A safety timing synchronization control method, system, device, medium and product of a spacecraft formation

Abstract

The application discloses a spacecraft formation safety timing synchronization control method, system, device, medium and product, relates to the spacecraft formation flight control technical field, and the method comprises the following steps: constructing a spacecraft formation dynamics model; constructing a timing synchronization controller with a weight matrix based on the model and a preset timing synchronization convergence sequence; obtaining the current state information of each follower spacecraft and inputting the controller to obtain a control input instruction; quantizing the control instruction to obtain a digital signal, and then performing encryption authentication processing to obtain ciphertext data and an authentication tag; decrypting and verifying the ciphertext data and the authentication tag and decoding and reconstructing the same to obtain a reconstructed control instruction; and each follower spacecraft executes the reconstructed control instruction to realize safety timing synchronization control. The application realizes the orderly convergence of the spacecraft formation according to priorities, solves the problems of timing coordination, quantization error suppression and communication security guarantee, and improves the flexibility, reliability and safety of the spacecraft formation flight task.

Description

Technical Field

[0001] This application relates to the field of spacecraft formation flight control technology, and in particular to a method, system, device, medium and product for safe timing synchronization control of spacecraft formations. Background Technology

[0002] With the rapid development of aerospace technology, spacecraft formation flying has become an important means of space exploration and mission execution. In formation flying, multiple spacecraft move in a coordinated manner with specific geometric configurations to jointly complete various complex space missions, such as space exploration, Earth observation, and on-orbit servicing. Formation flying can improve mission efficiency, reduce energy consumption, and increase accuracy. Therefore, spacecraft formation flying technology has become an important direction for the development of space science and technology.

[0003] In practical applications such as emergency braking, spacecraft formation operations, and space observation, the system state needs to converge to an equilibrium point rapidly within a finite time. Traditional asymptotic stability control methods cannot meet this requirement. Most finite-time control methods emphasize the overall convergence behavior of the system while neglecting the temporal coordination between state components. In more complex formation missions, spacecraft not only need to reach the target state but also need to follow a specific temporal sequence. Traditional finite-time and time-synchronization control theories mainly emphasize simultaneous convergence and lack the ability to flexibly configure the convergence order of state components. Furthermore, during spacecraft formation flight, information exchange relies on wireless communication networks. Continuous system states or control commands must be encoded into digital form before transmission. To efficiently reduce bandwidth consumption, quantization is typically employed. However, quantization introduces quantization errors, which, if not properly handled, can reduce control accuracy and even jeopardize system stability. Simultaneously, the communication network of spacecraft formation flight systems is vulnerable. If the communication network is damaged, communication information may be leaked or forged, leading to mission failure and system security issues.

[0004] Therefore, there is an urgent need for a safe timing synchronization control method for spacecraft formations to solve the technical problems of simultaneously achieving sequential convergence of state components, suppression of quantization errors, and assurance of communication security, thereby improving the flexibility, reliability, and safety of spacecraft formation flight missions. Summary of the Invention

[0005] The purpose of this application is to provide a safe timing synchronization control method, system, device, medium and product for spacecraft formations. In a communication environment where limited bandwidth and network threats coexist, it can achieve synchronous convergence of various state components of spacecraft formations in a preset order within a limited time, while ensuring the security, integrity and authenticity of communication data, effectively suppressing the accumulation of quantization errors, and improving the flexibility, reliability and robustness of spacecraft formation flight missions.

[0006] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a method for safe timing synchronization control of spacecraft formations, including: A spacecraft formation dynamics model is constructed based on dynamic equations; the spacecraft formation dynamics model includes a lead spacecraft dynamics model and multiple follower spacecraft dynamics models. Based on the spacecraft formation dynamics model and a preset timing synchronization convergence sequence, a timing synchronization controller with a weight matrix is ​​constructed; the preset timing synchronization convergence sequence is used to represent the convergence priority of each following spacecraft. Obtain the current status information of each follower spacecraft; the current status information includes the relative position vector and relative velocity vector with respect to the lead spacecraft. The current status information of each follower spacecraft is input into the timing synchronization controller to obtain the control input commands for each follower spacecraft. The control input commands of each follower spacecraft are quantized to obtain the quantized digital control signals corresponding to the control input commands of each follower spacecraft. The quantized digital control signals corresponding to the control input commands of each follower spacecraft are encrypted and authenticated to obtain the control ciphertext data and authentication tags of each follower spacecraft. The control ciphertext data and authentication tags corresponding to each follower spacecraft are decrypted and verified to obtain the decrypted quantized digital control signals corresponding to each follower spacecraft. The decrypted quantized digital control signals corresponding to each follower spacecraft are decoded and reconstructed to obtain the reconstructed control input commands for each follower spacecraft. Each follower spacecraft executes its corresponding reconfiguration control input command to achieve safe timing synchronization control of the spacecraft formation.

[0007] Secondly, this application provides a safe timing synchronization control system for spacecraft formations, comprising: A dynamics model construction module is used to construct a spacecraft formation dynamics model based on dynamics equations; the spacecraft formation dynamics model includes a lead spacecraft dynamics model and multiple follower spacecraft dynamics models. A timing synchronization controller construction module is used to construct a timing synchronization controller with an introduced weight matrix based on a spacecraft formation dynamics model and a preset timing synchronization convergence sequence; the preset timing synchronization convergence sequence is used to represent the convergence priority of each following spacecraft. The status information acquisition module is used to acquire the current status information of each follower spacecraft; the current status information includes the relative position vector and relative velocity vector with respect to the lead spacecraft. The control command generation module is used to input the current status information of each follower spacecraft into the timing synchronization controller to obtain the control input commands for each follower spacecraft. The quantization processing module is used to quantize the control input commands of each follower spacecraft to obtain the quantized digital control signals corresponding to the control input commands of each follower spacecraft. The encryption and authentication processing module is used to perform encryption and authentication processing on the quantized digital control signals corresponding to the control input commands of each follower spacecraft, so as to obtain the control ciphertext data and authentication tags of each follower spacecraft. The decryption and verification processing module is used to decrypt and verify the control ciphertext data and authentication tags corresponding to each follower spacecraft, and obtain the decrypted quantized digital control signal corresponding to each follower spacecraft. The decoding and reconstruction module is used to decode and reconstruct the decrypted quantized digital control signals corresponding to each follower spacecraft to obtain the reconstruction control input commands for each follower spacecraft. The control execution module is used by each following spacecraft to execute the corresponding reconfiguration control input commands, thereby achieving safe timing synchronization control of the spacecraft formation.

[0008] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the safe timing synchronization control method for spacecraft formations described in any one of the above-described methods.

[0009] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the spacecraft formation safe timing synchronization control method described in any one of the above descriptions.

[0010] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the safe timing synchronization control method for spacecraft formations described in any one of the above-described methods.

[0011] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method, system, device, medium, and product for secure timing synchronization control of spacecraft formations. By constructing a timing synchronization controller with a weighted matrix based on a spacecraft formation dynamics model and a preset timing synchronization convergence sequence, the current state information of each following spacecraft is input into the timing synchronization controller to obtain control input commands for each following spacecraft. This solves the technical problem of the inability to flexibly configure the convergence order of state components, achieving synchronous convergence of each state component of the spacecraft formation in a preset order within a finite time, thus improving the flexibility and adaptability of formation flight missions. By quantizing the control input commands of each following spacecraft to obtain quantized digital control signals, and then decoding and reconstructing these signals, the error accumulation problem introduced during quantization is solved, achieving bounded control of quantization errors under limited bandwidth communication conditions, ensuring control accuracy and system stability. By encrypting and authenticating the quantized digital control signals to generate ciphertext data and authentication tags, and then decrypting and verifying these ciphertext data and authentication tags, the security threats faced by wireless communication networks during spacecraft formation flight are solved, ensuring the security, integrity, and authenticity of communication data, and improving the safety of formation flight missions. In summary, this application achieves sequential convergence of state components, suppression of quantization errors, and assurance of communication security in a communication environment where limited bandwidth and network security coexist, effectively improving the flexibility, reliability, and robustness of spacecraft formation flight missions. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 A flowchart illustrating a safe timing synchronization control method for spacecraft formations provided in an embodiment of this application; Figure 2 A flowchart illustrating a safe timing synchronization control method for spacecraft formations, provided as another embodiment of this application; Figure 3 A communication topology diagram of a spacecraft formation provided in one embodiment of this application; Figure 4 A target trajectory diagram of a spacecraft formation provided in one embodiment of this application; Figure 5 A schematic diagram illustrating decoding errors of a follower spacecraft in a spacecraft formation, provided as an embodiment of this application; wherein, Figure 5 (a) represents a schematic diagram of the decoding error following spacecraft 1; Figure 5 (b) represents a schematic diagram of the decoding error following spacecraft 2; Figure 5 (c) represents a schematic diagram of the decoding error following spacecraft 3; Figure 6 A schematic diagram of the tracking trajectory error of a following spacecraft in a spacecraft formation is provided as an embodiment of this application; Figure 7 A schematic diagram illustrating the convergence rate of consistency error of a following spacecraft in a spacecraft formation, provided as an embodiment of this application; Figure 8 A schematic diagram of the control force curve provided in an embodiment of this application; Figure 9 A functional module diagram of a spacecraft formation safety timing synchronization control system provided in an embodiment of this application; Figure 10 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0014] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0015] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] In one exemplary embodiment, such as Figure 1 As shown, a method for safe timing synchronization control of spacecraft formations is provided, including the following steps 201 to 209. Wherein: Step 201: Construct a spacecraft formation dynamics model based on the dynamic equations; the spacecraft formation dynamics model includes a lead spacecraft dynamics model and multiple follower spacecraft dynamics models.

[0017] Step 202: Based on the spacecraft formation dynamics model and the preset timing synchronization convergence sequence, a timing synchronization controller with an introduced weight matrix is ​​constructed; the preset timing synchronization convergence sequence is used to represent the convergence priority of each following spacecraft.

[0018] Step 203: Obtain the current status information of each following spacecraft; the current status information includes the relative position vector and relative velocity vector with respect to the lead spacecraft.

[0019] Step 204: Input the current status information of each follower spacecraft into the timing synchronization controller to obtain the control input commands for each follower spacecraft.

[0020] Step 205: Quantize the control input commands of each follower spacecraft to obtain the quantized digital control signals corresponding to the control input commands of each follower spacecraft.

[0021] Step 206: Encrypt and authenticate the quantized digital control signals corresponding to the control input commands of each follower spacecraft to obtain the control ciphertext data and authentication tags of each follower spacecraft.

[0022] Step 207: Decrypt and verify the control ciphertext data and authentication tags corresponding to each follower spacecraft to obtain the decrypted quantized digital control signal corresponding to each follower spacecraft.

[0023] Step 208: Decode and reconstruct the decrypted quantized digital control signals corresponding to each follower spacecraft to obtain the reconstructed control input commands for each follower spacecraft.

[0024] Step 209: Each following spacecraft executes its corresponding reconfiguration control input command to achieve safe timing synchronization control of the spacecraft formation.

[0025] By implementing steps 201 to 209 above, this application solves the problem of unadjustable convergence order by constructing a timing synchronization controller with an introduced weight matrix, achieving synchronous convergence within a finite time according to a preset order. Through a collaborative mechanism of quantization processing and decoding reconstruction, it solves the problem of quantization error accumulation, ensuring control accuracy and system stability under limited bandwidth communication conditions. Furthermore, through a collaborative mechanism of encryption authentication processing and decryption verification processing, it addresses the security threats faced by wireless communication networks, ensuring the security, integrity, and authenticity of communication data. In a communication environment where limited bandwidth and network security coexist, this application simultaneously achieves sequential convergence of state components, quantization error suppression, and communication security assurance, effectively improving the flexibility, reliability, and robustness of spacecraft formation flight missions.

[0026] In another exemplary embodiment of this application, the following spacecraft dynamics model is: .

[0027] in, This represents the relative acceleration vector of the i-th follower spacecraft relative to the lead spacecraft; This represents the relative velocity vector of the i-th follower spacecraft relative to the lead spacecraft; This represents the relative position vector of the i-th follower spacecraft relative to the lead spacecraft; , and These represent the first, second, and third coefficient matrices, respectively, related to the orbit of the pilot spacecraft. This represents the control input for the i-th following spacecraft.

[0028] In another exemplary embodiment of this application, a timing synchronization controller incorporating a weight matrix is ​​constructed based on a spacecraft formation dynamics model and a preset timing synchronization convergence sequence, specifically including: Based on the spacecraft formation dynamics model and a pre-set time-series synchronous convergence sequence, the sliding mode surface function is constructed using the following formula: .

[0029] .

[0030] .

[0031] in, Let i represent the sliding surface function of the i-th following spacecraft in the j-axis direction. j=x represents the x-axis of the orbital coordinate system, j=y represents the y-axis of the orbital coordinate system, and j=z represents the z-axis of the orbital coordinate system. express The derivative; This represents the weighted tracking error of the i-th following spacecraft along the j-axis. This represents the communication weight between the i-th follower spacecraft and the lead spacecraft. Represents the desired trajectory coupling coefficient of the i-th following spacecraft; This represents the relative position of the i-th following spacecraft with respect to the lead spacecraft along the j-axis. Let represent the desired trajectory of the i-th spacecraft along the j-axis. This represents the sliding mode auxiliary term for the i-th spacecraft along the j-axis. Let represent the weight matrix of the i-th following spacecraft along the j-axis. Indicates the first nonlinear power parameter; Represents a symbolic function; Indicates the second nonlinear power parameter; Let represent the sliding surface state variable of the i-th following spacecraft in the j-axis direction; Indicates the segment switching threshold; and These represent the nonlinear convergence rate adjustment coefficient and the linear convergence rate adjustment coefficient, respectively. and These represent the nonlinear chattering suppression coefficient and the linear chattering suppression coefficient, respectively.

[0032] Based on the sliding mode surface function, a timing synchronization controller is constructed using the following formula: .

[0033] in, This represents the control input of the i-th following spacecraft along the j-axis. Let represent the input gain matrix of the i-th following spacecraft along the j-axis. This represents the system dynamics term for the i-th spacecraft along the j-axis. Indicates proportional control gain; The exponential parameter represents the first type of nonlinear term; Indicates higher-order control gain; The exponential parameter represents the second type of nonlinear term; express The derivative; Let represent the second derivative of the desired trajectory of the i-th spacecraft along the j-axis.

[0034] In another exemplary embodiment of this application, the control input commands of each follower spacecraft are quantized to obtain quantized digital control signals corresponding to the control input commands of each follower spacecraft, specifically including: The control input commands for each follower spacecraft are quantized using the following expressions to obtain the quantized digital control signals corresponding to the control input commands for each follower spacecraft: .

[0035] .

[0036] in, Let k be the quantized digital control signal of the i-th following spacecraft along the j-axis; This represents a uniform quantizer; This represents the control input of the i-th following spacecraft along the j-axis at time k; This represents the internal state of the uniform quantizer at time k-1 in the j-axis direction of the i-th following spacecraft. The dynamic scaling factor at time k-1 is represented. This represents the internal state of the uniform quantizer at time k-2 on the j-axis direction of the i-th following spacecraft, and the initial internal state of the uniform quantizer on the j-axis direction of the i-th following spacecraft. ; The dynamic scaling factor at time k-2; Let be the quantized digital control signal of the i-th following spacecraft in the j-axis direction at time k-1.

[0037] In another exemplary embodiment of this application, the quantized digital control signals corresponding to the control input commands of each follower spacecraft are encrypted and authenticated to obtain the control ciphertext data and authentication tags of each follower spacecraft, specifically including: Based on the preset encryption key, preset initialization vector, and additional authentication data, the AES-GCM authentication encryption algorithm is used to encrypt and authenticate the quantized digital control signals corresponding to the control input commands of each follower spacecraft, thereby obtaining the control ciphertext data and authentication tags of each follower spacecraft.

[0038] In another exemplary embodiment of this application, the control ciphertext data and authentication tags corresponding to each follower spacecraft are decrypted and verified to obtain the decrypted quantized digital control signal corresponding to each follower spacecraft, specifically including: Each accompanying spacecraft undergoes decryption and verification processing through the following steps: Based on the preset encryption key, preset initialization vector, and additional authentication data, the local authentication tag following the spacecraft is calculated.

[0039] If the authentication tag matches the local authentication tag, the AES-GCM decryption algorithm is used to decrypt the control ciphertext data corresponding to the spacecraft based on the preset encryption key and preset initialization vector, and the decrypted quantized digital control signal is obtained.

[0040] If the authentication tag does not match the local authentication tag, the control encrypted data and authentication tag corresponding to the spacecraft are discarded.

[0041] The following example illustrates this application using a specific spacecraft formation safety timing synchronization control process.

[0042] This application addresses the communication environment of formation flying, where limited bandwidth and security risks coexist. It discloses a secure timing synchronization control method for spacecraft formation flying, providing an integrated approach combining timing synchronization control, dynamic uniform quantization, and AES-GCM (Advanced Encryption Standard-Galois / Counter Mode) encryption. The method configures the convergence order of each state component using a weight matrix and constructs a finite-time sliding mode control law. The transmitting end performs incremental quantization encoding with a dynamic scaling factor, and the receiving end decodes and reconstructs the data. The quantized data is then authenticated and encrypted using AES-GCM, forming a secure and verifiable link. This achieves: 1) significantly reducing communication bits and suppressing error accumulation at a given accuracy; 2) ensuring security and integrity simultaneously through authentication encryption; and 3) achieving finite-time synchronization convergence under a preset timing sequence and adapting to communication conditions. Specifically, firstly, a timing synchronization controller is designed for each following spacecraft. By introducing a weight matrix to configure the convergence order of each state component, control commands are generated to ensure finite-time convergence according to a preset sequence. Next, before command transmission, the control signal is compressed using a dynamic uniform quantizer, and then the quantized data is encrypted and authenticated using the AES-GCM encryption algorithm to ensure the security and integrity of communication. Subsequently, the encrypted data is transmitted to each spacecraft via a wireless channel; the receiving end decrypts and verifies the data, and then uses the corresponding decoder to accurately reconstruct the original control signal. Finally, each spacecraft executes the reconstructed control commands, achieving synchronous convergence of all spacecraft states to the target trajectory according to a predetermined sequence while ensuring communication security, thus completing the formation flight mission.

[0043] like Figure 2 As shown, this application provides a safe timing synchronization control method for spacecraft formation flight, specifically including the following steps: Step 1, System Modeling and Timing Synchronization Convergence Definition: First, establish a formation system model containing one lead spacecraft and N follower spacecraft. Considering the relative motion of the spacecraft in an elliptical orbit, the dynamic model of the follower spacecraft is as follows: .

[0044] in, This represents the relative acceleration vector of the i-th follower spacecraft relative to the lead spacecraft; This represents the relative velocity vector of the i-th follower spacecraft relative to the lead spacecraft; This represents the relative position vector of the i-th follower spacecraft relative to the lead spacecraft; , and Let represent the first coefficient matrix, the second coefficient matrix, and the third coefficient matrix, respectively, related to the orbit of the pilot spacecraft. This represents the control input for the i-th following spacecraft. The lead spacecraft operates along an elliptical orbit, and its trajectory is a known reference trajectory.

[0045] To achieve ordered convergence of the state components (following the spacecraft), a pre-defined timing synchronization convergence sequence is introduced. : .

[0046] in, and These represent the convergence priorities of the 1st and nth follower spacecraft, respectively, where n represents the total number of follower spacecraft. This indicates transpose.

[0047] Step 2: Design a weighted sliding surface and a timing synchronization control law. To achieve the timing synchronization convergence defined in Step 1, a sliding surface with an introduced weight matrix is ​​designed. This sliding surface is defined as a combination of the weighted function of the tracking error and its derivative: .

[0048] in, Let i represent the sliding surface function of the i-th following spacecraft in the j-axis direction. j=x represents the x-axis of the orbital coordinate system, j=y represents the y-axis of the orbital coordinate system, and j=z represents the z-axis of the orbital coordinate system. express The derivative; The weighted tracking error of the i-th following spacecraft along the j-axis is defined as follows: ;; This represents the communication weight between the i-th follower spacecraft and the lead spacecraft. Represents the desired trajectory coupling coefficient of the i-th following spacecraft; This represents the relative position of the i-th following spacecraft with respect to the lead spacecraft along the j-axis. This represents the desired trajectory of the i-th spacecraft along the j-axis. The orbital coordinate system is constructed with the x-axis along the Earth's center, the y-axis along the direction of orbital motion, and the z-axis perpendicular to the orbital plane.

[0049] This represents the sliding mode assistance term for the i-th spacecraft along the j-axis, and its specific form is: .

[0050] in, This represents the weight matrix of the i-th following spacecraft along the j-axis. , is a diagonal weight matrix, whose elements are configured according to the time-series convergence sequence S. Let represent the weights of the i-th following spacecraft in the x-axis direction, the y-axis direction, and the z-axis direction, respectively. Indicates the first nonlinear power parameter; Represents a symbolic function; Indicates the second nonlinear power parameter; Let represent the sliding surface state variable of the i-th following spacecraft in the j-axis direction; Indicates the segment switching threshold. ; and These represent the nonlinear convergence rate adjustment coefficient and the linear convergence rate adjustment coefficient, respectively. and These represent the nonlinear chattering suppression coefficient and the linear chattering suppression coefficient, respectively. All are positive constants. Therefore, it can be seen that the convergence speed and convergence order of each state component are determined by the corresponding axial weights. Individual adjustment. Based on this sliding surface, a finite-time timing synchronization control law is constructed: .

[0051] in, This represents the control input of the i-th following spacecraft along the j-axis. Let represent the input gain matrix of the i-th following spacecraft along the j-axis. express The inverse matrix; This represents the system dynamics term for the i-th spacecraft along the j-axis. Indicates proportional control gain; The exponential parameter represents the first type of nonlinear term; Indicates higher-order control gain; The exponential parameter represents the second type of nonlinear term; express The derivative; Let represent the second derivative of the desired trajectory of the i-th spacecraft along the j-axis. This control law is expressed through a weight matrix. By adjusting the convergence rate of different state channels, the system states are forced to converge sequentially according to a preset sequence S, while ensuring the global finite-time stability of the system.

[0052] Step 3: Construct a dynamic encoding-decoding quantization mechanism. To achieve efficient and reliable transmission of system status or control commands in digital communication networks and to suppress the cumulative effect of quantization errors, a dynamic encoding-decoding mechanism is constructed. The dynamic process at the transmitting end (encoder) is described as follows: .

[0053] .

[0054] in, Let k be the quantized digital control signal of the i-th following spacecraft along the j-axis; This indicates a uniform quantizer with a fixed sensitivity. This represents the control input of the i-th following spacecraft along the j-axis at time k; This represents the internal state of the uniform quantizer at time k-1 in the j-axis direction of the i-th following spacecraft. This represents the dynamic scaling factor at time k-1, and the dynamic scaling factor is greater than 0. This represents the internal state of the uniform quantizer at time k-2 on the j-axis direction of the i-th following spacecraft, and the initial internal state of the uniform quantizer on the j-axis direction of the i-th following spacecraft. ; The dynamic scaling factor at time k-2; Let be the quantized digital control signal of the i-th following spacecraft in the j-axis direction at time k-1.

[0055] Step 4: Design the AES-GCM encryption algorithm. To protect inter-spacecraft communication data from unauthorized access and data forgery, the AES-GCM authentication encryption algorithm is integrated after quantization encoding to securely process the data. The encryption process inputs include: plaintext P (quantized digital control signal), a preset encryption key K, a preset initialization vector IV, and additional authentication data A. The encryption outputs are control ciphertext data C and an authentication tag T. The encryption process can be formally described as follows: .

[0056] Where H represents the hash subkey; This represents the AES encryption function; Indicates the initial counter block; Indicates the concatenation operator; This represents the length function used to calculate the bit length of the data; This represents the GCM authentication hash function; Represents a set of empty data blocks; Indicates the first One counter block; This represents the increment function of the counter; m represents the total number of counter blocks; Indicates the first One counter block; Indicates the first One encrypted data block; Indicates the first One plaintext data block; This indicates a bitwise XOR operation; This represents the m-th ciphertext data block; This represents the m-th plaintext data block; Indicates taking the highest value Bit; This represents the m-th counter block; This means taking the highest t bits (t is the length of the authentication tag). Let i be the AES encryption function that follows the spacecraft along the j-axis. This represents the quantized digital control signal of the i-th following spacecraft along the j-axis at time k. enter The resulting encrypted quantized digital control signal.

[0057] Step 5: When decrypting, each follower spacecraft first uses the same preset encryption key, preset initialization vector and additional authentication data to calculate the local authentication tag T′, and compares it with the received T.

[0058] If a match is found, the AES-GCM decryption algorithm is used to decrypt the control ciphertext data corresponding to the following spacecraft based on the preset encryption key and preset initialization vector, obtaining the decrypted quantized digital control signal; otherwise, it is determined to be a transmission error or unauthorized operation, and the data packet is discarded. This step ensures the security, integrity, and authenticity of the communication data.

[0059] Step 6: The receiver (decoder) of each follower encoder uses the received quantized digital control signal. Reconfigure control input : .

[0060] in, Let k represent the reconstructed control input of the i-th following spacecraft along the j-axis at time k. This mechanism ensures that the reconstruction error is minimized through recursive updates and dynamic scaling of the internal state. Boundedness effectively avoids the error accumulation problem that may be caused by traditional fixed-parameter quantizers in closed-loop control.

[0061] Step 7: System stability verification and closed-loop control implementation. The finite-time synchronous convergence characteristics of the proposed control method are verified using Lyapunov stability theory. First, for the i-th sliding mode variable following the spacecraft in the j-axis direction... Choosing Lyapunov functions Substituting into the control law, it can be proven that its derivative satisfies: .

[0062] in, express The derivative; Let Lyapunov function be the sliding surface of the i-th spacecraft following the j-axis.

[0063] According to the finite-time stability theory, this indicates that sliding mode variables It can converge to zero within a finite time. When the system state reaches the sliding surface... Subsequently, the tracking error dynamics were determined by Definition. The Lyapunov function representing the tracking error of the i-th following spacecraft along the j-axis. This can prove the tracking error. It can converge to zero within a finite time, and because it satisfies the weighted ratio persistence condition, each state component converges strictly according to the preset time-series convergence sequence S. Finally, combined with a secure communication link, a complete closed-loop secure time-series synchronization control system is formed.

[0064] In summary, this application achieves the synchronous convergence of multiple spacecraft state components in a predetermined order within a finite time by introducing a weighted timing synchronization control law, a dynamic encoding-decoding quantization mechanism, and the AES-GCM secure communication algorithm, while ensuring the security and integrity of the communication data.

[0065] In an exemplary embodiment, firstly, a formation system comprising a lead spacecraft and three follower spacecraft is designed, with a star-shaped communication topology. The lead spacecraft is responsible for information aggregation and encrypted broadcasting, while the follower spacecraft communicate only with the lead spacecraft and do not interconnect with each other. Figure 3 As shown, a communication topology diagram of a spacecraft formation is provided; as Figure 4 The diagram shows a target trajectory for a spacecraft formation. The specific implementation process is as follows: Step (1) System Modeling and Formation Structure Establishment. In this embodiment, a lead spacecraft L and three follower spacecraft F1, F2, and F3 are set. Each spacecraft moves along an elliptical orbit, and the dynamic equation is expressed as follows: Furthermore, the above formula can be rearranged into an affine form commonly used in controller design: ,in, , To control the input vector, The input matrix is ​​denoted as Matrix A, B, and C, which are determined by the reference orbital parameters and are used to express the Coriolis effect, gravity term, and other equivalent effects.

[0066] Step (2) Design the weighted sliding surface and timing synchronization control law. This is achieved by defining the tracking error and its derivative. Construction of sliposome surface Weight matrix According to the preset timing convergence sequence, different state components converge sequentially. Based on this sliding surface, a control law is constructed: This control law enables the system to achieve synchronous stability within a finite time frame according to a preset timing sequence. The preset timing convergence sequence is as follows: first, the three followers converge simultaneously along the z-axis, and then converge in the x and y directions in the order of Follower3→Follower2→Follower1. The convergence weight matrix is: .

[0067] Step (3) Constructing a dynamic encoding-decoding quantization mechanism. To achieve high-precision transmission of control commands under limited bandwidth conditions, this embodiment adopts a dynamic uniform quantization strategy. Encoding end Decoding end: The quantization error is less than 1 / 2, ensuring the boundedness of signal transmission error and closed-loop stability.

[0068] Step (4) Design the AES-GCM encrypted communication mechanism. After quantization encoding, the transmitted data is authenticated and encrypted using the AES-GCM algorithm. The input includes plaintext P (quantized digital control signal), preset encryption key K, preset initialization vector IV, and additional authentication data A. The encrypted output is control ciphertext data C and authentication tag T. The receiving end completes the integrity verification by calculating tag T and comparing it with T. If they match, the data is decrypted and recovered; otherwise, it is discarded, ensuring data security and integrity.

[0069] Step (5) Formation control process and verification. To verify the control effect, the initial position is set as follows: .

[0070] The reference trajectory is generated using a two-stage Bézier curve: .

[0071] in, Let represent the expected trajectory of the i-th spacecraft at time k along the j-axis. This represents the normalized time parameter. These represent the starting control point, intermediate control point, and ending control point of the Bézier curve, respectively. This indicates the expected trajectory generation switching time. The three follower spacecraft launch from different initial orbits and eventually converge near the lead spacecraft to form a stable formation. For example... Figure 5 The diagram illustrates the decoding error of a following spacecraft in a spacecraft formation; wherein, Figure 5 (a) represents a schematic diagram of the decoding error of spacecraft 1 (F1); Figure 5 (b) represents a schematic diagram of the decoding error of the following spacecraft 2 (F2); Figure 5 (c) represents a schematic diagram of the decoding error of spacecraft 3 (F3). , and These represent the decoding errors of the x-axis, y-axis, and z-axis in the orbital coordinate system, respectively. Figure 6 A schematic diagram illustrating the tracking trajectory error of a spacecraft following another in a spacecraft formation is provided. These represent the tracking trajectory errors of spacecraft F1 along the x-axis, y-axis, and z-axis, respectively. These represent the tracking trajectory errors of spacecraft F2 along the x-axis, y-axis, and z-axis, respectively. These represent the tracking trajectory errors of spacecraft F3 along the x, y, and z axes, respectively; Figure 6 It can be seen that the error converges to zero within a finite amount of time; Figure 7 A schematic diagram illustrating the convergence rate of consistency error of following spacecraft in a spacecraft formation is provided. These represent the consistency errors of the following spacecraft F1 along the x, y, and z axes, respectively. These represent the consistency errors of the F2 spacecraft along the x, y, and z axes, respectively. These represent the consistency errors of the F3 spacecraft along the x, y, and z axes, respectively. Figure 7 This indicates that each state component converges in the order of Z-axis → X-axis, Y-axis, achieving the predetermined timing synchronization; Figure 8 A schematic diagram of the control force curve is provided. These represent the control forces following spacecraft F1 along the x-axis, y-axis, and z-axis, respectively. These represent the control forces following spacecraft F2 along the x-axis, y-axis, and z-axis, respectively. These represent the control forces along the x, y, and z axes of the spacecraft F3, respectively; (The rest of the text appears to be a fragment and requires further context for accurate translation.) Figure 8 It can be seen that the change in control force is smooth and without abrupt changes, indicating that the system is stable and reliable.

[0072] Based on the same inventive concept, this application also provides a spacecraft formation safety timing synchronization control system for implementing the aforementioned spacecraft formation safety timing synchronization control method. The solution provided by this system is similar to the implementation scheme described in the above method; therefore, the specific limitations of one or more spacecraft formation safety timing synchronization control system embodiments provided below can be found in the limitations of the spacecraft formation safety timing synchronization control method described above, and will not be repeated here.

[0073] In one exemplary embodiment, such as Figure 9 As shown, a safe timing synchronization control system for spacecraft formations is provided, comprising: The dynamic model construction module 301 is used to construct a spacecraft formation dynamic model based on dynamic equations; the spacecraft formation dynamic model includes a lead spacecraft dynamic model and multiple follower spacecraft dynamic models.

[0074] The timing synchronization controller construction module 302 is used to construct a timing synchronization controller with a weight matrix based on the spacecraft formation dynamics model and a preset timing synchronization convergence sequence; the preset timing synchronization convergence sequence is used to represent the convergence priority of each following spacecraft.

[0075] The status information acquisition module 303 is used to acquire the current status information of each following spacecraft; the current status information includes the relative position vector and relative velocity vector with respect to the lead spacecraft.

[0076] The control command generation module 304 is used to input the current status information of each follower spacecraft into the timing synchronization controller to obtain the control input commands for each follower spacecraft.

[0077] The quantization processing module 305 is used to quantize the control input commands of each follower spacecraft to obtain the quantized digital control signals corresponding to the control input commands of each follower spacecraft.

[0078] The encryption and authentication processing module 306 is used to perform encryption and authentication processing on the quantized digital control signals corresponding to the control input commands of each follower spacecraft, so as to obtain the control ciphertext data and authentication tags of each follower spacecraft.

[0079] The decryption and verification processing module 307 is used to decrypt and verify the control ciphertext data and authentication tags corresponding to each follower spacecraft, and obtain the decrypted quantized digital control signal corresponding to each follower spacecraft.

[0080] The decoding and reconstruction module 308 is used to decode and reconstruct the decrypted quantized digital control signals corresponding to each follower spacecraft to obtain the reconstruction control input commands for each follower spacecraft.

[0081] The control execution module 309 is used for each following spacecraft to execute the corresponding reconfiguration control input command to achieve safe timing synchronization control of the spacecraft formation.

[0082] In another exemplary embodiment of this application, a safe timing synchronization control system for spacecraft formations is provided, comprising: Timing Synchronization Control Module: This module, by introducing a weight matrix, can flexibly adjust the convergence order of different state components. Specifically, it designs a time-series synchronization controller based on finite-time stability theory. By adjusting the parameters in the weight matrix, it precisely controls the convergence rate of each state component, thereby achieving synchronous convergence in a predetermined order. In complex aerospace mission scenarios, this module can ensure that the spacecraft completes its mission in a specific time sequence, significantly improving mission flexibility and reliability. This module meets the requirements of finite-time stability and enhances the adaptability of the control strategy through flexible configuration of the weight matrix.

[0083] As an optional implementation, the timing synchronization control module specifically includes: A timing synchronization controller based on sliding mode control is constructed. This controller includes a configurable weight matrix, which adjusts the convergence order of different state components by changing the numerical relationships of the diagonal elements in the weight matrix. The convergence order of each state component is preset according to task requirements, mapping the convergence order to the relative magnitudes of the elements in the weight matrix. State components with larger weights converge first, while state components with the same weight converge simultaneously. The controller combines standard and normalized sign functions to construct a piecewise continuous sliding surface function, ensuring that the system state stabilizes to the equilibrium point within a finite time according to the preset convergence sequence. The finite-time stability of the system is proven using Lyapunov stability theory, and the upper bound of the convergence time for each state component is calculated.

[0084] In this implementation, when two state components are set to converge simultaneously, the diagonal elements of their corresponding weight matrices have equal values; when one state component is required to converge before the other, a larger weight value is assigned to it; the values ​​of the weight matrix are designed offline or adjusted online according to the requirements of the state convergence order in the actual task.

[0085] Secure Communication Module: To ensure the security of communication between spacecraft, this invention proposes a secure communication module that combines a dynamic uniform quantization strategy with an AES-GCM encryption mechanism. During information transmission, the data is first processed using a dynamic uniform quantizer to adapt to the requirements of the digital communication channel. Subsequently, the AES-GCM algorithm is used to encrypt and authenticate the quantized data, thereby ensuring the security of transmitted control commands and status information during communication. The AES-GCM algorithm is widely used in high-security communication scenarios due to its efficient encryption performance and strong authentication capabilities. Through this encryption mechanism, even if the communication network suffers unauthorized interception and data forgery, the communication information can be effectively protected, thus ensuring the safe execution of spacecraft formation flight missions.

[0086] As an optional implementation, the secure communication module specifically includes: The dynamic uniform quantizer is used to preprocess the continuous state signals and control commands that need to be transmitted, converting the continuous amplitude signals into discrete digital signals of a finite level to meet the transmission requirements of digital communication channels. The quantized data is then sent to the AES-GCM encryption and authentication unit.

[0087] The AES-GCM encryption authentication unit is used to encrypt data using a preset encryption key and initialization vector to generate corresponding ciphertext data; at the same time, it calculates an authentication tag for the additional authentication data and the ciphertext, which is used to verify the integrity and authenticity of the data at the receiving end; at the receiving end, the ciphertext is decrypted using the same key and initialization vector, and the authentication tag is recalculated and compared. If the tags match, the data is accepted; otherwise, the data is discarded and a security alarm is triggered.

[0088] Encoding-Decoding Module: To address the error accumulation problem during quantization, this application designs a dynamic encoding-decoding mechanism based on incremental encoding. This mechanism performs integer quantization only on the system output and limits the accumulation of quantization errors through a predictive recursive update mechanism. This design can adapt to dynamically changing communication conditions, effectively suppress error accumulation in the closed-loop dynamics, and significantly improve the robustness and practicality of the control system. Under limited bandwidth communication conditions, this quantization and decoding strategy can ensure the control accuracy and stability of the system, avoiding performance degradation or system instability caused by excessive quantization errors. By precisely controlling the quantization process, this module provides reliable technical support for real-time control during spacecraft formation flight.

[0089] As an optional implementation, the encoding-decoding module specifically includes: The encoder is used to perform integer quantization of the system output signal by maintaining internal state variables and dynamically adjusting the scaling factor, using a dynamic quantization mechanism based on incremental coding. During the quantization process, the encoder performs quantization encoding based on the difference between the current input signal and the predicted value of the internal state, and tracks the signal change trend by recursively updating the internal state.

[0090] The decoder, with a structure symmetrical to the encoder, is used to gradually reconstruct the original signal from the transmitter based on the received quantized encoded signal and the same dynamic scaling factor. The module limits the range of single-step quantization error and uses a predictive recursive update mechanism to suppress the cumulative effect of error, ensuring that the system can maintain high control accuracy and closed-loop stability under limited bandwidth and dynamically changing communication conditions.

[0091] In summary, this application has the following beneficial effects: 1. This application introduces a time-series synchronization control strategy using a weighted matrix, which can flexibly adjust the convergence order of different state components, ensuring that each state component of the spacecraft converges to the equilibrium point in a preset order within a finite time. This design not only meets the requirements of finite-time stability but also improves the adaptability and flexibility of the control strategy. It is particularly suitable for complex space mission scenarios, such as phased mission scheduling, batch orbit insertion, and dynamic role switching, significantly enhancing the flexibility and reliability of the mission.

[0092] 2. This application combines a dynamic uniform quantization strategy with the AES-GCM encryption mechanism to quantize, encrypt, and authenticate transmitted control commands and status information, ensuring the security, integrity, and anti-replay interference capability of communication data. The AES-GCM algorithm is widely used in high-security communication scenarios due to its efficient encryption performance and strong authentication capabilities. Through this encryption mechanism, even if the communication network is subjected to security threats, communication information can be effectively protected, thereby ensuring the safe execution of spacecraft formation flight missions.

[0093] 3. This application employs a dynamic encoder-decoder mechanism based on incremental coding, performing integer quantization only on the system output and limiting the accumulation of quantization errors through a predictive recursive update mechanism. This design can adapt to dynamically changing communication conditions, effectively suppressing error accumulation in the closed-loop dynamics, and significantly improving the robustness and practicality of the control system. Under limited bandwidth communication conditions, this quantization and decoding strategy can ensure the control accuracy and stability of the system, avoiding performance degradation or system instability caused by excessive quantization errors.

[0094] 4. The control method of this application can adapt to various complex aerospace mission requirements, including but not limited to emergency braking, spacecraft formation operations, and space observation scenarios. By flexibly configuring the weight matrix and dynamically adjusting the quantization parameters, this method can effectively cope with dynamic changes in different missions, ensuring the stability and reliability of the system in various complex environments, and improving the adaptability and execution efficiency of spacecraft formation flight missions; 5. By employing a dynamic uniform quantization strategy, this application can efficiently reduce bandwidth consumption and ensure high-quality information transmission under limited communication resources. This quantization strategy not only improves communication efficiency but also further optimizes the quantization process through a predictive recursive update mechanism, ensuring the control accuracy and stability of the system under low bandwidth conditions, and providing reliable technical support for real-time control during spacecraft formation flight.

[0095] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 10As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores data for the safe timing synchronization control processing of spacecraft formations. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a safe timing synchronization control method for spacecraft formations.

[0096] Those skilled in the art will understand that Figure 10 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0097] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0098] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0099] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0100] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0101] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0102] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0103] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for safe timing synchronization control of spacecraft formations, characterized in that, include: A spacecraft formation dynamics model was constructed based on dynamic equations. The spacecraft formation dynamics model includes a lead spacecraft dynamics model and multiple follower spacecraft dynamics models; Based on the spacecraft formation dynamics model and a preset timing synchronization convergence sequence, a timing synchronization controller with a weight matrix is ​​constructed; the preset timing synchronization convergence sequence is used to represent the convergence priority of each following spacecraft. Obtain the current status information of each follower spacecraft; the current status information includes the relative position vector and relative velocity vector with respect to the lead spacecraft. The current status information of each follower spacecraft is input into the timing synchronization controller to obtain the control input commands for each follower spacecraft. The control input commands of each follower spacecraft are quantized to obtain the quantized digital control signals corresponding to the control input commands of each follower spacecraft. The quantized digital control signals corresponding to the control input commands of each follower spacecraft are encrypted and authenticated to obtain the control ciphertext data and authentication tags of each follower spacecraft. The control ciphertext data and authentication tags corresponding to each follower spacecraft are decrypted and verified to obtain the decrypted quantized digital control signals corresponding to each follower spacecraft. The decrypted quantized digital control signals corresponding to each follower spacecraft are decoded and reconstructed to obtain the reconstructed control input commands for each follower spacecraft. Each follower spacecraft executes its corresponding reconfiguration control input command to achieve safe timing synchronization control of the spacecraft formation.

2. The safe timing synchronization control method for spacecraft formations according to claim 1, characterized in that, The following spacecraft dynamics model is: ； in, This represents the relative acceleration vector of the i-th follower spacecraft relative to the lead spacecraft; This represents the relative velocity vector of the i-th follower spacecraft relative to the lead spacecraft; This represents the relative position vector of the i-th follower spacecraft relative to the lead spacecraft; , and These represent the first, second, and third coefficient matrices, respectively, which are related to the orbit of the pilot spacecraft. This represents the control input for the i-th following spacecraft.

3. The safe timing synchronization control method for spacecraft formations according to claim 1, characterized in that, Based on the spacecraft formation dynamics model and a pre-defined timing synchronization convergence sequence, a timing synchronization controller incorporating a weight matrix is ​​constructed, specifically including: Based on the spacecraft formation dynamics model and a pre-set time-series synchronous convergence sequence, the sliding mode surface function is constructed using the following formula: ； ； ； in, Let i represent the sliding surface function of the i-th following spacecraft in the j-axis direction. j=x represents the x-axis of the orbital coordinate system, j=y represents the y-axis of the orbital coordinate system, and j=z represents the z-axis of the orbital coordinate system. express The derivative; This represents the weighted tracking error of the i-th following spacecraft along the j-axis. This represents the communication weight between the i-th follower spacecraft and the lead spacecraft. Represents the desired trajectory coupling coefficient of the i-th following spacecraft; This represents the relative position of the i-th following spacecraft with respect to the lead spacecraft along the j-axis. Let represent the desired trajectory of the i-th spacecraft along the j-axis. This represents the sliding mode auxiliary term for the i-th spacecraft along the j-axis. Let represent the weight matrix of the i-th following spacecraft along the j-axis. Indicates the first nonlinear power parameter; Represents a symbolic function; Indicates the second nonlinear power parameter; Let represent the sliding surface state variable of the i-th following spacecraft in the j-axis direction; Indicates the segment switching threshold; and These represent the nonlinear convergence rate adjustment coefficient and the linear convergence rate adjustment coefficient, respectively. and These represent the nonlinear chattering suppression coefficient and the linear chattering suppression coefficient, respectively. Based on the sliding mode surface function, a timing synchronization controller is constructed using the following formula: ； in, This represents the control input of the i-th following spacecraft along the j-axis. Let represent the input gain matrix of the i-th following spacecraft along the j-axis. This represents the system dynamics term for the i-th spacecraft along the j-axis. Indicates proportional control gain; The exponential parameter represents the first type of nonlinear term; Indicates higher-order control gain; The exponential parameter represents the second type of nonlinear term; express The derivative; Let represent the second derivative of the desired trajectory of the i-th spacecraft along the j-axis.

4. The safe timing synchronization control method for spacecraft formations according to claim 1, characterized in that, The control input commands of each follower spacecraft are quantized to obtain the quantized digital control signals corresponding to the control input commands of each follower spacecraft, specifically including: The control input commands for each follower spacecraft are quantized using the following expressions to obtain the quantized digital control signals corresponding to the control input commands for each follower spacecraft: ； ； in, Let k be the quantized digital control signal of the i-th following spacecraft along the j-axis; This represents a uniform quantizer; This represents the control input of the i-th following spacecraft along the j-axis at time k; This represents the internal state of the uniform quantizer at time k-1 in the j-axis direction of the i-th following spacecraft. The dynamic scaling factor at time k-1 is represented. This represents the internal state of the uniform quantizer at time k-2 on the j-axis direction of the i-th following spacecraft, and the initial internal state of the uniform quantizer on the j-axis direction of the i-th following spacecraft. ; The dynamic scaling factor at time k-2 is represented. Let be the quantized digital control signal of the i-th following spacecraft in the j-axis direction at time k-1.

5. The safe timing synchronization control method for spacecraft formations according to claim 1, characterized in that, The quantized digital control signals corresponding to the control input commands of each follower spacecraft are encrypted and authenticated to obtain the control ciphertext data and authentication tags for each follower spacecraft, specifically including: Based on the preset encryption key, preset initialization vector, and additional authentication data, the AES-GCM authentication encryption algorithm is used to encrypt and authenticate the quantized digital control signals corresponding to the control input commands of each follower spacecraft, thereby obtaining the control ciphertext data and authentication tags of each follower spacecraft.

6. The safe timing synchronization control method for spacecraft formations according to claim 5, characterized in that, The control ciphertext data and authentication tags corresponding to each follower spacecraft are decrypted and verified to obtain the decrypted quantized digital control signals corresponding to each follower spacecraft, specifically including: Each accompanying spacecraft undergoes decryption and verification processing through the following steps: Based on the preset encryption key, preset initialization vector, and additional authentication data, the local authentication tag following the spacecraft is calculated. If the authentication label matches the local authentication label, the AES-GCM decryption algorithm is used to decrypt the control ciphertext data corresponding to the following spacecraft based on the preset encryption key and preset initialization vector, and the decrypted quantized digital control signal is obtained. If the authentication tag does not match the local authentication tag, the control encrypted data and authentication tag corresponding to the spacecraft are discarded.

7. A safe timing synchronization control system for spacecraft formations, characterized in that, The spacecraft formation safety timing synchronization control system applies the spacecraft formation safety timing synchronization control method according to any one of claims 1-6, and the spacecraft formation safety timing synchronization control system includes: A dynamics model construction module is used to construct a spacecraft formation dynamics model based on dynamics equations; the spacecraft formation dynamics model includes a lead spacecraft dynamics model and multiple follower spacecraft dynamics models. A timing synchronization controller construction module is used to construct a timing synchronization controller with an introduced weight matrix based on a spacecraft formation dynamics model and a preset timing synchronization convergence sequence; the preset timing synchronization convergence sequence is used to represent the convergence priority of each following spacecraft. The status information acquisition module is used to acquire the current status information of each follower spacecraft; the current status information includes the relative position vector and relative velocity vector with respect to the lead spacecraft. The control command generation module is used to input the current status information of each follower spacecraft into the timing synchronization controller to obtain the control input commands for each follower spacecraft. The quantization processing module is used to quantize the control input commands of each follower spacecraft to obtain the quantized digital control signals corresponding to the control input commands of each follower spacecraft. The encryption and authentication processing module is used to perform encryption and authentication processing on the quantized digital control signals corresponding to the control input commands of each follower spacecraft, so as to obtain the control ciphertext data and authentication tags of each follower spacecraft. The decryption and verification processing module is used to decrypt and verify the control ciphertext data and authentication tags corresponding to each follower spacecraft, and obtain the decrypted quantized digital control signal corresponding to each follower spacecraft. The decoding and reconstruction module is used to decode and reconstruct the decrypted quantized digital control signals corresponding to each follower spacecraft to obtain the reconstruction control input commands for each follower spacecraft. The control execution module is used by each following spacecraft to execute the corresponding reconfiguration control input commands, thereby achieving safe timing synchronization control of the spacecraft formation.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the safe timing synchronization control method for spacecraft formations according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the safe timing synchronization control method for spacecraft formations as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the safe timing synchronization control method for spacecraft formations as described in any one of claims 1-6.

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