Metalearning ARX model multi-task parameter collaborative identification method for small samples

Abstract

The invention provides a small sample-oriented meta-learning ARX model multi-task parameter collaborative identification method, and relates to the technical field of control science and engineering and machine learning. The method comprises the following steps: initializing system information vectors and parameter vectors of a plurality of tasks; defining a context feature vector with task specificity for each task; establishing a mapping relation from the context feature vector to different task parameters through a neural network; constructing a task-level loss function based on a prediction error, and updating a context feature vector; constructing a multi-task joint loss function, and updating shared parameters of the neural network; and iteratively executing collaborative updating of the context feature vectors and the shared parameters until convergence. According to the method, the problems of poor adaptability and generalization ability, high sample size requirement, high calculation overhead and insufficient identification precision of a traditional algorithm in a multi-task scene are effectively solved, and the efficiency, precision and stability of multi-task parameter identification in a small sample are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of control science and engineering and machine learning, and particularly relates to a small sample-oriented meta-learning ARX model multi-task parameter collaborative identification method. BACKGROUND

[0002] As a basic and important tool for modeling, prediction and control of linear dynamic systems with input in engineering, science and economic fields, the optimization research of the identification algorithm of the AutoRegressive with eXogenous input (ARX) model with external input has important practical significance. However, the existing related technologies still have many defects when facing complex scenes such as multi-task switching and multi-modal coordination.

[0003] On the one hand, the traditional single linear system identification model is difficult to adapt to the adaptability and generalization requirements in the multi-task scene. In the multi-task environment with the same context, such model cannot effectively extract the features of different tasks, and often needs to be repeatedly trained for each task, resulting in poor adaptability and weak generalization ability when switching tasks.

[0004] On the other hand, the traditional identification algorithm has deficiencies in computational efficiency and stability. For example, the least square identification algorithm is prone to unstable results when directly inverting large data or ill-conditioned data; while the improved generalized least square method improves the stability to some extent, but significantly increases the computational complexity, and the robust estimation method also has the problem of large amount of calculation, which is difficult to meet the demand of low computational overhead for real-time application.

[0005] In addition, there is a dynamic coupling characteristic between different tasks and context features, which further affects the parameter identification accuracy of the traditional identification model, making it difficult to achieve accurate system parameter estimation in complex dynamic scenarios.

[0006] The above problems limit the effective application of the ARX model in the multi-task, small sample and dynamic coupling scenarios, and therefore, there is an urgent need for an ARX model parameter identification method that can improve multi-task adaptability, reduce computational overhead and improve identification accuracy. SUMMARY

[0007] To this end, the embodiment of the present application provides a small sample-oriented meta-learning ARX model multi-task parameter collaborative identification method, which is used to solve the problems in the prior art that the traditional single linear system identification model has poor adaptability and generalization ability in the multi-task switching and multi-modal coordination scene, and the traditional algorithm has large amount of calculation, high requirement for sample data amount, and insufficient identification accuracy due to the influence of the dynamic coupling characteristic of the task and the context feature.

[0008] To solve the above problems, the embodiment of the present application provides a small sample-oriented meta-learning ARX model multi-task parameter collaborative identification method, which comprises the following steps:

[0009] S1: initializing system information vectors and parameter vectors of multiple tasks;

[0010] S2: defining a context feature vector for each task;

[0011] S3: establishing a mapping relationship from the context feature vector to the task parameter through a neural network;

[0012] S4: constructing a task-level loss function based on a prediction error, and updating the context feature vector;

[0013] S5: constructing a multi-task joint loss function, and updating shared parameters of the neural network;

[0014] S6: iteratively performing collaborative updating of the context feature vector and the shared parameters until convergence is achieved;

[0015] Among them, the shared parameters are transferred between multiple tasks through meta-learning, so as to realize rapid parameter identification of a new task under a small sample.

[0016] Preferably, the neural network comprises an input layer, a hidden layer and an output layer; the input layer receives the context feature vector, the hidden layer performs nonlinear transformation, and the output layer generates an ARX model parameter vector.

[0017] Preferably, the updating of the context feature vector in step S4 comprises:

[0018] calculating a gradient of the task-level loss function on the context feature vector, and updating the context feature vector by using a gradient descent method:

[0019]

[0020] wherein, is an updated value of the qth component of the context feature vector of the ith task in the kth iteration; is an updated value of the qth component of the context feature vector of the ith task in the (k-1)th iteration; and η is a learning rate of the context parameter. is a partial derivative of the task-level loss function J(c i ) on the context component c q,i .

[0021] Preferably, the updating of the shared parameters in step S5 comprises:

[0022] calculating a gradient of the multi-task joint loss function on the neural network weight and bias, and updating the shared parameters by using a gradient descent method:

[0023]

[0024] In the formula, These are the weights from the j-th node in the hidden layer to the p-th node in the output layer after the k-th and k-1-th iterations, respectively. These are the biases of the p-th node in the output layer after the k-th and (k-1)-th iterations, respectively. These are the weights from the q-th node in the input layer to the j-th node in the hidden layer after the k-th and (k-1)-th iterations, respectively. λ represents the bias of the j-th node in the hidden layer after the k-th and (k-1)-th iterations, respectively; λ is the learning rate of the output layer; μ is the learning rate of the hidden layer. For multi-task joint loss function For weight v p,j The partial derivatives; For multi-task joint loss function For bias β p The partial derivatives; For multi-task joint loss function For weight w j,q The partial derivatives; For multi-task joint loss function For bias α j The partial derivatives of .

[0025] Preferably, the task-level loss function is defined as:

[0026]

[0027] In the formula, J(c i ) represents the task-level loss function; c i is the context feature vector; i is the task index; t is the time index; l is the amount of training data in a single task mini-batch; This represents the actual system output value for the i-th task at time t. Let θ be the information vector of the i-th task at time t; i Let be the parameter vector of the ARX model for the i-th task; This is the ARX model prediction output for the i-th task at time t.

[0028] Preferably, the multi-task joint loss function is defined as:

[0029]

[0030] In the formula, For multi-task joint loss function; For shared parameters; i is the task index; M is the number of tasks involved in the training phase; t is the time index; L is the length of the full dataset for a single task; y i(t) is the actual output value of the system of the i th task at time t; is the information vector of the i th task at time t; and i is the parameter vector of the ARX model of the i th task; is the predicted output of the ARX model of the i th task at time t.

[0031] Preferably, the parameter identification of the new task is realized through the following steps:

[0032] The shared parameters obtained by training are fixed, the context feature vectors thereon are updated based on a small amount of data of the new task, and the parameter estimation is obtained through neural network mapping.

[0033] The embodiment of the application also provides a small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification system, which is used to realize the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method described above, and specifically comprises:

[0034] A task initialization module is configured to initialize system information vectors and parameter vectors of multiple tasks.

[0035] A context definition module is configured to define context feature vectors for each task.

[0036] A meta-learning mapping construction module is configured to establish a mapping relationship from the context feature vectors to the task parameters through a neural network.

[0037] A task-level optimization module is configured to construct a task-level loss function based on a prediction error, and update the context feature vectors.

[0038] A shared knowledge transfer module is configured to construct a multi-task joint loss function, and update shared parameters of the neural network.

[0039] A collaborative convergence module is configured to iteratively perform collaborative updating of the context feature vectors and the shared parameters until convergence.

[0040] The shared parameters are transferred between the multiple tasks through meta-learning, so that the parameter identification of the new task under a small sample is realized quickly.

[0041] The embodiment of the application also provides an electronic device, which comprises a processor, a memory and a bus system, the processor and the memory are connected through the bus system, the memory is used to store instructions, and the processor is used to execute the instructions stored in the memory to realize the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method described above.

[0042] The embodiment of the present application also provides a computer storage medium, which stores a computer software product, and the computer software product comprises a plurality of instructions for enabling a computer device to execute the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method.

[0043] From the above technical solutions, the present application has the following beneficial effects:

[0044] (1) Based on the meta-learning framework, the present application constructs a mapping relationship from the context feature vector to the task parameter through the neural network, so that the shared parameter realizes knowledge transfer between multiple tasks. For a new task, without a large amount of repeated training, only the context feature vector is updated based on a small amount of data, and the parameter estimation can be quickly obtained through the pre-trained neural network, thereby effectively solving the problems of poor adaptability and weak generalization ability of the traditional single model in the multi-task switching, and dynamically adapting to the context mode commonly followed by different tasks.

[0045] (2) The traditional identification algorithm has a high requirement for the sample data amount, while the present application significantly reduces the dependence on the sample amount through the collaborative optimization mechanism of the context feature and the shared parameter. In the small sample scene, the context feature vector and the neural network shared parameter are precisely adjusted by using the gradient descent method through iterative updating of the task-level loss function and the multi-task joint loss function, so that accurate parameter identification can be realized even if only a small amount of training data (such as 15 data points in the simulation experiment) is used for each task, thereby meeting the modeling demand in the small sample scene.

[0046] (3) Compared with the problems of instability of the traditional least square algorithm under large data or ill-conditioned data and high computational complexity of the improved algorithm such as the generalized least square method, the present application avoids the complex matrix inversion operation through the neural network mapping and gradient descent collaborative updating strategy, significantly reduces the computational cost, and meets the demand of real-time application for low computational cost. At the same time, the algorithm effectively captures the dynamic coupling characteristics of the task and the context feature, improves the precision and stability of the parameter identification through the double optimization of the task-level and multi-task joint loss functions, and the simulation results verify the above-mentioned advantages. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly described below. The features and advantages of the present application can be more clearly understood by referring to the drawings. The drawings are schematic and should not be construed as any limitation on the present application. Those skilled in the art can obtain other drawings according to the drawings without any creative effort. Among them:

[0048] Figure 1A flow chart of a small sample oriented meta learning ARX model multi task parameter collaborative identification method provided by the present application is provided.

[0049] Figure 2 A flow chart of a small sample oriented meta learning ARX model multi task parameter collaborative identification method provided by the present application is provided.

[0050] Figure 3 A neural network schematic diagram of the present application is provided.

[0051] Figure 4 A relationship curve of the identification error δ and the iteration number k of the training set under 20 different noise seeds and step lengths is provided.

[0052] Figure 5 A box plot of the context feature vector obtained by training under 20 different noise seeds and step lengths is provided.

[0053] Figure 6 A box plot of the system parameter obtained by training under 20 different noise seeds and step lengths is provided.

[0054] Figure 7 A comparison chart of the predicted output and the real output of the test set of four tasks is provided.

[0055] Figure 8 A context feature vector clustering result of the test set of four tasks is provided.

[0056] Figure 9 A block diagram of a small sample oriented meta learning ARX model multi task parameter collaborative identification system provided by the present application is provided. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0058] Embodiment one: In order to solve the problems of poor adaptability and generalization ability of the conventional single linear system identification model in the multi task switching and multi modal coordination scene, large calculation amount of the traditional algorithm, high requirement for sample data amount, and insufficient identification accuracy due to the influence of the dynamic coupling characteristics of the task and the context feature, as shown in the prior art Figure 1 or Figure 2 The present application proposes a small sample oriented meta learning ARX model multi task parameter collaborative identification method, which comprises:

[0059] S1: initialize system information vectors and parameter vectors of multiple tasks;

[0060] S2: define a context feature vector for each task;

[0061] S3: establish a mapping relationship from the context feature vector to the task parameter through a neural network;

[0062] S4: construct a task-level loss function based on prediction error to update the context feature vector;

[0063] S5: construct a multi-task joint loss function to update shared parameters of the neural network;

[0064] S6: iteratively perform collaborative update of the context feature vector and the shared parameters until convergence;

[0065] Among them, the shared parameters are transferred between multiple tasks through meta-learning, realizing fast parameter identification of new tasks under small samples.

[0066] From the above technical solution, the present application proposes a meta-learning ARX model multi-task parameter collaborative identification method for small samples. By initializing the system information and parameter vectors of multiple tasks, defining a context feature vector for each task, and using a neural network to construct a mapping relationship from the context feature to the task parameter, a task-level loss function based on prediction error and a multi-task joint loss function are constructed, and the context feature vector and the shared parameters of the neural network are alternately updated using gradient descent method, realizing collaborative convergence of the two. Among them, the shared parameters are transferred between multiple tasks through meta-learning. This scheme effectively solves the problems of poor adaptability and generalization ability of traditional algorithms in the multi-task scene, high requirement for sample data volume, large computational overhead, and insufficient identification accuracy affected by dynamic coupling. Not only can it quickly realize parameter identification of new tasks under small samples and reduce computational cost, but also can improve the adaptability and generalization ability of multiple tasks, ensure the accuracy and stability of parameter identification, and the simulation results verify its effectiveness.

[0067] The present application provides a meta-learning ARX model multi-task parameter collaborative identification method for small samples, which realizes knowledge transfer between multiple tasks through meta-learning, and realizes efficient parameter identification under small samples by combining neural network and collaborative optimization strategy. The specific steps are as follows:

[0068] In this embodiment, in step S1, the system information vectors and parameter vectors of multiple tasks are initialized.

[0069] Task definition: suppose that M tasks are involved in the training stage, and the i-th task is represented as Γ i , and its ARX model form is:

[0070] Γ i : A i (z)y i (t) = B i (z)u i (t) + v i (t) ;

[0071] where u i (t), y i (t) are the system input and output of the ith task, respectively, v i (t) is a random noise with zero mean and variance σ i 2 A i (z) and B i (z) are polynomials of the unit delay operator in Z -1 [ Z -1 y i t = y i t ] :

[0072]

[0073] where a are the output coefficients, b are the input coefficients, n a is the lag order (autoregressive term order) of the system output y(t), and n b is the lag order (external input term order) of the system input u(t).

[0074] Information vector and parameter vector initialization: define the information vector of the ith task at time t as:

[0075] The parameter vector is:

[0076]

[0077] At initialization, the parameter vector θ i can be assigned a random value or prior knowledge. Finally, the vector form of the regression model is obtained according to the above formula:

[0078]

[0079] Further, the traditional least squares identification algorithm:

[0080] is defined by the vector form of the regression model as follows:

[0081]

[0082] Take the partial derivative of θ and set it to zero:

[0083]

[0084] Therefore, the least squares estimate of θ is:

[0085]

[0086] Definition

[0087]

[0088] v(t i )=[v(t1) T ,v(t2) T ,...,v(t n ) T ] T ∈R n , we know

[0089]

[0090] Therefore, the least squares estimate of θ can also be written as:

[0091]

[0092] In this embodiment, in step S2, a context feature vector is defined for each task.

[0093] For the i-th task, the context feature vector c i is defined as: i1 i2 imi mi where m i is the context feature dimension. The context feature vector is used to characterize the unique properties of the task and is a bridge connecting the task and the model parameters.

[0094] In this embodiment, in step S3, a mapping relationship from the context feature vector to the task parameters is established by a neural network.

[0095] The present application adopts a neural network comprising an input layer, a hidden layer, and an output layer to construct the mapping relationship, denoted as θ i (c i )=NN θ (c i ), where NN θ is a neural network, and θ is the shared parameters (including weights and biases) of the network. The input layer receives the context feature vector, the hidden layer performs a nonlinear transformation, and the output layer generates the ARX model parameter vector.

[0096] As​​​Figure 3 The diagram shows the case of a BP neural network with s nodes. For task Γ... i The relationships between nodes at each level are as follows:

[0097]

[0098] Where h j It is the output of the hidden layer node, w jq Let α be the weight from the q-th node in the input layer to the j-th node in the hidden layer. j θ is the bias of the j-th node in the hidden layer. i,p It is θ i The p-th parameter in the equation, v pj Let β be the weight from the j-th node in the hidden layer to the p-th node in the output layer. p Let g(·) be the bias of the p-th node in the output layer, and g(·) and f(·) be the activation functions of the hidden layer and the output layer, respectively.

[0099] In this embodiment, in step S4, a task-level loss function based on the prediction error is constructed, and the context feature vector is updated.

[0100] Task-level loss function definition: For the i-th task, the loss function is the squared error between the predicted output and the actual output:

[0101]

[0102] In the formula, J(c i ) represents the task-level loss function; c i is the context feature vector; i is the task index; t is the time index; l is the amount of training data in a single task mini-batch; This represents the actual system output value for the i-th task at time t. Let θ be the information vector of the i-th task at time t; i Let be the parameter vector of the ARX model for the i-th task; This is the ARX model prediction output for the i-th task at time t.

[0103] Context feature vector update: c is updated using gradient descent. i The update formula for the q-th component in the k-th iteration is:

[0104]

[0105] In the formula, This represents the update value of the q-th component of the context feature vector for the i-th task in the k-th iteration; Let be the update value of the q-th component of the context feature vector for the i-th task in the (k-1)-th iteration; η is the learning rate of the context parameters; The task-level loss function J(c i ) is the partial derivative of the context component c q,i .

[0106] Further, the above calculation process needs to combine the neural network chain derivation method:

[0107]

[0108]

[0109] In this embodiment, in step S5, a multi-task joint loss function is constructed, and the shared parameters of the neural network are updated.

[0110] Multi-task joint loss function definition: the loss of all M tasks is integrated to define the joint loss function:

[0111]

[0112] In the formula, is the multi-task joint loss function; is the shared parameter; i is the task index; M is the number of tasks involved in the training stage; t is the time index; L is the length of the single-task full data; y i (t) is the actual output value of the i-th task at time t; is the information vector of the i-th task at time t; θ i is the parameter vector of the ARX model of the i-th task; is the ARX model prediction output of the i-th task at time t.

[0113] Shared parameter update: the gradient descent method is used to update the shared parameter, and the specific formula is as follows:

[0114] The weight from the j-th node of the hidden layer to the p-th node of the output layer:

[0115]

[0116] The bias of the p-th node of the output layer:

[0117]

[0118] Wherein

[0119]

[0120] In the formula, are the weights from the j-th node of the hidden layer to the p-th node of the output layer after the k-th and k-1-th iterations, respectively; respectively, are the bias of the pth node of the output layer after the kth and (k-1)th iteration, respectively; λ is the learning rate of the output layer; is the multi-task joint loss function is the partial derivative of the bias β p,j . is the multi-task joint loss function is the partial derivative of the bias β p .

[0121] is the weight of the qth node of the input layer to the jth node of the hidden layer:

[0122]

[0123] is the bias of the jth node of the hidden layer:

[0124]

[0125] wherein

[0126]

[0127] wherein respectively, are the weight of the qth node of the input layer to the jth node of the hidden layer after the kth and (k-1)th iteration, respectively; respectively, are the bias of the jth node of the hidden layer after the kth and (k-1)th iteration, respectively; μ is the learning rate of the hidden layer; is the multi-task joint loss function is the partial derivative of the weight w j,q . is the multi-task joint loss function is the partial derivative of the bias α j .

[0128] In the present embodiment, in step S6, the co-updating of the context feature vector and the shared parameter is iteratively performed until convergence.

[0129] Steps S4 and S5 are repeated to alternately update the context feature vector c i and the shared parameter until the multi-task joint loss function converges (e.g. the change of the loss in consecutive iterations is less than a preset threshold).

[0130] Further, new task parameter identification: for a small sample new task, the shared parameter trained is fixed, and based on a small amount of data (e.g. 15 data points) of the new task, the context feature vector c new of the new task is updated by the gradient descent method of step S4, and the neural network mapping θ new = NN θ (c new) obtain parameter estimation, realize fast identification.

[0131] In order to further illustrate the advantages of the method of the present application, the following will be described in combination with specific simulation verification.

[0132] n a The order is 3, n b The simulation experiment is carried out on the multi-task ARX model with order 2:

[0133] Γ i : A i (z)y i (t)=B i (z)u i (t)+v i (t),i∈{1,2,3};

[0134] The system input u i (t) is a zero-mean, unit-variance uncorrelated random signal sequence, v i (t) is a white noise sequence with zero mean and variance The training set is set with three tasks for training context parameters and shared parameters, and the parameters take the following values:

[0135] θ1=[a 1,1 ,a 2,1 ,a 3,1 ,b 1,1 ,b 2,1 ,b 3,1 ] T =[0.525,0.117,0.080,0.142,1.350] T ∈R 5 ;

[0136] θ2=[a 1,2 ,a 2,2 ,a 3,2 ,b 1,2 ,b 2,2 ,b 3,2 ] T =[0.375,0.325,0.084,0.124,1.227] T ∈R 5 ;

[0137] θ3=[a 1,3 ,a 2,3 ,a 3,3 ,b 1,3 ,b 2,3 ,b 3,3 ] T =[0.175,0.637,0.088,0.071,1.181]T ∈R 5 ;

[0138] The test set adds a fourth new task, and the parameters take the following values:

[0139] θ4=[a 1,4 ,a 2,4 ,a 3,4 ,b 1,4 ,b 2,4 ,b 3,4 ] T =[0.150,0.460,0.080,0.054,1.377] T ∈R 5 ;

[0140] During the test set recognition process, the shared parameters obtained during training are kept unchanged, and the context is updated. Each of the four tasks is trained using only 15 data points, and 50 data points are used for prediction verification. During the verification process, the task is converted every 50 data points. The experimental results verify the effectiveness of the present application, that is:

[0141] (1) The method of the present application can accurately identify the parameters of different tasks and has good stability, as shown in Figure 4 , Figure 5 , Figure 6 .

[0142] (2) After the context and shared parameters are extracted by the method of the present application, the recognition of new tasks in the same situation can be effectively realized, as shown in Figure 7 .

[0143] (3) The method of the present application can effectively identify the dynamic differences between context parameters of different tasks in the same situation, as shown in Figure 8 , and after obtaining the context parameters of a task, the system parameters of the task can be accurately identified.

[0144] Embodiment Two: As shown in Figure 9 , the present application provides a small sample-oriented meta-learning ARX model multi-task parameter collaborative recognition system, which is used to implement the small sample-oriented meta-learning ARX model multi-task parameter collaborative recognition method of Embodiment One, and specifically comprises:

[0145] A task initialization module 100 is used to initialize the system information vector and the parameter vector of a plurality of tasks.

[0146] A context definition module 200 is used to define a context feature vector for each task.

[0147] A meta-learning mapping construction module 300 is used to establish a mapping relationship from the context feature vector to the task parameter through a neural network.

[0148] The task-level optimization module 400 is configured to construct a task-level loss function based on a prediction error, and update the context feature vector;

[0149] The shared knowledge transfer module 500 is configured to construct a multi-task joint loss function, and update the shared parameters of the neural network;

[0150] The collaborative convergence module 600 is configured to iteratively perform collaborative updating of the context feature vector and the shared parameters until convergence.

[0151] The shared parameters are transferred between the multi-tasks through meta-learning, so as to realize rapid parameter identification of a new task under a small sample.

[0152] The small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification system of the embodiment is used to implement the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method, and therefore the specific embodiments in the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification system can be seen from the foregoing embodiment part of the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method. For example, the task initialization module 100, the context definition module 200, the meta-learning mapping construction module 300, the task-level optimization module 400, the shared knowledge transfer module 500, and the collaborative convergence module 600 are respectively used to implement steps S1, S2, S3, S4, S5, and S6 in the foregoing small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method. Therefore, the specific embodiments can be referred to the description of the respective embodiments, and details are not described herein again to avoid redundancy.

[0153] Embodiment three: The embodiment of the present application provides an electronic device, which comprises a processor, a memory, and a bus system. The processor and the memory are connected through the bus system. The memory is used to store instructions, and the processor is used to execute the instructions stored in the memory to implement the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method.

[0154] Embodiment four: The embodiment of the present application provides a computer storage medium, which stores a computer software product. The computer software product comprises a plurality of instructions, and is used to make a computer device execute the small-sample-oriented meta-learning ARX model multi-task parameter collaborative identification method.

[0155] Those skilled in the art will appreciate that embodiments of the present application can be readily used as software, hardware, or a combination of software and hardware. In one

[0156] The present application is described in reference to the flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart Figure 1 one or more functions specified in the flowchart block or blocks. Figure 1 one or more functions specified in the flowchart block or blocks.

[0157] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more functions specified in the flowchart block or blocks. Figure 1 one or more functions specified in the flowchart block or blocks. These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more functions specified in the flowchart block or blocks. Figure 1 one or more functions specified in the flowchart block or blocks.

[0158] Obviously, the embodiments described above are only examples and are not intended to limit the present application. Based on the above description, other variations or modifications can be made by those skilled in the art. Here, it is not necessary or possible to exhaust all embodiments. The obvious changes or modifications derived from the above description are still within the scope of the present application.

Claims

1. A small sample oriented meta-learning ARX model multi-task parameter collaborative identification method, characterized in that, Comprise: S1: initialize system information vectors and parameter vectors of multiple tasks; S2: define a context feature vector for each task; S3: establish a mapping relationship from the context feature vector to the task parameters through a neural network; S4: construct a task-level loss function based on prediction error to update the context feature vector; S5: construct a multi-task joint loss function to update shared parameters of the neural network; S6: iteratively perform collaborative updates of the context feature vector and the shared parameters until convergence is achieved; Wherein, the shared parameters are transferred between multiple tasks through meta-learning, realizing fast parameter identification of new tasks under small samples.

2. The small sample oriented meta-learning ARX model multi-task parameter collaborative identification method according to claim 1, characterized in that, The neural network includes an input layer, a hidden layer, and an output layer; wherein the input layer receives the context feature vector, the hidden layer performs nonlinear transformation, and the output layer generates an ARX model parameter vector.

3. The small sample oriented meta-learning ARX model multi-task parameter collaborative identification method according to claim 1, characterized in that, Updating the context feature vector in step S4 includes: Calculating the gradient of the task-level loss function with respect to the context feature vector, and updating the context feature vector using gradient descent method: wherein, is the updated value of the qth component of the context feature vector for the ith task in the kth iteration; is the updated value of the qth component of the context feature vector for the ith task in the k-1th iteration; and η is the learning rate of the context parameter; is the task-level loss function J(c i ) with respect to the context component c q,i .

4. The small sample oriented meta-learning ARX model multi-task parameter collaborative identification method according to claim 1, characterized in that, Updating the shared parameters in step S5 includes: Calculating the gradient of the multi-task joint loss function with respect to the neural network weights and biases, and updating the shared parameters using gradient descent method: wherein, respectively are the weights from the jth node in the hidden layer to the pth node in the output layer after the kth, k-1th iteration; respectively are the biases of the pth node in the output layer after the kth, k-1th iteration; respectively are the weights from the qth node in the input layer to the jth node in the hidden layer after the kth, k-1th iteration; respectively are the biases of the jth node in the hidden layer after the kth, k-1th iteration; λ is the learning rate of the output layer; μ is the learning rate of the hidden layer; is the multi-task joint loss function is the partial derivative of the weight v p,j ; is the multi-task joint loss function is the partial derivative of the bias β p ; is the multi-task joint loss function is the partial derivative of the weight w j,q ; is the multi-task joint loss function is the partial derivative of the bias α j .

5. The small sample oriented meta-learning ARX model multi-task parameter collaborative identification method according to claim 1, characterized in that, The task-level loss function is defined as: where J(c i ) is the task-level loss function; c i is the context feature vector; i is the task index; t is the time index; l is the single-task mini-batch size; is the actual output value of the i-th task at time t; is the information vector of the i-th task at time t; θ i is the parameter vector of the ARX model of the i-th task; is the predicted output of the ARX model of the i-th task at time t.

6. The small sample oriented meta-learning ARX model multi-task parameter collaborative identification method according to claim 1, characterized in that, The multi-task joint loss function is defined as: In the formula, is a multi-task joint loss function; is a shared parameter; i is a task index; M is the number of tasks involved in the training stage; t is time index; L is single task full data length; y i (t) is the actual output value of the system of the i-th task at time t; is the information vector of the i-th task at time t; θ i is the parameter vector of the ARX model of the i-th task; is the predicted output of the ARX model of the i-th task at time t.

7. The small sample oriented meta-learning ARX model multi-task parameter collaborative identification method according to claim 1, characterized in that, Parameter identification of new tasks is achieved through the following steps: Fix the trained shared parameters, update the context feature vector of the new task based on a small amount of data, and obtain parameter estimation through neural network mapping.

8. A small sample oriented meta-learning ARX model multi-task parameter collaborative identification system, characterized in that, The system is used to implement the meta-learning ARX model multi-task parameter collaborative identification method for small samples according to any one of claims 1 to 7, and specifically comprises: A task initialization module for initializing system information vectors and parameter vectors of multiple tasks; A context definition module for defining a context feature vector for each task; A meta-learning mapping construction module for establishing a mapping relationship from the context feature vector to the task parameters through a neural network; A task-level optimization module for constructing a task-level loss function based on prediction error to update the context feature vector; A shared knowledge transfer module for constructing a multi-task joint loss function to update shared parameters of the neural network; A collaborative convergence module for iteratively performing collaborative updates of the context feature vector and the shared parameters until convergence is achieved; Wherein, the shared parameters are transferred between multiple tasks through meta-learning, realizing fast parameter identification of new tasks under small samples.

9. An electronic device, comprising: The electronic device includes a processor, a memory, and a bus system, the processor and the memory are connected through the bus system, the memory is used to store instructions, and the processor is used to execute the instructions stored in the memory to realize the meta-learning ARX model multi-task parameter collaborative identification method for small samples according to any one of claims 1 to 7.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer software product, the computer software product includes a plurality of instructions to make a computer device execute the meta-learning ARX model multi-task parameter collaborative identification method for small samples according to any one of claims 1 to 7.

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