JP7227940B2 - MODEL LEARNING DEVICE, MODEL LEARNING METHOD, CONTROL DEVICE, CONTROL METHOD, AND COMPUTER PROGRAM - Google Patents

Description

The present invention relates to techniques for learning and using models of nonlinear systems.

It is known to perform model learning (system identification) of a system using a priori knowledge of the system. For example, in Patent Document 1, in a system identification method, after determining a set of constraints based on a priori knowledge, constrained parametric optimization of the system based on an initial parametric model and the determined set of constraints to generate an improved parametric model of the system.

JP 2004-272916 A

Here, the technique described in Patent Document 1 is based on the fact that a linear system can express a model with a small number of parameters (matrix) and that the stability of the model can be determined only by the eigenvalues of the matrix. established. That is, the technique described in Patent Document 1 assumes that a system to be modeled (identified) can be represented as a linear system, and has a problem that it cannot be applied to a nonlinear system.

As a method of determining the stability of a nonlinear system, it is generally known to confirm the existence of a Lyapunov function. That is, if there exists a function called a "Lyapunov function" that satisfies a certain condition, it can be determined that the system is stable. However, the Lyapunov function cannot always be discovered by a fixed procedure, and in order to discover the Lyapunov function, it is necessary to deal with it individually while considering the physical structure and mathematical formula structure of the object. Therefore, there is a problem that it is not easy to guarantee stability in model learning (system identification) of a nonlinear system.

Also, in a nonlinear system, there is not always only one point (equilibrium point) where dynamic changes converge, but there may be multiple equilibrium points. Even if it is known that the nonlinear system to be learned does not have multiple equilibrium points and has only one equilibrium point, there is no known technique for learning a model that guarantees this. Therefore, in model learning (system identification) of a nonlinear system, there is a problem that it is not easy to guarantee convergence (in other words, guarantee uniqueness of equilibrium points).

SUMMARY OF THE INVENTION The present invention has been made to solve at least a part of the above-mentioned problems, and an object thereof is to provide a technique capable of guaranteeing stability and convergence in model learning of a nonlinear system.

上記式において、等号の左辺は、前記状態方程式によって予測しようとする状態変数ｘを表すｎ（ｎは整数）次元ベクトルの時間微分であり、等号の右辺のうち、ｕは状態変数ｘの変化に影響する入力変数を表すｍ（ｍは整数）次元のベクトルであり、ｆ（ｘ）は状態変数ｘを入力としてｎ次元のベクトルを出力する全単射な写像であり、関数ψはｎ次元のベクトルを出力する任意の非線形関数であり、前記学習部は、前記モデル構造における前記関数ψを、次式により表される構造とし、

上記式において、等号の左辺は、前記関数ψであり、等号の右辺のうち、Ａはｎ行ｎ列の正方行列であり、ｇはｎ次元のベクトルを出力する任意の非線形関数であり、ｃは正の値をとる任意のスカラー関数である、モデル学習装置。そのほか、本発明は、以下の形態としても実現可能である。 The present invention has been made to solve at least part of the above problems, and can be implemented as the following modes. A model learning device comprising: a model storage unit for storing a model structure used for learning a nonlinear state equation for predicting a state variable x; said model structure; and a set of input data and output data for said model structure. and a learning unit that learns the state equation using the input/output data set including a plurality of the state variable x. is an equation, and the model structure is defined by

In the above equation, the left side of the equal sign is the time differentiation of the n (n is an integer) dimensional vector representing the state variable x to be predicted by the state equation, and u is the state variable x of the right side of the equal sign. is an m (m is an integer) dimensional vector representing an input variable that affects change, f(x) is a bijective mapping that takes the state variable x as an input and outputs an n-dimensional vector, and the function ψ is n is an arbitrary nonlinear function that outputs a vector of dimensions, and the learning unit makes the function ψ in the model structure a structure represented by the following equation,

In the above equation, the left side of the equal sign is the function ψ, and in the right side of the equal sign, A is a square matrix with n rows and n columns, and g is an arbitrary nonlinear function that outputs an n-dimensional vector. , c is any positive scalar function. In addition, the present invention can also be implemented as the following modes.

(1) According to one aspect of the present invention, a model learning device is provided. This model learning device stores a model storage unit that stores a model structure used for learning a nonlinear state equation for predicting a state variable x, the model structure, and a set of input data and output data for the model structure. and a learning unit for learning the equation of state using a plurality of input/output data sets, wherein the model structure includes the equation of state including a bijective mapping f(x) with a state variable x as an input. is.

According to this configuration, the model structure used in the learning section is a state equation including a bijective map f(x) with state variable x as an input. Such a state equation can be transformed into a simple state equation expressing the time change of the internal variable ξ obtained by transforming the state variable x. By analyzing the characteristics such as stability and convergence of the state equation related to the internal variable ξ, it is possible to know the characteristics such as the stability and convergence of the state variable x, which were difficult to analyze in the past. can. As a result, according to the model learning device of this configuration, it is possible to guarantee stability and convergence in model learning of a nonlinear system.

上記式において、等号の左辺は、前記状態方程式によって予測しようとする状態変数ｘを表すｎ（ｎは整数）次元ベクトルの時間微分であり、等号の右辺のうち、ｕは状態変数ｘの変化に影響する入力変数を表すｍ（ｍは整数）次元のベクトルであり、ｆ（ｘ）は状態変数ｘを入力としてｎ次元のベクトルを出力する全単射な写像であり、関数ψはｎ次元のベクトルを出力する任意の非線形関数であってもよい。
この構成によれば、学習部において用いられるモデル構造は、上記式により定義される。このとき、関数ξ＝ｆ（ｘ）を定義し、関数ξ＝ｆ（ｘ）の時間微分を取ることにより、学習部において用いられるモデル構造を、状態変数ｘを変換した内部変数ξの時間変化を表す平易な形式の状態方程式に式変形できる。ここで、関数ｆ（ｘ）は全単射であるため一意の逆関数が存在し、ｘ＝ｆ^-1（ξ）として、ｘはξを静的な関数で変換した形で表される。したがって、内部変数ξに関する状態方程式について、安定性や収束性などの特性を解析することで、従来であれば解析困難であった、状態変数ｘの安定性や収束性などの特性を知ることができる。この結果、本構成のモデル学習装置によれば、非線形システムのモデル学習において、安定性及び収束性の保証を可能とできる。 (2) In the model learning device of the above aspect, the model structure may be defined by the following equation.

In the above equation, the left side of the equal sign is the time differentiation of the n (n is an integer) dimensional vector representing the state variable x to be predicted by the state equation, and u is the state variable x of the right side of the equal sign. is an m (m is an integer) dimensional vector representing an input variable that affects change, f(x) is a bijective mapping that takes the state variable x as an input and outputs an n-dimensional vector, and the function ψ is n It can be any non-linear function that outputs a vector of dimensions.
According to this configuration, the model structure used in the learning section is defined by the above formula. At this time, by defining a function ξ=f(x) and taking the time derivative of the function ξ=f(x), the model structure used in the learning section can be expressed as the time change of the internal variable ξ obtained by transforming the state variable x can be transformed into a simple form of the state equation representing Here, since the function f(x) is bijective, it has a unique inverse function, and x=f ⁻¹ (ξ), where x is represented by transforming ξ with a static function. Therefore, by analyzing the characteristics such as stability and convergence of the state equation related to the internal variable ξ, it is possible to know the characteristics such as the stability and convergence of the state variable x, which were difficult to analyze in the past. can. As a result, according to the model learning device of this configuration, it is possible to guarantee stability and convergence in model learning of a nonlinear system.

上記式において、等号の左辺は、前記関数ψであり、等号の右辺のうち、Ａはｎ行ｎ列の正方行列であり、ｇはｎ次元のベクトルを出力する任意の非線形関数であり、ｃは正の値をとる任意のスカラー関数であってもよい。
この構成によれば、モデル構造における関数ψは、上記式により定義される。ここで、ｃは正の値をとるスカラー関数であるため、上記の通りｘ＝ｆ^-1（ξ）とし、一旦関数ｃを無視して考えると、ξに関する線形状態方程式を得ることができる。この線形状態方程式においては、行列Ａの固有値の実部が全て負であれば、ξは安定であり、かつ、唯一の平衡点を持つことが一般的に知られている。このため、ξに関する線形状態方程式を解析することによって、状態変数ｘの安定性や収束性などの特性をより容易に判定できる。また、関数ｃを考慮したとき、ｃは正の値をとるスカラー関数であるため、関数ψの出力であるベクトルの向きは変化しない。すなわち、関数ｃの存在は、上記式の安定性に影響を与えない。 (3) In the model learning device of the above aspect, the learning unit may have the function ψ in the model structure represented by the following equation.

In the above equation, the left side of the equal sign is the function ψ, and in the right side of the equal sign, A is a square matrix with n rows and n columns, and g is an arbitrary nonlinear function that outputs an n-dimensional vector. , c may be any positive scalar function.
According to this configuration, the function ψ in the model structure is defined by the above formula. Here, c is a scalar function that takes a positive value, so if x=f ^-1 (ξ) as described above and the function c is ignored, a linear state equation regarding ξ can be obtained. In this linear state equation, it is generally known that ξ is stable and has only one equilibrium point if all the real parts of the eigenvalues of matrix A are negative. Therefore, by analyzing the linear state equation for ξ, the characteristics of the state variable x, such as stability and convergence, can be determined more easily. Also, when considering the function c, c is a scalar function that takes a positive value, so the direction of the vector that is the output of the function ψ does not change. That is, the presence of function c does not affect the stability of the above equation.

(4) In the model learning device of the above aspect, the learning unit provides the input data set of the input/output data set to the model structure to estimate an output, and estimates the output; The equation of state may be learned by evaluating the degree of matching between the output data set and the input data set, and updating learning parameters for the model structure according to the evaluation result. .
According to this configuration, the learning unit estimates the output using the input data set of the input/output data sets, evaluates the degree of matching using the output data set, updates the learning parameters for the model structure, Learn the equation of state by Therefore, the learning unit can learn the nonlinear equation of state in accordance with a learning method using an input/output data set prepared in advance as teacher data.

(5) According to one aspect of the invention, a control device is provided. This control device includes a state equation storage unit that stores a nonlinear state equation for predicting a state variable x for an arbitrary controlled object, an acquisition unit that acquires various parameters related to the state equation, and the acquired a prediction unit that predicts a future state variable x from the state equation using parameters.
According to this configuration, the prediction unit predicts the future state variable x using various parameters related to the state equation and the state equation. As such, the predicted state variable x can be used for analysis and control of any controlled object (eg, internal combustion engine, hybrid engine, powertrain, etc.).

(6) The control device of the above aspect may further include a determination unit that determines an operation amount for controlling the controlled object using the state variable x predicted by the prediction unit.
According to this configuration, the predictive state variable x is used to determine the manipulated variable for controlling the controlled object. can be used.

It should be noted that the present invention can be implemented in various aspects, for example, an apparatus and method for learning a model of a nonlinear system, an apparatus and method for estimating a state using a model obtained by learning, and the like. It can be realized in the form of a system including devices, a computer program executed in these devices and systems, a server device for distributing the computer program, a non-temporary storage medium storing the computer program, etc.

1 is an explanatory diagram illustrating the configuration of a model learning device; FIG. 4 is a flowchart illustrating a procedure of learning processing; It is a figure explaining an example of an effect of learning processing. It is an explanatory view showing an example of composition of a control device. 6 is a flowchart illustrating a procedure of prediction processing; It is an explanatory view which illustrated the composition of the model learning device of a 2nd embodiment. FIG. 11 is an explanatory diagram illustrating the configuration of a control device according to a third embodiment;

<First Embodiment>
FIG. 1 is an explanatory diagram illustrating the configuration of a model learning device 100 as one embodiment of the present invention. A model learning device 100 is a device for learning a model of a nonlinear system. Here, the "nonlinear system" means a controlled object (system) having a property that the relationship between input and output parameters for any controlled object (system) cannot be represented by a linear expression or cannot be approximated. Moreover, in this embodiment, a nonlinear equation of state is exemplified as a "model". That is, in the present embodiment, the "nonlinear system model" is a nonlinear state equation for predicting the state variable x for any nonlinear controlled object. It should be noted that the "state equation" means that the state x(t) of itself at the current time, such as "x(t)=f(x(t),...)" ) means the equation that determines Hereinafter, the time differential of x represented by symbol 1 below will be described as "x.", and the time differential of .xi. represented by symbol 2 below will be described as ".xi..".

An object to be controlled can be arbitrarily determined, and examples thereof include an internal combustion engine, a hybrid engine, and a power train. When a driving engine such as an internal combustion engine, a hybrid engine, or a power train is the object to be controlled, the model learned by the model learning device 100 includes various parameters related to the driving of the object to be controlled (for example, the operation of the actuator of the part to be controlled). quantity, disturbance to the controlled object, state of the controlled object, output of the controlled object, output target value of the controlled object, etc.).

The model learning device 100 is, for example, a personal computer (PC), and includes a CPU 110 , a storage section 120 , a ROM/RAM 130 , a communication section 140 and an input/output section 150 . Each part of the model learning device 100 is interconnected by a bus.

The CPU 110 includes a control section 111 and a learning section 112 . The control unit 111 controls each unit of the model learning apparatus 100 by expanding the computer program stored in the ROM 130 into the RAM 130 and executing it. The learning unit 112 executes learning processing, which will be described later. The learning process is a process of learning a nonlinear state equation for predicting the state variable x regarding an arbitrary controlled object (nonlinear system).

The storage unit 120 is a storage medium such as a hard disk, flash memory, or memory card. A model storage unit 121 and an input/output data set 122 are stored in advance in the storage unit 120 . The model storage unit 121 is a model structure used for learning the equation of state by the learning unit 112 . In this embodiment, the model structure stored in the model storage unit 121 is defined by Equation 3 below.

式３において、等号の左辺は、状態方程式によって予測しようとする状態変数ｘを表すｎ（ｎは整数）次元ベクトルの時間微分である。また、等号の右辺のうち、ｕは状態変数ｘの変化に影響する入力変数を表すｍ（ｍは整数）次元のベクトルであり、ｆ（ｘ）は状態変数ｘを入力としてｎ次元のベクトルを出力する全単射な写像であり、関数ψはｎ次元のベクトルを出力する任意の非線形関数である。ここで、「全単射」とは、集合Ａの写像の結果が集合Ｂであるとした場合に、ＡとＢの各要素が必ず一対一の対応関係を持つことを意味する。関数ｆが全単射である場合、一意の逆関数ｆ^-1が存在する。

In Equation 3, the left side of the equal sign is the time derivative of the n (n is an integer) dimensional vector representing the state variable x to be predicted by the state equation. Also, of the right side of the equal sign, u is an m-dimensional vector (m is an integer) representing an input variable that affects the change of the state variable x, and f(x) is an n-dimensional vector with the state variable x as an input. is a bijective mapping that outputs , and the function ψ is any nonlinear function that outputs an n-dimensional vector. Here, "bijection" means that, when the result of mapping of set A is set B, each element of A and B always has a one-to-one correspondence. If a function f is bijective, there exists a unique inverse f ⁻¹ .

The input/output data set 122 contains multiple sets of input data and output data for the model structure represented by Equation 3. This set of input data and output data is obtained in advance through experiments and calculations on the object to be controlled. The input/output data set 122 is used as teacher data for learning the equation of state by the learning unit 112 . Hereinafter, among the input/output data sets 122, a plurality of input data will also be collectively referred to as an "input data set", and a plurality of output data will also be collectively referred to as an "output data set".

Communication unit 140 controls communication via a communication interface between model learning device 100 and another device. Other devices include, for example, a control device 200 to be described later, other information processing devices, and measuring instruments for acquiring the input/output data set 122 . The input/output unit 150 is various interfaces used for inputting/outputting information between the model learning device 100 and the user. As the input/output unit 150, for example, a touch panel, keyboard, mouse, operation button, and microphone as an input unit, and a touch panel, monitor, speaker, LED (Light Emitting Diode) indicator, etc. as an output unit can be adopted.

FIG. 2 is a flowchart illustrating a procedure of learning processing. The learning process can be executed, for example, triggered by a request from the user (startup of a predetermined application, etc.). In the following examples, in the state equation shown in the following equation 4, each data of x, u, x · is prepared in advance as a known input/output data set 122, and using this input/output data set 122, the functional form of the function F A case of learning (estimating) will be described. As mentioned above, x is an n-dimensional vector and u is an m-dimensional vector.

First, in step S<b>10 , the learning unit 112 acquires the model structure (Equation 3) stored in the model storage unit 121 . The learning unit 112 assumes that the model structure for learning the function F is the structure shown in Equation 5 below. Equation 5 expresses the state equation to be learned in the learning process with the model structure stored in the model storage unit 121 (equations 3 and 4). The learning unit 112 initializes each variable in the structure of Equation 5 by setting the value of each variable to zero or a random value.

Here, in the structure of Equation 5, it is necessary to assume some structure also for the functions f and ψ. In this embodiment, for the function f, for example, a neural network is used to define the structure of Equation 6 below. In Equation 6, W _f is the weight, b _f is the bias, and φ _f is the activation function. W _f is an n×n square matrix and b _f is an n-dimensional vector in order to satisfy the condition of “being a bijection” explained in Equation 3 for the function f. φ _f is set as some bijective mapping (eg, hyperbolic sine function, etc.). Once the form of the function f is determined, (∂f/∂x) ⁻¹ is determined by the partial differential operation and the inverse matrix operation.

Further, regarding the function ψ, for example, by defining the structure of the following formula 7, the stability and convergence can be evaluated more easily (details will be described later). In Equation 7, A is an n×n square matrix, c is any positive scalar function, and g is any nonlinear function that outputs an n-dimensional vector. It should be noted that functions c and g in Equation 7 also need to assume some structure, but these structures can also be defined using a neural network.

In step S<b>12 , the learning unit 112 acquires input/output data sets for x, u, x· from the input/output data sets 122 . In the example of this embodiment, the input/output data set 122 includes j sets (j is a natural number, j=1 to N) of data x, u, and x. Of the input/output data sets 122, x _j and u _j correspond to input data sets, and x· _j corresponds to output data sets.

In step S14, the learning unit 112 gives the input data set to the model structure and estimates the output. Specifically, the learning unit 112 converts the input data set (x _j , u _j ) acquired in step S12 to the structure of formula 5 (and formulas 6 and 7) defined and initialized in step S10. give. Then, an estimated value of the output x· _j can be obtained as shown in Equation 8 below. Since (∂f/∂x) ⁻¹ is also a function of x, it can be evaluated by substituting x _j .

In step S16, the learning unit 112 evaluates the degree of matching between the estimated output and the output data set. Specifically, the learning unit 112 evaluates the degree of matching between the estimated value of the output x· _j obtained in step S14 and the output data set (x· _j ) obtained in step S12. The learning unit 112 can use, for example, the mean square error (MSE) shown in Equation 9 below as an indicator of the degree of matching. In the case of MSE, the smaller the value of the left side J of the equal sign, the higher the degree of matching. Note that the learning unit 112 may evaluate the degree of matching using an index other than the MSE, such as the absolute average error rate or the cross entropy.

In step S18, the learning unit 112 determines whether or not the degree of matching is sufficient. For example, when using MSE (Formula 9), the learning unit 112 can determine that the degree of matching is sufficient when the value of J is equal to or less than a predetermined value. Note that the learning unit 112 may determine that the degree of matching is sufficient when the change rate of the value of J is equal to or less than a predetermined value. The predetermined value can be arbitrarily determined.

If the degree of matching is not sufficient (step S18: NO), the learning unit 112 shifts the process to step S20. In step S20, the learning unit 112 updates the learning parameters (eg, W _f , b _f , A, etc.) in the structure of formula 5 (and formulas 6 and 7) defined in step S10. The learner 112 can, for example, evaluate the gradient of J for each learning parameter by backpropagation and update each learning parameter based on various gradient methods. After that, the learning unit 112 shifts the process to step S14, and repeats output estimation and evaluation.

If the degree of matching is sufficient (step S18: YES), the learning unit 112 terminates the process. At this time, the learning unit 112 may output the learned function F to the input/output unit 150, store it in the storage unit 120, or transmit it to another device via the communication unit 140. .

Next, the reason why the stability and convergence can be guaranteed in the model (state equation) learned by the learning process described with reference to FIG. 2 will be described. In general, when constructing a dynamic model that can reproduce transient phenomena using a neural network (machine learning), there is no guarantee that the model is stable (in other words, does not diverge). However, the model structure shown in Equation 3 (Equation 5) described above is a simpler model that expresses the time change of an internal variable (hereinafter also referred to as "internal variable ξ") obtained by transforming the state variable x by transformation of the equation. can be transformed into a state equation of the form If characteristics such as stability and convergence are known for the state equation regarding this internal variable ξ, the characteristics such as stability and convergence can be known because the state variable x also preserves the characteristics. That is, the properties of the state variable x can be determined by analysis on the simple form of the state equation.

It is difficult to analyze the model structure shown in Formula 3 (Formula 5) of the learning process as it is. At this time, define a function ξ=f(x) and take a time derivative of the function ξ=f(x). Then, a state equation regarding the function ξ is obtained as shown in Equation 10 below.

Here, since the function f(x) is bijective, it has a unique inverse function, and x=f ⁻¹ (ξ), where x is represented by transforming ξ with a static function. Therefore, if the stability and convergence of the function ξ can be determined by analyzing Equation 10, the stability and convergence of the state variable x can be determined because the state variable x also preserves the properties. Specifically, if the function ξ does not diverge, the state variable x does not diverge, and if the function ξ always converges to one equilibrium point, the state variable x also always converges to one equilibrium point. I can say.

As described above, according to the model learning device 100 of the first embodiment, the model structure (equations 3 and 5) used in the learning unit 112 is a bijective mapping f(x) with the state variable x as an input is a state equation containing Such state equations (equations 3 and 5) can be transformed into simple state equations representing the time change of the internal variable ξ (equation 10). Then, by analyzing the characteristics such as stability and convergence of the state equation (Equation 10) related to the internal variable ξ, the characteristics such as stability and convergence of the state variable x, which were difficult to analyze in the past can know As a result, according to the model learning device 100 of this embodiment, it is possible to guarantee stability and convergence in model learning of a nonlinear system.

Further, according to the model learning device 100 of the first embodiment, the analysis can be made easier by changing the structure of the function ψ in the model structure (Formula 3, Formula 5) to the structure represented by Formula 7. Specifically, since c is a scalar function that takes a positive value, when x=f ⁻¹ (ξ) as described above, Equation 7 is expressed as Equation 11 below. Once neglecting the function c in Equation 11, the following Equation 12 is obtained.

Here, Equation 12 is a linear state equation for ξ, and it is generally known that ξ is stable and has only one equilibrium point if the real parts of the eigenvalues of matrix A are all negative. there is The function c ignored in Equation 12 is multiplied by the right side in Equation 11. Since the function c is a positive scalar function, the vectors ξ· determined by Equations 11 and 12 have different lengths but always have the same direction. The time change of ξ can be obtained by time-integrating ξ·, but if the direction of the vector is always the same, the trajectories passing through are the same even if the speed of convergence is different. Thus, the stability and the number of equilibrium points (convergence) that can be determined by the analysis for Equation 12 are preserved in Equation 11 as well. Therefore, by analyzing Equation 12, the properties of Equation 10 (characteristics such as stability and convergence of state variable x) can be determined more easily. Note that when the function c is considered, c is a scalar function that takes a positive value, so the direction of the vector that is the output of the function ψ does not change. That is, the presence of function c does not affect the stability of Eq.

In equations 11 and 12, the function ψ is converted into a linear expression with respect to ξ. form can be used. For example, for a nonlinear model, stability is guaranteed if a function called the Lyapunov function can be found. For this reason, a form capable of discovering the Lyapunov function may be adopted.

Furthermore, according to the model learning device 100 of the first embodiment, the learning unit 112 estimates the output using the input data set of the input/output data set 122 ( FIG. 2 : step S14), The equation of state is learned by evaluating the degree of matching used (step S16) and updating the learning parameters for the model structures (equations 3 and 5) (step S20). Therefore, the learning unit 112 can learn the nonlinear equation of state according to a learning method using the prepared input/output data set 122 as teacher data.

FIG. 3 is a diagram explaining an example of the effect of the learning process. In FIG. 3, the model M0 obtained by the conventional method and the model M1 obtained by the learning process of this embodiment are compared for the simple model MS prepared for confirmation of the effect. Each of the diagrams simulatively illustrating the models MS, M0, and M1 shows an arrow representing the direction of the x vector on the plane of x1 and x2, and a curve obtained by integrating the x vector. In other words, if one point on a certain curve is taken as the initial state, the state x changes over time according to the curved arrow (x and direction of the vector).

The left side of FIG. 3 represents a simple model MS (that is, a model MS to be learned) prepared for confirmation of effects. The simplified model MS was set to n=2 dimensions and no input g(u)=0. The simple model MS is logically guaranteed to be stable and always converges to the origin CP, but it is a model that easily diverges depending on the learning error. Note that the learning range RA is indicated by a dashed line in the figure.

The upper right part of FIG. 3 represents the model M0 obtained by learning the simple model MS by the conventional method. Specifically, a standard neural network was used to learn the functional form of the function F for the nonlinear state equation (equation 4) described above. As shown in the figure, in the model M0 obtained by the conventional method, there are regions RE (one-dot chain lines) where the state variable x diverges at the ends of the learning range RA and outside the learning range RA. Therefore, it can be seen that the model M0 obtained by the conventional method cannot guarantee stability and convergence.

The lower right part of FIG. 3 shows a model M1 obtained by learning the simple model MS through the learning process of this embodiment. As shown, in the model M1 obtained by the learning process of the present embodiment, the state variable x always converges to the origin CP not only from the end of the learning range RA but also from outside the learning range RA. Therefore, it can be seen that the model M1 obtained by the learning process of this embodiment can guarantee stability and convergence.

FIG. 4 is an explanatory diagram illustrating the configuration of the control device 200. As shown in FIG. The control device 200 is a device that uses the nonlinear state equation learned by the model learning device 100 to predict the future state variable x.

The control device 200 can be realized, for example, as a personal computer or an in-vehicle ECU (Electronic Control Unit). For example, in the former case, the control device 200 can be used for analysis of the control object, and in the latter case, the control device 200 can be used for control of the control object. The object to be controlled can be arbitrarily determined as described above, and examples thereof include an internal combustion engine, a hybrid engine, and a power train.

The control device 200 includes a CPU 210 , a storage section 220 , a ROM/RAM 230 , a communication section 240 and an input/output section 250 . Each part of the control device 200 is interconnected by a bus. At least part of the functional units of the control device 200 may be realized by an ASIC (Application Specific Integrated Circuit).

The CPU 210 includes a control section 211 , an acquisition section 212 and a prediction section 213 . The control unit 211 controls each unit of the control device 200 by developing a computer program stored in the ROM 230 into the RAM 230 and executing the program. Acquisition unit 212 and prediction unit 213 cooperate to execute prediction processing, which will be described later. The prediction process is a process of predicting the future state variable x using a nonlinear state equation.

The storage unit 220 is a storage medium such as a hard disk, flash memory, or memory card. A state equation storage unit 221 is stored in advance in the storage unit 220 . The state equation storage unit 221 stores a nonlinear state equation learned by the model learning device 100 ( FIG. 2 : learning process).

The communication unit 240 controls communication via the communication interface between the control device 200 and other devices. Other devices include, for example, the model learning device 100, other ECUs, other information processing devices, and measuring instruments for acquiring various parameters used in the estimation process. The input/output unit 250 is various interfaces used for inputting/outputting information between the control device 200 and the user. As the input/output unit 250, for example, a configuration similar to that of the input/output unit 150 of the model learning device 100 can be exemplified.

FIG. 5 is a flowchart illustrating a procedure of prediction processing. The prediction process can be triggered by, for example, a request from a user (startup of a predetermined application), a request from another ECU, or the like.

First, in step S<b>50 , the prediction unit 213 acquires the state equation stored in the state equation storage unit 221 . In step S52, the acquisition unit 212 acquires various parameters related to the state equation. Here, the various parameters include the input u to the state equation, the current time t, the current state x, the calculation cycle Δt, and the predicted end time T. The prediction end time T is a time indicating how far ahead the state variable x is to be predicted. The acquisition unit 212 can acquire the input u and the current state x from other ECUs, measuring instruments, and the like. Further, for other parameters, an instruction value from another ECU may be obtained, or a setting value stored in advance in the storage unit 220 may be obtained.

In step S54, the prediction unit 213 calculates the state change rate x·(t). Specifically, the prediction unit 213 can calculate the state change rate x·(t) by inputting the input u obtained in step S52 and the current state x into the state equation obtained in step S50. . In step S56, the prediction unit 213 predicts the estimated value x(t+Δt) of the state at the next time using Equation 13 below.

In step S58, the prediction unit 213 updates the time (t←t+Δt). In step S<b>60 , the prediction unit 213 determines whether or not the updated time t has reached the prediction end time T. If the predicted end time T has not been reached (step S60: NO), the prediction unit 213 shifts the process to step S54, and repeats the calculation of the state change rate and the update of the time.

When the predicted time T has been reached (step S60: YES), the prediction unit 213 shifts the process to step S62. In step S62, the prediction unit 213 outputs the predicted state variable x, and terminates the process. The output may be made to the input/output unit 250 , stored in the storage unit 220 , or transmitted to another device (caller ECU, etc.) via the communication unit 240 .

Thus, according to the control device 200 of the first embodiment, the prediction unit 213 includes various parameters u, t, x, Δt, and T related to the state equation, the state equation learned by the model learning device 100, is used to predict the future state variable x. As such, the predicted state variable x can be used for analysis and control of any controlled object (eg, internal combustion engine, hybrid engine, powertrain, etc.).

<Second embodiment>
FIG. 6 is an explanatory diagram illustrating the configuration of the model learning device 100a of the second embodiment. The model learning device 100a is a device that has both the function of the model learning device 100 described in the first embodiment and the function of the control device 200 . The CPU 110a of the model learning device 100a includes the control unit 111 and the learning unit 112 described with reference to FIG. 1, and the acquisition unit 212 and the prediction unit 213 described with reference to FIG. The storage unit 120a of the model learning device 100a includes the model storage unit 121 and the input/output data set 122 described with reference to FIG. 1, and the state equation storage unit 221 described with reference to FIG. According to the model learning device 100a, it is possible to predict the future state variable x using the learned state equation while learning the nonlinear state equation (model) for predicting the state variable x. Note that the model learning device 100 a may feed back the prediction result of the future state variable x to the model in the state equation storage unit 221 . With such a configuration of the second embodiment, the same effects as those of the first embodiment can be obtained.

<Third Embodiment>
FIG. 7 is an explanatory diagram illustrating the configuration of the control device 200b of the third embodiment. The control device 200b uses the nonlinear state equation learned by the model learning device 100 to predict the future state variable x, and uses the predicted state variable x to calculate the manipulated variable of an arbitrary controlled object. to decide. The control device 200b is realized, for example, as an in-vehicle ECU.

The control device 200b includes a CPU 210b instead of the CPU 210 in the configuration of the first embodiment. The CPU 210 b further includes a determination unit 214 and is connected to the controlled object 300 . The connection means may be wired connection or wireless connection. A controlled object 300 is, for example, a driving engine such as an internal combustion engine, a hybrid engine, or a power train, as in the first embodiment. After executing the prediction process (FIG. 5), the determination unit 214 uses the future state variable x obtained in the prediction process (FIG. 5) to determine the manipulated variable of the actuator for controlling the controlled object 300. FIG. The determination of the manipulated variable can be realized by using, for example, a relational expression, a map, a neural network, or the like, in which the future state variable x is input and the manipulated variable is output.

Thus, in addition to predicting the future state variable x, the control device 200b may determine the manipulated variable of the controlled object using the predicted state variable x. The same effects as those of the first embodiment can be obtained with such a configuration of the third embodiment. Further, according to the control device 200b of the third embodiment, since the determination unit 214 is provided for determining the operation amount for controlling the controlled object 300 using the predicted state variable x, the predicted state variable x x can be used to control any controlled object 300 .

<Modification of this embodiment>
The present invention is not limited to the above-described embodiments, and can be implemented in various aspects without departing from the scope of the invention. For example, the following modifications are possible. Further, in the above embodiments, part of the configuration realized by hardware may be replaced with software, and conversely, part of the configuration realized by software may be replaced with hardware. may

[Modification 1]
In the above embodiment, an example of the configuration of the model learning device and the control device has been shown. However, the configurations of the model learning device and the control device can be modified in various ways. For example, at least one of the model learning device and the control device may be configured by cooperation of a plurality of information processing devices (including a server device, an in-vehicle ECU, etc.) arranged on a network.

[Modification 2]
In the above embodiment, an example of the procedures of the learning process (FIG. 2) and the prediction process (FIG. 5) has been shown. However, these processes can be modified in various ways, some steps may be omitted, other steps not described may be added, and the execution order of some steps may be changed. .

For example, in the learning process (FIG. 2), the definition of the function f shown in Equation 6 and the definition of the function ψ shown in Equation 7 are merely examples, and the functions f and ψ can be defined in any form. good.

For example, in step S18 of the learning process (FIG. 2), the learning unit 112 may determine whether or not the constraint conditions are satisfied in addition to the degree of matching. The constraint can be arbitrarily defined, and may be, for example, a range to be satisfied by the learning parameters W _f , b _f , and A, or a range to be satisfied by the output x·.

The present aspect has been described above based on the embodiments and modifications, but the above-described embodiments are intended to facilitate understanding of the present aspect, and do not limit the present aspect. This aspect may be modified and modified without departing from the spirit and scope of the claims, and this aspect includes equivalents thereof. Also, if the technical features are not described as essential in this specification, they can be deleted as appropriate.

100, 100a... Model learning device 110, 110a... CPU
DESCRIPTION OF SYMBOLS 111... Control part 112... Learning part 120... Storage part 121... Model storage part 122... Input/output data set 130... ROM/RAM
DESCRIPTION OF SYMBOLS 140... Communication part 150... Input-output part 200,200b... Control apparatus 210... CPU
211... Control unit 212... Acquisition unit 213... Prediction unit 214... Determination unit 220... Storage unit 221... State equation storage unit 230... ROM/RAM
240... Communication unit 250... Input/output unit 300... Object to be controlled

Claims (8)

A model learning device,
a model storage unit that stores a model structure used for learning a nonlinear state equation for predicting the state variable x;
a learning unit that learns the state equation using the model structure and an input/output data set including a plurality of pairs of input data and output data for the model structure;
with
The model structure is a state equation including a bijective map f(x) with a state variable x as an input ,
The model structure is defined by the following formula,

In the above formula,
The left side of the equal sign is the time derivative of the n (n is an integer) dimensional vector representing the state variable x to be predicted by the state equation,
Of the right side of the equal sign, u is an m-dimensional vector (m is an integer) representing an input variable that affects the change of the state variable x, and f(x) is an n-dimensional vector output with the state variable x as an input. is a bijective mapping that
The learning unit sets the function ψ in the model structure to a structure represented by the following equation,

In the above formula,
The left side of the equal sign is the function ψ,
In the right side of the equal sign, A is an n-by-n square matrix, g is any nonlinear function that outputs an n-dimensional vector, and c is any positive scalar function. Model learning device. The model learning device according to claim 1 ,
The learning unit
estimating an output given the input data set of the input/output data set for the model structure;
Evaluating the degree of match between the estimated output and the output data set of the input/output data set;
A model learning device that learns the equation of state by updating learning parameters for the model structure according to evaluation results. A model learning method, wherein an information processing device
obtaining a model structure that is used to learn a nonlinear equation of state for predicting the state variable x;
learning the equation of state using the model structure and an input/output data set including a plurality of sets of input data and output data for the model structure;
with
The model structure is a state equation including a bijective map f(x) that takes a state variable x as an input and outputs an n-dimensional vector (n is an integer ),
The model structure is defined by the following formula,

In the above formula,
The left side of the equal sign is the time derivative of the n (n is an integer) dimensional vector representing the state variable x to be predicted by the state equation,
Of the right side of the equal sign, u is an m-dimensional vector (m is an integer) representing an input variable that affects the change of the state variable x, and f(x) is an n-dimensional vector output with the state variable x as an input. is a bijective mapping that
In the learning step, the function ψ in the model structure is a structure represented by the following formula,

In the above formula,
The left side of the equal sign is the function ψ,
In the right side of the equal sign, A is an n-by-n square matrix, g is any nonlinear function that outputs an n-dimensional vector, and c is any positive scalar function. model learning method. A computer program,
obtaining a model structure used for learning a non-linear equation of state for predicting the state variable x;
learning the equation of state using the model structure and an input/output data set containing a plurality of sets of input data and output data for the model structure;
is executed by the information processing device,
The model structure is a state equation including a bijective map f(x) that takes a state variable x as an input and outputs an n-dimensional vector (n is an integer) ,
The model structure is defined by the following formula,

In the above formula,
The left side of the equal sign is the time derivative of the n (n is an integer) dimensional vector representing the state variable x to be predicted by the state equation,
Of the right side of the equal sign, u is an m-dimensional vector (m is an integer) representing an input variable that affects the change of the state variable x, and f(x) is an n-dimensional vector output with the state variable x as an input. is a bijective mapping that
In the learning step, the function ψ in the model structure is a structure represented by the following formula,

In the above formula,
The left side of the equal sign is the function ψ,
In the right side of the equal sign, A is an n-by-n square matrix, g is any nonlinear function that outputs an n-dimensional vector, and c is any positive scalar function. computer program. a controller,
a state equation storage unit that stores the nonlinear state equation learned by the model learning device according to claim 1 or claim 2 ;
an acquisition unit that acquires various parameters related to the equation of state;
a prediction unit that predicts a future state variable x from the state equation using the obtained parameters;
A controller. The control device according to claim 5 , further comprising:
A control device comprising a determination unit that determines an operation amount for controlling an arbitrary controlled object using the state variable x predicted by the prediction unit. A control method, wherein the information processing device
obtaining a nonlinear state equation learned by the model learning device according to claim 1 or claim 2 ;
obtaining various parameters for the equation of state;
predicting a future state variable x from the state equation using the obtained parameters;
A control method comprising: A computer program,
obtaining a nonlinear state equation learned by the model learning device according to claim 1 or claim 2 ;
obtaining various parameters for the equation of state;
predicting a future state variable x from the state equation using the obtained parameters;
A computer program that causes an information processing device to execute

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