Oscillator Dynamic Synchronization Control System and Method Based on Graph Attention Mechanism

Abstract

This invention discloses an oscillator dynamics synchronization control system and method based on a graph attention mechanism. The system is a graph structure formed by coupling several oscillators as nodes. The graph structure uses a proximity matrix to characterize the connection between arbitrary units. The state of each node is controlled by the internal dynamics of the oscillator and the influence of other oscillators on that oscillator. The influence of other oscillators is obtained by mapping the multi-head attention coefficients of each attention head to the state space of each neuron using a multi-layer neural network. The multi-head attention coefficients are dynamically generated by combining the state of each node in the network and the user-specified desired phase. This invention defines the node coupling relationship in the oscillator network as graph attention weights and autonomously learns the coupling parameters of the network. It can be trained in small-scale oscillator networks, and the trained model can directly generate synchronous oscillation modes satisfying arbitrary phase relationships in arbitrarily large-scale oscillator networks.

Description

Technical Field

[0001] This invention relates to the field of robot control and artificial intelligence, and in particular to an oscillator dynamics synchronization control system and method based on graph attention mechanism. Background Technology

[0002] Traditional central mode generator models often employ oscillator networks with fixed coupling structures, achieving gait synchronization by adjusting the coupling strength. However, these methods have the following limitations: (1) the network structure is fixed and difficult to adapt to topology changes; (2) the coupling parameters need to be manually designed and lack adaptive capabilities; and (3) it is difficult to achieve cross-scale generalization. In recent years, although some studies have used reinforcement learning to directly adjust the oscillation frequency, they face the curse of dimensionality and are difficult to extend to the generation and switching of large-scale synchronization waveforms. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by proposing a synchronous control system and method for oscillator dynamics based on graph attention mechanism.

[0004] The objective of this invention is achieved through the following technical solution: an oscillator dynamics synchronization control system based on graph attention mechanism, wherein the system is a graph structure formed by coupling several oscillators as nodes, and the graph structure describes the connection mode between arbitrary units through a proximity matrix;

[0005] The state of each node is controlled by the internal dynamics of the oscillator and the influence of the other oscillators on that oscillator. The influence of the other oscillators is obtained by mapping the multi-head attention coefficients of each attention head to the state space of each neuron using a multi-layer neural network. The multi-head attention coefficients are dynamically generated by combining the state of each node in the network with the desired phase specified by the user.

[0006] Furthermore, the state of each node, specifically defined by the internal dynamics of the oscillator and the influence of the other oscillators on that oscillator, includes: for any unit i in the system, its dynamic differential equation is:

[0007] ;

[0008] in, , representing the state of the m-dimensional oscillator itself. This represents the internal dynamic equations of the oscillator, which relate only to the oscillator's own state variables. related, This indicates the magnitude of the effect of other oscillators in the system on this oscillator.

[0009] Furthermore, the effects of the remaining oscillators on this oscillator specifically include: ;

[0010] The `clamp()` function is used to limit... Size; It is a multi-layer neural network used to map high-dimensional feature information to the state space of each neuron; This is a learnable projection matrix used to represent the state variables of node i's neighboring node j. Mapped to a high-dimensional representation space, For multi-head attention coefficients, k represents the number of the attention head; The neighbor mapping is obtained through the proximity matrix.

[0011] Furthermore, the dynamic generation of the multi-head attention coefficients, combining the state of each node in the network and the user-specified desired phase, specifically includes: for an oscillator network containing N oscillating units, defining the desired phase difference as an N-dimensional vector. ,in, This represents the expected phase difference between the i-th unit and the first unit; to construct the attention coefficients, we will... Encoding Among them;

[0012] For the same attention head, the calculation process includes:

[0013] First of all Encode itself, for ,have

[0014]

[0015] Then, using the learnable coefficient matrix Project the encoded desired phase onto 3D expression space:

[0016]

[0017] Finally, to enhance the system's real-time performance and global convergence capability, positional encoding techniques from the Transformer are used to incorporate system state encoding, ultimately yielding... and The expression:

[0018]

[0019] in, For is a learnable coefficient matrix; and The matrices, with subscripts s and t, are the source and target matrices, respectively. The indexed matrix projects the user-given desired phase difference into source or target features, without any subscripts. The projection matrix of the subscripts projects the system's state variables into source and target features;

[0020] For any given head, the attention coefficient is calculated as follows:

[0021]

[0022] LeakyReLU is a classic improved version of the ReLU activation function in deep learning.

[0023] Furthermore, the system also incorporates a proportional-derivative feedback controller to correct the desired phase input of the system based on the real-time waveform. The design is as follows:

[0024]

[0025] in This is for proportional control of the gain. For the differential control part of the variety show, The error between the phase difference between the system output waveforms and the desired phase difference. Let the first derivative of this error be the error at the current time step and the error at the previous time step. and , It can be estimated as

[0026]

[0027] The desired phase input of the system is .

[0028] According to another aspect of the specification, a training method based on the system is also provided, the method comprising:

[0029] The intelligent coupled dynamics system is treated as a reinforcement learning environment, and the influence of other oscillators on that oscillator is used as the influence of the agent on the i-th unit of the coupled dynamics system for reinforcement learning:

[0030] Construct an environment reset function to reset the desired phase and initial state of the system at the beginning of each training cycle and output the observations in the initial state of the system. Construct an environment step function to output the next moment's observations and reward function based on the input action.

[0031] Define the phase relationship to be learned, initialize the trainable parameters, and initialize the replay buffer. The trainable parameters include: These are the source and target matrices that project the user-given desired phase difference into source or target features, respectively; the source and target matrices that project the system's state variables into source and target feature source and target feature source matrices; and the attention coefficient calculation parameters, which are the state variables of node i's neighboring node j. Parameters mapped to a high-dimensional representation space;

[0032] At the beginning of each training cycle, the desired phase relationship is randomly selected from the phase relationships that need to be learned, and the desired phase and initial state of the system are reset using the environment reset function to obtain the observation value.

[0033] The agent's actions on the network are obtained using the environment step function, and the next state and reward function are obtained.

[0034] Store the observation, action, next state, and reward function as a tuple in the replay cache;

[0035] After each preset reinforcement learning cycle, a batch of tuple data is randomly selected and the parameters are trained using a reinforcement learning algorithm.

[0036] Furthermore, the environment reset function specifically includes:

[0037] ,in These are flattened neuron state quantities. For the flattened desired phase,

[0038] The flattened neuron state variables are:

[0039] ;

[0040] in and Let I represent the first and second components of the state of the i-th neuron, and let I be the number of oscillator units.

[0041] The state variables of the i-th neuron are:

[0042]

[0043] Where Rand() is the random number generation function and r is the reward function;

[0044]

[0045] in Let be the desired phase of the state of the i-th neuron.

[0046] Furthermore, the environment step function specifically includes:

[0047] ;

[0048] in For the next moment of observation, For the next state variable of a flattened system,

[0049] The system's state variable in the next step is ,

[0050] The node status is output by the system. and The first and second components of the node state output by the system;

[0051] According to another aspect of the specification, an oscillator dynamics synchronization control device based on a graph attention mechanism is also provided, including a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it implements the aforementioned oscillator dynamics synchronization control system based on a graph attention mechanism.

[0052] According to another aspect of the specification, a computer-readable storage medium is also provided, on which a program is stored, which, when executed by a processor, implements the aforementioned oscillator dynamics synchronization control system based on a graph attention mechanism.

[0053] The beneficial effects of this invention are:

[0054] This invention develops a machine learning framework for coupled oscillation dynamics by defining the node coupling relationships in an oscillator network as graph attention weights, enabling the network to autonomously learn its coupling parameters. This framework can be trained in small-scale oscillator networks, and the trained model can directly generate synchronous oscillation modes with arbitrary phase relationships in arbitrarily large-scale oscillator networks. Simultaneously, feedback control is introduced to eliminate model bias in machine learning, further improving the phase accuracy of the generated waveforms in coupled oscillation networks. Applications of this invention include, but are not limited to, gait generation and switching in multi-legged robots, coordinated control of multi-agent systems, and adaptive control of oscillator networks. Attached Figure Description

[0055] Figure 1 This is a diagram illustrating the overall system framework of the present invention;

[0056] Figure 2 This is a diagram illustrating the overall learning framework of the present invention;

[0057] Figure 3 This is a diagram of the overall feedback control framework of the present invention;

[0058] Figure 4 The experimental waveform diagram for uniform phase generation in a 36-element coupled oscillator network according to the present invention is shown.

[0059] Figure 5 The diagram shows the angle error in the uniform phase generation experiment of the present invention in a 2-120 element coupled oscillator network.

[0060] Figure 6 This is a convergence time diagram of the uniform phase generation experiment in a 2-120 element coupled oscillator network according to the present invention.

[0061] Figure 7 The diagram shows the angle error in the random phase generation experiment of the present invention in a coupled oscillator network of 2 to 120 elements.

[0062] Figure 8 A uniform phase generation diagram in the coupled oscillator network provided by the present invention;

[0063] Figure 9 This invention presents an angle error diagram of 50 desired phases randomly tested in a 36-unit coupled oscillator network.

[0064] Figure 10 This is an experimental structure diagram of the present invention in a hexapod robot experiment;

[0065] Figure 11 This is an experimental diagram of the present invention in a hexapod robot experiment;

[0066] Figure 12 The figure shows the experimental results of this invention in a hexapod robot experiment.

[0067] Figure 13 This is a schematic diagram of the oscillator dynamics synchronization control device based on graph attention mechanism provided by the present invention. Detailed Implementation

[0068] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0069] like Figure 1 As shown, the present invention provides an oscillator dynamics synchronization control system and method based on graph attention mechanism.

[0070] This invention proposes an intelligent coupled oscillator system (ICOS), which enables all units to exhibit desired emergent modes on a population scale by endowing each oscillator unit in the coupled oscillator system with simple artificial intelligence.

[0071] An oscillator dynamics synchronization control system based on graph attention mechanism, wherein the system is a graph structure formed by coupling several oscillators as nodes, and the graph structure describes the connection mode between arbitrary units through a proximity matrix;

[0072] The state of each node is controlled by the internal dynamics of the oscillator and the influence of the other oscillators on that oscillator. The influence of the other oscillators is obtained by mapping the multi-head attention coefficients of each attention head to the state space of each neuron using a multi-layer neural network. The multi-head attention coefficients are dynamically generated by combining the state of each node in the network with the desired phase specified by the user.

[0073] The specific structure of the system is as follows:

[0074] A coupled oscillator system consists of multiple oscillators coupled as nodes, and the resulting topology is a graph structure. This graph structure can be represented by an adjacency matrix. This matrix represents the connection between any i-th and j-th units. Specifically, it is achieved through the proximity matrix. For any node i, its neighbor mapping can be obtained. The input to this mapping is the node's index, and the output is the set of indices of all nodes connected to that node (assuming that node i is not connected to itself). Based on this, a smart coupled oscillator system can be constructed, and for any element i in the system, its dynamic differential equation is:

[0075] ;

[0076] in, , representing the state of the m-dimensional oscillator itself. This represents the internal dynamic equations of the oscillator, which relate only to the oscillator's own state variables. Related to (e.g., two-dimensional Hough or Van der Pol oscillator equations). This represents the effect of other oscillators in the system on this oscillator. Since the coupling relationship between an oscillator i and other oscillators in a system can be represented by... This means we can further define for

[0077] ;

[0078] The `clamp()` function is used to limit... Size; It is a multi-layer neural network used to map high-dimensional feature information to the state space of each neuron; This is a learnable projection matrix used to represent the state variables of node i's neighboring node j. Mapped to a high-dimensional representation space. is the multi-head attention coefficient, where k represents the number of the attention head.

[0079] The intelligent coupled oscillator system possesses a series of learnable parameter matrices, allowing for effective control of its emergent behavior through machine learning. In this patent, we primarily control the intelligent coupled oscillator system to emerge into an arbitrary desired synchronization mode. In the synchronization mode, the state vectors of all oscillators rotate at the same angular velocity. However, a fixed phase difference exists between each state vector. This is achieved by constructing appropriate attention coefficients. This enables the intelligent coupled oscillator system to converge to a synchronous mode with arbitrary phase difference. For an oscillator network containing N oscillating units, the desired phase difference is defined as an N-dimensional vector. ,in, This represents the expected phase difference between the i-th unit and the first unit. To construct the attention coefficients, we need to... Encoding Within this context, the following calculations are all performed under a single attention head, thus omitting all k-indices. First, for... Encode itself, for ,have

[0080] ;

[0081] Then, using the learnable coefficient matrix Project the encoded desired phase onto 3D expression space:

[0082] ;

[0083] Finally, to enhance the system's real-time performance and global convergence capability, positional encoding techniques from the Transformer are used to incorporate system state encoding, ultimately yielding... and The expression:

[0084] ;

[0085] in, It is a learnable coefficient matrix.

[0086] Note: For and The matrices, with subscripts 's' and 't', are the source and target matrices, respectively. These matrices project a state variable into source and target features for attention calculation (source and target features are technical terms used in attention-based learning methods). The indexed matrix projects the user-given desired phase difference as source or target features. Conversely, the projection matrix without the index projects the system's state variables as source and target features. Dynamically generated by combining the state of each network node and the user-specified desired phase, the attention coefficient for any head, based on the system state encoding formula, is calculated as follows:

[0087] ;

[0088] LeakyReLU (Leaky Rectified Linear Unit) is a classic improved version of the ReLU (Rectified Linear Unit) activation function in deep learning, defined as follows:

[0089] ;

[0090] in, It is a small constant (such as 0.01, 0.2, etc.) used to control the gradient magnitude of negative inputs and prevent the output from returning to zero.

[0091] Preferably, to further improve the phase accuracy of the waveform generated by the present invention, a proportional-derivative (PD) feedback controller is introduced to correct the desired phase input of the Graph-CPG based on the real-time waveform. The design is as follows:

[0092] ;

[0093] in This is for proportional control of the gain. For the differential control part of the variety show, The error between the phase difference between the system output waveforms and the desired phase difference. Let the first derivative of this error be the error at the current time step and the error at the previous time step. and , It can be estimated as

[0094] ;

[0095] The desired phase input of the system is .

[0096] Corresponding to the aforementioned embodiment of an oscillator dynamics synchronization control system based on a graph attention mechanism, the present invention also provides an embodiment of a training method for an oscillator dynamics synchronization control system based on a graph attention mechanism.

[0097] Optimization is performed based on reinforcement learning to obtain various learnable matrices within the system. The intelligent coupled dynamics system is treated as a reinforcement learning environment. This is considered as the influence (Action) of an intelligent agent on the i-th unit of a coupled dynamic system; a reinforcement learning algorithm is designed based on this to optimize the network.

[0098] A reinforcement learning environment is constructed based on a 4-unit fully connected Hopf oscillator system, with input... Based on the current system observations Output system next observation and reward function It is divided into the following steps:

[0099] Step S1: Construct the environment reset function At the beginning of each training cycle, the desired phase and initial state of the system are reset, and the observations of the system in the initial state are output. In the function, the i-th unit of the 4-unit fully connected 2D Hopf oscillator network contains two components: To encourage exploration, the state variables of network units are randomized at the beginning of each cycle, with the first and second components of the state variables set as follows:

[0100] ;

[0101] The flattened neuron state quantities are

[0102] ;

[0103] Additionally, during a training cycle, the expected phase is... , , and We randomly select from these four values, and let the selected desired phase be... ,right Encoding is performed to obtain the flattened desired phase.

[0104] ;

[0105] Therefore, the aforementioned environment reset function The output is:

[0106] ;

[0107] Step S2: Construct the environment step function According to the input action Output the observation at the next moment. and reward function .

[0108] Step S21: Obtain the system's observations at the next moment. Based on the dynamic differential equation, the state variables of the system in the next step are obtained as follows:

[0109] ;

[0110] The state variable of the flattened system at the next moment is

[0111] ;

[0112] The system's next observation is:

[0113] ;

[0114] Step S22: Obtain the reward function based on the system's next state. Design a reinforcement learning function based on minimizing the difference between the expected phase and the actual phase:

[0115] ;

[0116] in, Let be a rotation matrix. This represents the expected phase difference between neurons i and j. These are adjustable hyperparameters.

[0117] Preferably, in a 4-unit fully connected Hopf oscillator network, the reinforcement learning algorithm Twin DelayedDDPG (TD3) is used to train the Graph-CPG system to generate four phase relationships, including the following steps:

[0118] Step S1: Define the phase relationships to be learned as follows , , and Initialize trainable parameters Initialize replay cache ;

[0119] Step S2: Reinforcement Learning Training Cycle

[0120] Step S21: At the beginning of each training cycle, The desired phase relationship is randomly selected.

[0121] Step S22: At the beginning of each training cycle, apply the above... The function randomly sets the initial values ​​of a 4-cell fully connected Hopf oscillator network and obtains the observed values. .

[0122] Step S23: Based on system definition Formula, to obtain the agent's actions on the network, using the above Function to get the next state and reward function .

[0123] Step S24: Transfer the tuples Store in playback cache ;

[0124] Step S3: Every 50 reinforcement learning cycles, in A batch of tuple data is randomly selected from the dataset, and the TD3 algorithm is used to optimize the trainable parameters. .

[0125] When applying intelligent coupled dynamics systems, it is necessary to obtain the proximity matrix A of the coupled network, which allows us to obtain the set of connected neighbors for each unit. Assume the phase difference vector of the synchronization mode desired by the user is... ,Will and system state variables according to The encoded data, along with the system state variables, is input into the trained network model, and the network model will then operate based on the formula... Generate intelligent perturbations for any unit. Then, based on the dynamic integral calculation of the intelligent dynamic system, the desired phase difference vector can be generated. The synchronous waveform.

[0126] Note: The network used for training is a 4-unit network, but in practical applications, a well-trained intelligent coupled system can adapt to networks of any size and any desired phase difference. For details, please refer to the embodiments.

[0127] Example 1: Synchronization Phase Control for Networks of Arbitrary Size

[0128] In a specific embodiment of the present invention, a CPG control network of arbitrary size consists of N fully connected neurons. The state vector of a neuron... It is governed by the following differential equation:

[0129] ;

[0130] in, The internal dynamics of neurons are modeled as a simple Hopf oscillator, based on... , The specific calculation method is as follows:

[0131] ;

[0132] in, Controlling the convergence rate of the coupled oscillator towards the limit cycle, Let be the radius of the limiting cycle. The system's natural angular frequency is set to . . The effect of Graph-CPG on neuronal dynamics.

[0133] Training is performed using a 4-unit coupled dynamical system Graph-CPG, and the training method is as follows: Figure 2 As shown. Based on Figure 1 The resulting network can be applied to coupled oscillator networks of any size. First, waveform generation for uniform phase relationships was tested in fully connected Hopf oscillator networks ranging from 2 to 120 elements. The uniform waveform generation for a 36-element network is shown in the figure below. Figure 4 As shown. Figure 5 and Figure 6 The numbers represent the error in generating a uniform waveform and the number of steps required to converge to a stable limiting cycle as the number of neurons increases. It can be seen that the magnitude of the error and the trend of the number of convergence steps are basically unrelated to the network size.

[0134] Furthermore, the generation of random desired phases (50 random desired phases were tested for each network) using fully connected Hopf oscillator networks ranging from 2 to 120 units. The results are as follows: Figure 7 As shown, the Graph-CPG model trained in a 4-unit network can be applied to the generation of random phases in arbitrarily large networks.

[0135] Example 2: Graph-CPG Architecture Based on Feedback Control

[0136] As a specific embodiment of the present invention, a Graph-CPG feedback control architecture was tested in a 36-cell fully connected coupled Hopf oscillator network. The feedback control loop is as follows: Figure 3 As shown. The feedback controller is designed and its parameters are set according to the corresponding formula in the system. First, the generation accuracy of the 36-unit uniform waveform was tested, and the experimental results are as follows. Figure 8 As shown, the left image shows the uniform phase generation diagram in a 36-element coupled oscillator network using the feedback control method of this invention, while the right image shows the uniform phase generation diagram in a 36-element coupled oscillator network without the feedback control method of this invention. It can be seen that the Graph-CPG architecture with feedback control can significantly improve the generation accuracy of uniform waveforms. Furthermore, the waveform generation accuracy of a 36-element fully connected coupled Hopf oscillator network for 50 random desired phases was tested, and the experimental results are as follows... Figure 9As shown, the red line represents the method without feedback control; the blue line represents the method without feedback control. It can be seen that the Graph-CPG architecture with feedback control can significantly improve the waveform generation accuracy of a 36-unit fully connected coupled Hopf oscillator network for random desired phases.

[0137] Example 3: Transtopological Gait Generation During Hexapod Robot Operation

[0138] As a specific embodiment of the present invention, such as Figure 10 and Figure 11 As shown, the Graph-CPG control architecture was tested in a 6-unit fully connected coupled Hopf oscillator network. The robot's six legs consist of left foreleg (FL), right foreleg (FR), middle legs (left middle leg (ML), right middle leg (MR), and left hind leg (HL), right hind leg (HR). This structure was applied to gait generation for the six-legged robot. During the robot's movement, the right middle leg and left middle leg of the disabled robot were deactivated. During this process, the fully connected coupled Hopf oscillator network changed from 6 units to 5 units and then to 4 units. The desired phase changed from a six-legged triangular gait to a five-legged uniform gait and then to a four-legged alternating gait. The experimental results are shown below. Figure 12 As shown, p1-p6 represent the phase signals of feet FR, MR, HR, FL, ML, and HL, respectively. It can be seen that when the availability of the robot's feet changes, the robot can smoothly transition to a suitable gait due to the synchronous changes in the coupled oscillator network. The overall transition results demonstrate that the system adjusts the gait smoothly and quickly.

[0139] Corresponding to the aforementioned embodiment of an oscillator dynamics synchronization control system based on a graph attention mechanism, the present invention also provides an embodiment of an oscillator dynamics synchronization control device based on a graph attention mechanism.

[0140] See Figure 13 The present invention provides an oscillator dynamics synchronization control device based on graph attention mechanism, comprising a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement an oscillator dynamics synchronization control system based on graph attention mechanism as described in the above embodiment.

[0141] The embodiment of the oscillator dynamics synchronization control device based on graph attention mechanism provided by this invention can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 13 The diagram shown is a hardware structure diagram of any device with data processing capabilities, where the oscillator dynamics synchronization control device based on graph attention mechanism provided by this invention is located. (Except for...) Figure 13 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0142] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0143] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0144] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements an oscillator dynamics synchronization control system based on a graph attention mechanism as described in the above embodiments.

[0145] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of any data processing device. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0146] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned oscillator dynamics synchronization control system based on a graph attention mechanism.

[0147] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0148] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this application. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A synchronous control system for oscillator dynamics based on a graph attention mechanism, characterized in that, The system is a graph structure formed by coupling several oscillators as nodes. The graph structure describes the connection between arbitrary units through a proximity matrix. The state of each node is controlled by the internal dynamics of the oscillator and the influence of the other oscillators on it. The influence of the other oscillators is obtained by mapping the multi-head attention coefficients of each attention head to the state space of each neuron using a multi-layer neural network. These multi-head attention coefficients are dynamically generated by combining the state of each node in the network with the user-specified desired phase. For an oscillator network containing N oscillating units, construct an N-dimensional expected phase difference vector from the expected phase difference between the i-th unit and the first unit, and encode it into the multi-head attention coefficient; For the same attention head, the calculation process includes: First, the desired phase difference vector itself is encoded. Then, the encoded desired phase is projected onto a learnable coefficient matrix. The system uses a dimensional representation space to obtain source and target features. Finally, to enhance the real-time performance and global convergence capability of the system, the system state encoding is added using the positional encoding technique in Transformer. The system state variables are projected as source and target features, which are then combined with the source and target features of the desired phase to obtain the final source and target features. The attention coefficients are obtained by processing the final source and target features using LeakyReLU. The influence of the remaining oscillators on this oscillator for: ； The `clamp()` function is used to limit... Size; For multi-layer neural networks, high-dimensional feature information is mapped to the state space of each neuron; The projective matrix is ​​a learnable matrix that represents the state variables of node i's neighboring node j. Mapped to a high-dimensional representation space, For multi-head attention coefficients, k represents the number of the attention head; The system training process includes: treating the intelligent coupled dynamics system as a reinforcement learning environment, and using the influence of the other oscillators on the oscillator as the influence of the agent on the i-th unit of the coupled dynamics system for reinforcement learning. Construct an environment reset function to reset the desired phase and initial state of the system at the beginning of each training cycle and output the observations in the initial state of the system. Construct an environment step function to output the next moment's observations and reward function based on the input action. Define the phase relationship to be learned, initialize the trainable parameters and initialize the replay buffer. The trainable parameters include: source matrix and target matrix that project the user-given expected phase difference into source features or target features, source matrix and target matrix that project the system state variables into source features and target features, attention coefficient calculation parameters, and parameters that map the state variables of node i's neighboring node j to a high-dimensional representation space. At the beginning of each training cycle, the desired phase relationship is randomly selected from the phase relationships that need to be learned, and the desired phase and initial state of the system are reset using the environment reset function to obtain the observation value. The agent's actions on the network are obtained using the environment step function, and the next state and reward function are obtained. Store the observation, action, next state, and reward function as a tuple in the replay cache; After each preset reinforcement learning cycle, a batch of tuple data is randomly selected and the parameters are trained using a reinforcement learning algorithm.

2. The oscillator dynamics synchronization control system based on graph attention mechanism according to claim 1, characterized in that, The state of each node is constituted by the internal dynamics of the oscillator and the influence of the other oscillators on the oscillator. Specifically, for any unit in the system, its dynamic differential equation is: the state derivative of the m-dimensional oscillator itself is obtained by adding the effect of the influence of the other oscillators in the system on the oscillator to the internal dynamic equation of the oscillator, which is the input of the oscillator itself.

3. The oscillator dynamics synchronization control system based on graph attention mechanism according to claim 1, characterized in that, The specific effects of the remaining oscillators on this oscillator include: High-dimensional feature information is mapped to the state space of each neuron through a multi-layer neural network, and the size is limited by the clamp() function. The high-dimensional feature information includes a learnable projection matrix and multi-head attention coefficients. The learnable projection matrix is ​​used to map the state variables of neighboring node j to the high-dimensional representation space.

4. The oscillator dynamics synchronization control system based on graph attention mechanism according to claim 1, characterized in that, The system also introduces a proportional-derivative feedback controller to correct the desired phase input of the system based on the real-time waveform. The proportional-derivative feedback controller processes the error between the phase difference between the system output waveform and the desired phase difference, as well as the first derivative of the error, through the gain of the proportional control part and the gain of the derivative control part, and then adds them together. The processed controller output is then integrated into the desired phase for correction.

5. The oscillator dynamics synchronization control system based on graph attention mechanism according to claim 1, characterized in that, The environment reset function takes flattened neuron state quantities and flattened expected phase as inputs. The flattened neuron state quantities include a first component and a second component of the state of each neuron in each oscillator unit. The first component is obtained through a random number generation function, and the second component is the square root of the reward function and the first component. The flattened expected phase includes the expected phase of each neuron state.

6. A synchronization control device for oscillator dynamics based on a graph attention mechanism, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements an oscillator dynamics synchronization control system based on a graph attention mechanism as described in any one of claims 1-5.

7. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements an oscillator dynamics synchronization control system based on a graph attention mechanism as described in any one of claims 1-5.

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