Data-driven end-to-end space flexible tethered multi-agent system modeling and optimal control method

Abstract

The invention particularly relates to an end-to-end spatial flexible tethered multi-agent system modeling and optimal control method based on data driving, which comprises the following steps of: representing a dynamic model of a spatial tethered agent in a spatial flexible tethered multi-agent system by using a data structure of a graph type, and performing parameterization processing; obtaining a graph neural network of the space tethered intelligent agent, and constructing an expression of a corresponding graph neural network dynamic model; based on the Kupman operator theory, configuring the graph neural network as an embedded function thereof, and converting the graph neural network dynamical model into an equivalent dimension raising linear model for representing the dynamical model of the space tethered agent; and designing an optimal controller according to the dimension raising linear model. According to the invention, the data-driven optimal control of the existing space flexible tethered multi-agent is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of space tethered robots, and in particular to a data-driven end-to-end space flexible tethered multi-agent system modeling and optimal control method. Background Art

[0002] In related technologies, space tethered multi-agent systems, such as space tethered robots, space flying net robots, and space tethered formations, are widely used in space attack and defense, ground exploration, and other space tasks due to their wide operating range, high flexibility, and low cost. However, the current modeling methods for flexible space tethered multi-agent systems have the following problems: "Models that accurately describe the dynamic characteristics require a large amount of computation and cannot be designed with controllers for stable control, while models that require a small amount of computation and can be designed with controllers cannot accurately describe the dynamic characteristics." In addition, most existing methods for modeling flexible space multi-agent systems make certain assumptions about the system, which leads to errors between the established dynamic model and the actual physical model, and cannot accurately describe the dynamic characteristics of flexible space tethered multi-agent systems.

[0003] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0004] The present invention provides a data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method, which can achieve a more accurate description of the dynamic characteristics of the spatial flexible tethered multi-agent system, thereby overcoming the defects existing in the existing technology to a certain extent.

[0005] Other features and advantages of the present invention will become apparent from the following detailed description, or may be learned in part by practice of the present invention.

[0006] According to a first aspect of the present invention, a data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method is provided, the method comprising:

[0007] The dynamic model of the space-tethered agent in the space flexible tethered multi-agent system is represented using a graph-type data structure and parameterized to obtain the graph neural network of the space-tethered agent and construct the expression of the corresponding graph neural network dynamic model.

[0008] Based on the Koopman operator theory, a graph neural network is configured as its embedding function to transform the graph neural network dynamics model into an equivalent dimensionality-increasing linear model to represent the dynamics model of the spatial tethered intelligent agent.

[0009] Design optimal controllers based on increasing-dimensional linear models.

[0010] In some exemplary embodiments, the dynamic model of the space-tethered agent in the space flexible tethered multi-agent system is represented using a graph-type data structure and parameterized to obtain a graph neural network of the space-tethered agent, and construct an expression for the corresponding graph neural network dynamic model, including:

[0011] A primitive dynamic model of a space-tethered agent is defined; wherein the space tether configuring the space-tethered agent includes N nodes;

[0012] Graph structure data is configured based on the relationship between the nodes corresponding to the spatial tethers; wherein each node configured with the flexible tether is a node of the graph structure data, the flexible tether relationship between any node and its adjacent nodes is configured as an edge of the graph structure data, and the node state parameters are configured as attributes of the node;

[0013] Defining a graph neural network dynamics model based on graph structure data and constructing a corresponding expression. In some exemplary embodiments, defining a graph neural network dynamics model based on graph structure data and constructing a corresponding expression includes:

[0014]

[0015] in, Nodes representing space tethers; Represents the relationship between nodes.

[0016] In some exemplary embodiments, the method further comprises:

[0017] Configuration node properties are represented as in is the state of node i at time t, and is a vector representing the type of node i;

[0018] Configuration edge attributes are expressed as Among them, m k 、n k Represent the two nodes at both ends of the edge, Indicates the type of edge; 1≤m k , n k ≤N.

[0019] In some exemplary embodiments, the method further comprises:

[0020] According to the message passing mechanism of the graph neural network, configure the node attribute function f O and edge attribute function f R ,include:

[0021]

[0022] Where k = 1, 2, ..., N 2 ; i = 1, 2, ..., N.

[0023] In some exemplary embodiments, the method of configuring a graph neural network as its embedding function based on the Koopman operator theory and converting the graph neural network dynamics model into an equivalent dimensionality-increasing linear model for representing the dynamics model of the spatial tethered intelligent agent includes:

[0024] The node attribute function f O Configured as an embedding function of the Koopman operator;

[0025] Based on the embedding function, the graph neural network dynamics model of node i is configured as follows:

[0026]

[0027] in, represents the embedding function of node i; u i represents the control input; represents the modeling residual; k=1...N 2 , i=1...N;

[0028] According to the graph neural network dynamics model of node i, a dimensional linear model of a spatial tethered agent containing N nodes is configured, which can be expressed as:

[0029]

[0030] in,

[0031]

[0032] In some exemplary embodiments, designing an optimal controller based on a dimensionality-raising linear model includes:

[0033] For the dimensionality-increasing linear model of the dynamics of a space tethered agent, the optimal release control law is designed based on a quadratic optimal regulator.

[0034] In some exemplary embodiments, the design of an optimal release control law based on a quadratic optimal regulator for the dimensionality-increasing linear model of the dynamics of the space-tethered intelligent agent includes:

[0035] Define the optimal control problem of the dimensionality-increasing linear model as:

[0036]

[0037] stz k+1 =Az k +Bu k

[0038] z0=Φ(x0),z d =Φ(x d )

[0039] Among them, Q and R are weight matrices;

[0040] Solve the optimal control problem through dynamic programming method and obtain the control gain K;

[0041] The optimal release control law is determined according to the control gain K, which is expressed as:

[0042]

[0043] According to a second aspect of the present invention, there is provided a computer program product having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method.

[0044] According to a third aspect of the present invention, there is provided an electronic device, comprising:

[0045] A processor and a memory; wherein the memory is used to store executable instructions of the processor; the processor is configured to implement the above-mentioned data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method when executing the executable instructions.

[0046] According to a fourth aspect of the present invention, there is provided a storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method.

[0047] The data-driven, end-to-end spatial flexible tethered multi-agent system modeling and optimal control method provided by the embodiments of the present invention provides a general algorithmic framework for modeling and controlling spatial flexible tethered multi-agent systems. By using a graph neural network to capture the intrinsic motion mechanism of the spatial flexible tether, a more accurate description of the dynamics is achieved. Based on the Koopman operator theory, the graph neural network dynamics used to represent the dynamics of the spatial flexible tethered multi-agent system is explicitly represented as a linear system, and an optimal controller is designed based on this. A more accurate description of the dynamic characteristics of the spatial flexible tethered multi-agent system is achieved.

[0048] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings are incorporated into and constitute a part of this specification, illustrate embodiments consistent with the present invention, and together with the description, serve to explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and it is clear that those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0050] Figure 1 A schematic diagram schematically illustrates a data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method according to an exemplary embodiment of the present invention;

[0051] Figure 2 A schematic diagram schematically illustrates a flexible tether of a space tethered robot discretized into nodes according to an exemplary embodiment of the present invention;

[0052] Figure 3 A schematic diagram schematically illustrates an electronic device according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0053] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0054] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0055] In view of the shortcomings and deficiencies of the existing technology, this example embodiment provides a data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method. Figure 1 As shown, the method may include the following steps:

[0056] Step S11: The dynamic model of the space-tethered agent in the space flexible tethered multi-agent system is represented using a graph-type data structure and parameterized to obtain a graph neural network of the space-tethered agent and construct an expression for the corresponding graph neural network dynamic model.

[0057] Step S12: Based on the Koopman operator theory, a graph neural network is configured as its embedding function to transform the graph neural network dynamics model into an equivalent dimensionality-increasing linear model to represent the dynamics model of the space tethered intelligent agent.

[0058] Step S13: designing an optimal controller based on the dimensionality-increasing linear model.

[0059] Below, the various steps of the data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method in this example implementation will be described in more detail with reference to the accompanying drawings and examples.

[0060] In this example embodiment, the data-driven, end-to-end spatial flexible tethered multi-agent system modeling and optimal control method can be executed by a smart terminal device, or by a server communicating with the smart terminal device; or alternatively, it can be executed collaboratively between the smart terminal device and the server. For example, a user can create an optimization task on a smart terminal device, execute the task locally on the terminal device, and output the optimal controller. Alternatively, the optimization task can be sent to a server, which executes the method and generates the optimal controller.

[0061] In step S11, the dynamic model of the space tethered agent in the space flexible tethered multi-agent system is represented by a graph-type data structure and parameterized to obtain a graph neural network of the space tethered agent and construct an expression for the corresponding graph neural network dynamic model.

[0062] An exemplary space flexible tethered multi-agent system may include: a tether retracting and retracting device mounted on a platform satellite, a space tether, and a capturer. The following embodiments illustrate this solution using a space tethered robot as an example.

[0063] Exemplarily, in the above-mentioned step S11, the dynamic model of the space tethered agent in the space flexible tethered multi-agent system is represented using a graph-type data structure and parameterized to obtain a graph neural network of the space tethered agent, and construct an expression of the corresponding graph neural network dynamic model, including:

[0064] Step S111, defining an original dynamic model of a space-tethered intelligent agent; wherein the space tether configuring the space-tethered intelligent agent includes N nodes;

[0065] Step S112: Graph structure data is configured based on the relationships between the nodes corresponding to the spatial tethers. Each node of the flexible tether is configured as a node of the graph structure data, the flexible tether relationship between any node and its adjacent nodes is configured as an edge of the graph structure data, and the node state parameters are configured as attributes of the node.

[0066] Step S113: define the graph neural network dynamics model based on the graph structure data and construct the corresponding expression.

[0067] Specifically, taking the space tethered robot as an example, we can first use a graph neural network to represent the dynamic model of the space tethered robot.

[0068] Assume that the dynamic equation of the space tethered robot can be expressed as follows:

[0069]

[0070] Among them, f TSR is an unknown nonlinear function.

[0071] With the help of differential thinking, the flexible tether in the space tethered robot can be discretized into N nodes, such as Figure 2 The relationships between nodes can be viewed as nodes and edges in a graph structure, and the state of each node (including position and velocity) can be viewed as a property of the node. In this way, the dynamics of the space tethered robot can be represented by a graph.

[0072] Therefore, for a tethered space robot that has been discretized into N nodes, its dynamic equation at time t can be expressed by a graph neural network G as follows:

[0073]

[0074] in, Nodes representing space tethers; Represents the relationship between nodes.

[0075] Exemplarily, the method further includes:

[0076] Configuration node properties are represented as in is the state of node i at time t, and is a vector representing the type of node i;

[0077] Configuration edge attributes are expressed as Among them, m k 、n k Represent the two nodes at both ends of the edge, Indicates the type of edge; 1≤mk , n k ≤N.

[0078] Specifically, for node attributes, define in is the state of node i at time t, and is a vector representing the type of node i. For edge attributes, define 1≤m k , n k ≤N, where m k and n k represents the two nodes connected by this edge, and is a vector representing the type of edge.

[0079] Exemplarily, the method further includes: configuring the node attribute function f according to the message passing mechanism of the graph neural network O and edge attribute function f R ,include:

[0080]

[0081] Where k = 1, 2, ..., N 2 ; k = 1, 2,…, N.

[0082] Specifically, according to the message passing mechanism of the graph neural network, the above formula (1.3) is used to express the node attribute function f O and edge attribute function f R Among them, the set S i Contains all edges pointing to node i. The above equation is the graph neural network dynamics equation of the space tethered robot, which defines the update equation for each node state. Therefore, the state of each node can be solved by the above equation at every moment.

[0083] In step S12, based on the Koopman operator theory, a graph neural network is configured as its embedding function, and the graph neural network dynamics model is converted into an equivalent dimensionality-increasing linear model to represent the dynamics model of the space tethered intelligent agent.

[0084] Exemplarily, step S12 may specifically include:

[0085] The node attribute function f O Configured as an embedding function of the Koopman operator;

[0086] Based on the embedding function, the graph neural network dynamics model of node i is configured as follows:

[0087]

[0088] in, represents the embedding function of node i; u i represents the control input; represents the modeling residual; k=1...N 2 , i=1...N;

[0089] According to the graph neural network dynamics model of node i, a dimensional linear model of a spatial tethered agent containing N nodes is configured, which can be expressed as:

[0090]

[0091] in,

[0092]

[0093] Specifically, the node attribute function f in formula (1.3) can be defined as O is the embedding function of the Koopman operator. According to the Koopman operator theory, for the graph neural network dynamics model of node i, it can be expressed as formula (1.4).

[0094] For a tethered space robot with N nodes, its graph neural network dynamics model can be expressed as formula (1.5). Among them, the matrix A and matrix B can be defined as:

[0095]

[0096] Consider the following dataset:

[0097]

[0098] The state reconstruction loss function is defined as:

[0099] L recons =||x i -Cz i ||=||x i -CΦ(x i )|| (1.8)

[0100] The multi-step prediction error loss function is defined as:

[0101]

[0102] Here, MSE stands for mean square error.

[0103]

[0104] in, The calculation formula is expressed as:

[0105]

[0106] The loss function for training a graph neural network is defined as:

[0107] L=λ1L recons +λ2L prediction (1.11)

[0108] Among them, λ1 and λ2 are hyperparameters.

[0109] In step S13, a graph neural network dynamics model is defined based on the graph structure data, and a corresponding expression is constructed.

[0110] For example, for the dimensionality-increasing linear model of the dynamics of a space-tethered intelligent agent, an optimal release control law is designed based on a quadratic optimal regulator.

[0111] The optimal control problem for the dimensionality-increasing linear model can be expressed as follows:

[0112]

[0113] Among them, Q and R are weight matrices.

[0114] The above optimal control problem can be solved by dynamic programming and other methods to obtain the control gain K. At this time, the optimal release control law can be expressed as:

[0115]

[0116] The method provided by the present invention is applied to space flexible tethered multi-agent systems such as space tethered robots, space flying net robots, and space tethered formations. An end-to-end data-driven algorithm is proposed for the modeling and control of space flexible tethered multi-agent systems. First, the dynamic equations of the space flexible tethered multi-agent system are represented using a graph-type data structure and parameterized into a graph neural network, and the graph neural network dynamic expression is derived. Subsequently, based on the Koopman operator theory, the graph neural network is regarded as its embedded function, and the graph neural network dynamics is converted into an equivalent dimensionality-increasing linear system, and the optimal controller is designed based on this. In addition, in order to ensure that the dimensionality-increasing linear system model is controllable, the present invention introduces controllability constraints. Unlike existing research methods that use first principles to establish a space flexible tethered multi-agent dynamics model, the algorithm of the present invention uses a data-driven method to establish a dynamics model from the system input and output data and design a controller. A general method for end-to-end data-driven modeling and optimal control is provided.

[0117] It should be noted that the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes illustrated in the above figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0118] It should be noted that, although several modules or units of the device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to an embodiment of the present invention, the features and functions of two or more modules or units described above can be concretized in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided into multiple modules or units to be concretized.

[0119] Figure 3 A schematic diagram of an electronic device suitable for implementing an embodiment of the present invention is shown.

[0120] It should be noted that Figure 3 The electronic device 1000 shown is only an example and should not limit the functions and scope of use of the embodiments of the present invention.

[0121] like Figure 3 As shown, electronic device 1000 includes a central processing unit (CPU) 1001, which can perform various appropriate actions and processes according to the program stored in read-only memory (ROM) 1002 or the program loaded from storage portion 1008 into random access memory (RAM) 1003. Various programs and data required for system operation are also stored in RAM 1003. CPU 1001, ROM 1002 and RAM 1003 are connected to each other via bus 1004. Input / output (I / O) interface 1005 is also connected to bus 1004.

[0122] The following components are connected to the I / O interface 1005: an input section 1006 including a keyboard, a mouse, and the like; an output section 1007 including devices such as a cathode ray tube (CRT), a liquid crystal display (LCD), and a speaker; a storage section 1008 including a hard disk; and a communication section 1009 including a network interface card such as a LAN (Local Area Network) card or a modem. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the I / O interface 1005 as needed. Removable media 1011, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, is installed in the drive 1010 as needed, so that computer programs read from the removable media can be installed in the storage section 1008 as needed.

[0123] In particular, according to an embodiment of the present invention, the process described below with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product that includes a computer program carried on a storage medium, the computer program containing program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 1009 and / or installed from a removable medium 1011. When the computer program is executed by the central processing unit (CPU) 1001, the various functions defined in the system of the present application are performed.

[0124] Specifically, the above-mentioned electronic device can be a computer, a tablet computer or a server device.

[0125] It should be noted that the storage medium shown in the embodiments of the present invention can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or device, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, device, or device. In the present invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any storage medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code contained on the storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, or any suitable combination thereof.

[0126] The flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or a part of code, and the above-mentioned module, program segment, or a part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0127] The units involved in the embodiments of the present invention may be implemented in software or hardware, and the units described may also be provided in a processor. In some cases, the names of these units do not limit the units themselves.

[0128] It should be noted that, as another aspect, the present application also provides a storage medium, which can be included in an electronic device; or it can exist independently without being installed in the electronic device. The above storage medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the method described in the following embodiments. For example, the electronic device can implement the following Figure 1 The individual steps of the method are shown.

[0129] In one embodiment, the present application provides a computer program product, including a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.

[0130] Furthermore, the figures above are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes illustrated in the figures above do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0131] Other embodiments of the present invention will readily occur to those skilled in the art after considering the specification and practicing the invention herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the claims.

[0132] It should be understood that the present invention is not limited to the exact construction described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof, which is limited only by the appended claims.

Claims

1. A data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method, characterized by: The method comprises: The dynamic model of the space-tethered agent in the space flexible tethered multi-agent system is represented using a graph-type data structure and parameterized to obtain the graph neural network of the space-tethered agent and construct the expression of the corresponding graph neural network dynamic model. Based on the Koopman operator theory, a graph neural network is configured as its embedding function to transform the graph neural network dynamics model into an equivalent dimensionality-increasing linear model to represent the dynamics model of the space tethered intelligent agent. Design optimal controllers based on increasing-dimensional linear models.

2. The method according to claim 1, characterized in that The dynamic model of the space tethered agent in the space flexible tethered multi-agent system is represented by a graph-type data structure and parameterized to obtain a graph neural network of the space tethered agent, and construct an expression of the corresponding graph neural network dynamic model, including: A primitive dynamic model of a space-tethered agent is defined; wherein the space tether configuring the space-tethered agent includes N nodes; Graph structure data is configured based on the relationship between the nodes corresponding to the spatial tethers; wherein each node configured with the flexible tether is a node of the graph structure data, the flexible tether relationship between any node and its adjacent nodes is configured as an edge of the graph structure data, and the node state parameters are configured as attributes of the node; Define the graph neural network dynamics model based on graph structure data and construct the corresponding expression.

3. The method according to claim 2, characterized in that Define the graph neural network dynamics model based on graph structure data and construct the corresponding expression, including: in, Nodes representing space tethers; Represents the relationship between nodes.

4. The method according to claim 3, characterized in that The method further comprises: Configuration node properties are represented as in is the state of node i at time t, and is a vector representing the type of node i; Configuration edge attributes are expressed as Among them, m k 、n k Represent the two nodes at both ends of the edge, Indicates the type of edge; 1≤m k , n k ≤N.

5. The method according to claim 4, characterized in that The method further comprises: According to the message passing mechanism of the graph neural network, configure the node attribute function f O and edge attribute function f R ,include: Where k = 1, 2, ..., N 2 ;i=1,2,…,N。 6. The method according to claim 5, characterized in that Based on the Koopman operator theory, the graph neural network is configured as its embedding function to transform the graph neural network dynamics model into an equivalent dimensionality-increasing linear model to represent the dynamics model of the space tethered intelligent agent, including: The node attribute function f O Configured as an embedding function of the Koopman operator; Based on the embedding function, the graph neural network dynamics model of node i is configured as follows: in, represents the embedding function of node i; u i represents the control input; represents the modeling residual; According to the graph neural network dynamics model of node i, a dimensional linear model of a spatial tethered agent containing N nodes is configured, which can be expressed as: in, 7. The method according to claim 1, characterized in that Design an optimal controller based on an ascending-dimensional linear model, including: For the dimensionality-increasing linear model of the dynamics of a space tethered agent, the optimal release control law is designed based on a quadratic optimal regulator.

8. The method according to claim 7, characterized in that The optimal release control law is designed based on a quadratic optimal regulator for the dimensional linear model of the dynamics of the space tethered intelligent body, including: Define the optimal control problem of the dimensionality-increasing linear model as: fire k+1 =The k +Bu k z0=Φ(x0),z d =Φ(x d ) Among them, Q and R are weight matrices; Solve the optimal control problem through dynamic programming method and obtain the control gain K; The optimal release control law is determined according to the control gain K, which is expressed as:

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method according to any one of claims 1 to 8 is implemented.

10. An electronic device, characterized in that: include: processor; a memory storing executable instructions of the processor; The processor is configured to execute the data-driven end-to-end spatial flexible tethered multi-agent system modeling and optimal control method described in any one of claims 1 to 8 by executing the executable instructions.

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