set of m-dimensional output trajectories, which are outputs of the motion of the dynamic system in K, and K data of the control target trajectories are converted into an internal state based on an n-dimensional dynamical system. A paraffin of an affine neurodynamic system that creates an interconnected neural network and an affine map, realizing the dynamics of the reference system that can be generated under the time evolution of the dynamic system and the output mechanism of the dynamic system Data creation means, the dynamic characteristic of the dynamic system to be controlled is changed to imitate the affine neural vector field of the dynamic characteristic of the reference system constituted by the interconnected neural network and the affine mapping, A layered neural network for creating a layered neural network for conversion from an n-dimensional state vector to an r-dimensional state vector and for generating an r-dimensional signal to be input to the dynamic system from the internal state of the dynamic system A network creation unit, and using the layered neural network created by the layered neural network creation unit, from the internal state of the dynamic system to be controlled at each time, to control the dynamic system at each time for control. Control signal generating means for generating an r-dimensional control signal to be input to the Control system of dynamic system by net. 3. A storage medium storing a control program of a dynamic system using a neural network for performing motion control of a dynamic system including a robot, wherein n internal state variables, r control input variables, For a dynamic system having m output variables, a dynamic characteristic and an output mechanism of the dynamic system are given, and as a control target of the dynamic system, an n-dimensional vector of an initial internal state, the n-dimensional vector, When K data of a set of m-dimensional output trajectories, which are outputs of the motion of the dynamic system at time [0, T] with respect to the vector, are specified, the data of the K control target trajectories is converted to an n-dimensional dynamic system. Af that creates an interconnected neural network and an affine mapping that realizes the dynamics of the reference system that can be generated under the time evolution of the internal state based on the dynamics and the output mechanism of the dynamic system The parameter creation process of the neurodynamic system and the dynamic characteristics of the dynamic system to be controlled are imitated by imitating the affine neural vector field of the dynamic characteristics of the reference system composed of the interconnected neural network and the affine mapping. , A layered neural network for converting an n-dimensional state vector to an r-dimensional state vector is created, and an r-dimensional signal to be input to the dynamic system is generated by a layered neural network that generates from an internal state of the dynamic system. Using the layered neural network creation process to be created, and using the layered neural network created in the layered neural network creation process, from the internal state at each time of the dynamic system to be controlled, at each time for control, Control signal generation process for generating an r-dimensional control signal to be input to the dynamic system Storage medium storing a control program of a dynamic system by neural network and having a.