Multi-satellite cooperative distributed game control method and device, computer program and storage medium

Abstract

The invention discloses a multi-satellite cooperative distributed game control method and device, a computer program and a storage medium, belongs to the technical field of spaceflight, and particularly relates to a satellite attitude control and game control method. The problem that in the prior art, resolving of the overall control quantity depends on a center unit, and constraint processing on the size of the microsatellite control torque is not accurate enough is solved. The method comprises the following steps: S1, according to attitude dynamics modeling and pseudo-linearization processing of the combined spacecraft, obtaining a state dependence coefficient model; s2, obtaining a local optimal control strategy of each satellite in the combined spacecraft through a model prediction control method according to the state dependence coefficient model in combination with a dynamic model in a prediction time domain and flywheel constraint conditions; and S3, obtaining a distributed Nash equilibrium solution through a distributed iteration and global coordination method according to the local optimal control strategy of each satellite in combination with communication topology information. The method is suitable for efficient cooperation tasks of large-scale satellite groups and microsatellite systems.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and particularly relates to satellite attitude control and game control methods. Background Art

[0002] With the rapid development of satellite technology, especially the wide application of multi-satellite cooperative control technology in the aerospace field, the importance of satellite attitude control in various tasks has become increasingly prominent. Especially in the construction of large-scale satellite constellations and microsatellite systems, how to achieve precise and efficient attitude control and cooperative work among satellites has become a key technical problem. Traditional satellite attitude control methods mainly rely on centralized control systems, that is, a central control unit calculates the control quantities for each satellite and directly transmits these control information to each execution unit. The advantage of this method is that the control algorithm is simple and easy to implement. When the number of satellites is small and the system structure is relatively simple, centralized control can effectively achieve global coordination and ensure the accuracy and stability of attitude control. However, with the increase in the number of satellites and the improvement of system complexity, the limitations of the centralized control method gradually emerge.

[0003] Firstly, the centralized control method completely depends on a central control unit. Once this unit fails, the control systems of the entire satellite group will immediately fail, which may lead to mission interruption. This single-point failure problem is particularly dangerous in critical missions, especially when high precision of attitude control is required. Secondly, due to the long distances between satellites and limited communication bandwidth, it is a great challenge to maintain a stable communication link. The central control unit needs to establish direct communication connections with each satellite. As the number of satellites increases, the amount of information and communication requirements increase sharply, often exceeding the carrying capacity of the existing communication system, thus affecting the transmission speed and accuracy of real-time control instructions. In addition, when calculating the global control quantity, the centralized control method often has a certain loss of accuracy. Especially in microsatellites or small satellite groups, small control torques may lead to error accumulation, thereby affecting the overall system accuracy.

[0004] In order to overcome the defects of centralized control methods, distributed game control methods have gradually become one of the mainstream technologies for multi-satellite collaborative control in recent years. In the distributed game control method, each satellite makes decisions based on local information, without relying on a single central control unit. In this way, satellites can update the control quantity based on communication and exchange information, thereby achieving the collaborative completion of attitude control tasks. The distributed game control method uses the principles of game theory to transform the control problem between multiple satellites into a local information game problem. The method consists of a total control quantity solution layer and a control allocation layer. In the control allocation layer, a distributed method is used to update the control allocation coefficients of each satellite through local information interaction, so that a flywheel with higher saturation is allocated to less torque. In the total control quantity solution layer, the constraint on the size of the control torque of each satellite is realized by solving the multi-satellite total control quantity based on the model predictive control method.

[0005] Although the distributed game control method performs well in all aspects, there are still some urgent problems to be solved in practical applications. For example, in the patent document CN118890083A-A multi-satellite on-orbit collaborative dynamic scheduling method and system under satellite resource failure, although a distributed method is adopted in the torque distribution layer, the solution of the overall control quantity still depends on a central unit. Once the unit fails, the entire system may still face the risk of collapse. Secondly, in the process of solving the overall control quantity, the constraint processing of the control torque size of the microsatellite is not accurate enough, which may lead to a decrease in control performance. In addition, when controlling the torque distribution, although the saturation of the flywheel speed is considered, the flywheel speed is not limited to a certain range, which may cause the flywheel speed to be saturated and unable to output the allocated torque, thereby affecting the control performance. These problems need to be further solved in future research to improve the reliability and accuracy of the distributed game control method in practical applications. Summary of the invention

[0006] In order to solve some deficiencies of the distributed game control method in practical applications, the present invention proposes the following solutions:

[0007] A distributed game control method for multi-satellite collaboration, the method comprising:

[0008] S1. A step of obtaining a state-dependent coefficients (SDC) model according to the attitude dynamics modeling and pseudo-linearization processing of the combined spacecraft;

[0009] S2, the step of obtaining the local optimal control strategy of each satellite in the combined spacecraft by using the model predictive control method according to the state dependence coefficient model combined with the dynamic model in the prediction time domain and the flywheel constraint conditions;

[0010] S3. Steps to obtain the distributed Nash equilibrium solution through distributed iteration and global coordination methods based on the local optimal control strategies of each satellite and the communication topology information.

[0011] Further, the S1 includes: introducing the error quaternion q e and the error angular velocity ω e , establishing the attitude error kinematics and dynamics equations based on the attitude dynamics principle, and obtaining the SDC model through pseudo-linearization:

[0012]

[0013] where, A(x) is the state-dependent matrix; x is the variable of the combined spacecraft motion state; N is the number of subsatellites included in the combined spacecraft; B i is the control action matrix of the i-th satellite, and u i is the control quantity vector of the i-th satellite.

[0014] Further, the S2 includes:

[0015] S21. Discretize the SDC model:

[0016]

[0017] where, x k is the system state at the current time k; x k+1 is the system state at the next time; is the discretized state transition matrix; is the discretized control action matrix; u i,k is the control quantity of the i-th satellite during the current time k and subsequent time periods;

[0018] S22. Obtain the dynamic model within the prediction horizon:

[0019]

[0020] where, U i,k is the control quantity sequence of the i-th satellite within the prediction horizon; X k is the system state sequence within the prediction horizon; Λ is the state transition matrix within the prediction horizon; Θ i is the control input matrix of the i-th satellite within the prediction horizon;

[0021] S23. Select the finite-horizon local objective functions for all satellites:

[0022]

[0023] where, J iis the local objective function of the i-th satellite; Q i,k is the state weight matrix within the prediction horizon; R i,k is the control input weight matrix within the prediction horizon; W i,k is the flywheel speed weight matrix within the prediction horizon; Ω i,k is the sequence of flywheel speeds of the i-th satellite within the prediction horizon;

[0024] S24. Set the flywheel constraint conditions, where the constraint conditions include the flywheel torque amplitude constraint and the speed constraint:

[0025]

[0026] Among them, represents the flywheel torque amplitude constraint; is the upper limit of the flywheel torque amplitude constraint;

[0027] represents the flywheel speed constraint; is the upper limit of the flywheel speed constraint; ε i is the block lower triangular matrix with the identity matrix as elements, represents the Kronecker product, N p is the control input sequence U i,k and the state sequence X k of length, represents N p column vector with all elements being 1;

[0028] S25. Combine X k and Ω i,k with the flywheel constraint conditions to obtain a quadratic programming problem:

[0029]

[0030]

[0031] Among them, M i,2 is the quadratic term coefficient matrix; M i,1 is the linear term coefficient matrix.

[0032] Furthermore, the S3 includes:

[0033] S31. Initialize the estimation vector, and set the initial estimation vector of the i-th satellite as:

[0034] μ i (0) = T i = Θ i U i,k ,

[0035] Among them, μ i(0) is the initial estimation vector of the i-th satellite; T i = Θ i U i,k is the true action of the i-th satellite on the system; U i,k is the control input sequence of the i-th satellite within the prediction time domain;

[0036] S32. Pre-iteration loop:

[0037] S321. All satellites run in parallel. The i-th satellite obtains the estimation vector μ j (t - 1) of its neighboring satellites through the communication topology and updates its own estimation vector according to the following rule:

[0038] μ i (t)= μ i (t - 1)+ γ∑ j∈V(i) (μ j (t - 1)- μ i (t - 1)),

[0039] where μ i (t) is the update of the i-th satellite's estimation vector; γ is the iteration step size; V(i) is the set of satellites connected to satellite i;

[0040] 322. When all satellites satisfy the tolerance condition of the pre-iteration loop:

[0041] ‖μ i (t)- μ i (t - 1)‖ < ε p ,

[0042] or reach the upper limit of the number of times of the pre-iteration loop:

[0043] t p = t p,max ,

[0044] then proceed to the subsequent iteration loop, otherwise return to S321;

[0045] S33. Subsequent loop iteration:

[0046] S331. All satellites run in parallel. The i-th satellite, based on μ i (t), takes it as the global sum information estimation value

[0047]

[0048] S332. Solve the quadratic programming problem to obtain the local optimal control strategy:

[0049]

[0050] where, is the local optimal control strategy of the i-th satellite at the t-th iteration;

[0051] S333. Introduce a step size parameter ξ and update the control strategy:

[0052]

[0053] S334. Add the policy change amount to the estimated vector μ i ;

[0054] S335. When all satellites satisfy the termination condition:

[0055]

[0056] or reach the upper limit of the total number of iterations:

[0057] t = t max ,

[0058] then end the iteration and obtain an approximate solution of the Nash equilibrium solution Otherwise, return to S331;

[0059] S34. Obtain the actual control quantity output, and take the first N i elements as the actual output quantities of each flywheel in the i-th satellite at the next control moment k

[0060] Furthermore, the local optimal control strategy is the solution that minimizes the local objective function of the i-th satellite when the total action of other satellites remains unchanged.

[0061] Furthermore, when the iteration step size satisfies the following conditions:

[0062]

[0063] the control quantity vector μ of the i-th satellite i can be iteratively approximated to the global sum information estimate value

[0064] where d max is the maximum degree of vertices in the communication topology graph.

[0065] A multi-satellite collaborative distributed game control device, the device includes:

[0066] A module that models and pseudo-linearly processes the attitude dynamics of the combined spacecraft to obtain the SDC model;

[0067] A module that, according to the state-dependent coefficient model, combines the dynamic model and the flywheel constraint conditions within the prediction horizon, and obtains the local optimal control strategies of each satellite in the combined spacecraft through the model predictive control method;

[0068] A module that, according to the local optimal control strategies of each satellite and combines the communication topology information, obtains the distributed Nash equilibrium solution through the distributed iteration and global coordination method.

[0069] Based on the same inventive concept, the present invention also provides a computer storage medium for storing a computer program, and when the computer program is read by a computer, the computer executes the method according to any one of the present invention.

[0070] Based on the same inventive concept, the present invention also provides a computer, including a processor and a storage medium, and when the processor reads the computer program stored in the storage medium, the computer executes the method according to any one of the present invention.

[0071] Based on the same inventive concept, the present invention also provides a computer program product, which, as a computer program, realizes the method according to any one of the present invention when the computer program is read.

[0072] The present invention has the following beneficial effects:

[0073] In view of the deficiencies of the existing distributed game control methods in multi-satellite cooperative attitude control, the present invention proposes an improved multi-satellite cooperative distributed game control method, device, computer program and storage medium. Through the following technical means and creative labor, the present invention achieves remarkable technical effects, which are specifically classified and described as follows:

[0074] (1) On the basis of the distributed game control method, the present invention further optimizes the control architecture, adopts a fully distributed control strategy, and avoids the dependence on a single central unit in the traditional method. By introducing a local information interaction and global coordination mechanism, each satellite can make independent decisions based on local information, and at the same time exchange information with neighboring satellites through the communication topology to achieve the distributed solution of the global control quantity. During the research and development process, a distributed iterative algorithm based on model predictive control (MPC) is designed, combined with the Nash equilibrium principle in game theory, to achieve the efficient solution of multi-satellite cooperative control. By introducing a two-layer loop structure of pre-iteration and subsequent iteration, the rapid convergence and global consistency of the control quantity are ensured. This method significantly improves the robustness and fault tolerance of the system. Even if some satellites or communication links fail, the system can still continue to operate through local information interaction, avoiding the system crash problem caused by a single point of failure in the traditional centralized control method.

[0075] (2) In the process of calculating the control quantity, the present invention accurately considers the torque amplitude constraint and speed constraint of the flywheel. By introducing the flywheel speed weight matrix and constraint conditions, the flywheel speed is limited within a reasonable range, avoiding the degradation of control performance caused by flywheel saturation. An optimization algorithm based on quadratic programming is designed, and the flywheel constraint conditions are incorporated into the solution of the local objective function, ensuring the accuracy and feasibility of control torque distribution. At the same time, by introducing a dynamic constraint mechanism for the flywheel speed, the utilization efficiency of the flywheel is further optimized. This method significantly improves the control performance of the flywheel, avoids the problem that the allocated torque cannot be output after the flywheel speed saturates, and ensures the accuracy and stability of attitude control, especially suitable for the high-precision control requirements of microsatellite systems.

[0076] (3) The present invention designs a local objective function for each satellite. By combining the state weight matrix, control quantity weight matrix and flywheel speed weight matrix, multi-objective optimization of satellite attitude control is achieved. Through the distributed iteration and global coordination mechanism, it is ensured that the local optimal control strategies of each satellite can converge to the global Nash equilibrium solution. A distributed iteration algorithm based on communication topology is proposed. Through the double-layer structure of pre-iteration loop and subsequent loop iteration, the rapid solution of the local objective function and global coordination are realized. At the same time, by introducing the step size parameter and tolerance condition, the convergence and computational efficiency of the algorithm are ensured. This method significantly improves the efficiency and accuracy of multi-satellite cooperative control, and can realize the rapid solution and allocation of global control quantities under limited computational resources and communication bandwidth, suitable for the efficient cooperative control of large-scale satellite constellations.

[0077] (4) The present invention combines the model predictive control (MPC) method with the flywheel dynamic constraint. Through the dynamic model and constraint conditions in the prediction time domain, dynamic optimization of satellite attitude control is achieved. By discretization processing and the application of the state-dependent coefficient (SDC) model, the real-time performance and adaptability of the control algorithm are ensured. During the R & D process, a pseudo-linearization processing method based on the SDC model is designed to transform the non-linear attitude dynamics equation into a linear form, simplifying the process of calculating the control quantity. At the same time, by introducing the flywheel constraint conditions in the prediction time domain, the robustness and adaptability of the control algorithm are further improved. This method significantly improves the real-time performance and adaptability of the control algorithm, and can achieve high-precision attitude control in a complex dynamic environment, especially suitable for the high-dynamic task requirements of microsatellite systems.

[0078] (5) By introducing communication topology information, the present invention realizes flexible information interaction among multiple satellites. Each satellite only needs to exchange information with its neighboring satellites without establishing direct communication connections with all satellites, significantly reducing the communication burden. During the research and development process, a distributed iterative algorithm based on communication topology is designed to solve the global control quantity through local information interaction. Meanwhile, by introducing the iteration step size and tolerance conditions, the convergence and computational efficiency of the algorithm are ensured. This method significantly reduces the communication bandwidth requirement and improves the scalability of the system, making it suitable for the efficient cooperative control of large-scale satellite constellations.

[0079] (6) By optimizing the distributed control architecture, precisely handling the flywheel constraint conditions, designing local objective functions, combining model predictive control with dynamic constraints, and introducing a flexible communication topology, the present invention significantly improves the robustness, accuracy, and efficiency of multi-satellite cooperative control. The combination of these technical means and creative efforts enables the present invention to effectively solve the deficiencies of existing distributed game control methods in practical applications and provides reliable technical support for the efficient cooperative control of large-scale satellite constellations and microsatellite systems.

[0080] The present invention belongs to the field of aerospace technology and is specifically applicable to the scenario of multi-satellite cooperative control, especially for large-scale satellite constellations, microsatellite systems, and space missions requiring high-precision attitude coordination. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a conceptual diagram of the combined spacecraft described in Embodiment 1 of the present invention;

[0082] Figure 2 is a flowchart of the distributed game control strategy described in Embodiment 4 of the present invention;

[0083] Figure 3 is a flowchart of the iterative loop described in Embodiment 4 of the present invention;

[0084] Figure 4 is a communication topology diagram described in Embodiment 7 of the present invention, where the reference numerals 1-5 respectively correspond to Satellite 1 - Satellite 5;

[0085] Figure 5 is the error angular velocity of the combined spacecraft described in Embodiment 7 of the present invention, reflecting the change of angular velocity error in three axes of the system;

[0086] Figure 6 is the error quaternion of the combined spacecraft described in Embodiment 7 of the present invention, reflecting the dynamic response of the error in the system attitude control;

[0087] Figure 7 is the output torque of each flywheel of Satellite 1 described in Embodiment 7 of the present invention;

[0088] Figure 8 are the rotational speeds of each flywheel of Star 1 described in Embodiment 7 of the present invention;

[0089] Figure 9 are the output torques of each flywheel of Star 2 described in Embodiment 7 of the present invention;

[0090] Figure 10 are the rotational speeds of each flywheel of Star 2 described in Embodiment 7 of the present invention;

[0091] Figure 11 are the output torques of each flywheel of Star 3 described in Embodiment 7 of the present invention;

[0092] Figure 12 are the rotational speeds of each flywheel of Star 3 described in Embodiment 7 of the present invention;

[0093] Figure 13 are the output torques of each flywheel of Star 4 described in Embodiment 7 of the present invention;

[0094] Figure 14 are the rotational speeds of each flywheel of Star 4 described in Embodiment 7 of the present invention;

[0095] Figure 15 are the output torques of each flywheel of Star 5 described in Embodiment 7 of the present invention;

[0096] Figure 16 are the rotational speeds of each flywheel of Star 5 described in Embodiment 7 of the present invention;

[0097] Figure 17 are the rotational speeds of all flywheels described in Embodiment 7 of the present invention, reflecting the optimization effect of this control method on the flywheel rotational speed.;

[0098] Figure 18 is the number of algorithm iterations described in Embodiment 7 of the present invention. Through multiple iterations and updates, the system response gradually tends to be stable and achieves the expected control effect. Embodiment

[0100] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0101] Embodiment 1

[0102] Combined with Figure 1 To illustrate this embodiment, a multi-star collaborative distributed game control method, the method includes:

[0103] S1. Steps to model and pseudo-linearly process according to the attitude dynamics of the combined spacecraft to obtain the SDC model;

[0104] S2. Steps to obtain the local optimal control strategy for each satellite in the combined spacecraft through the model predictive control method according to the state-dependent coefficient model, combining the dynamic model and the flywheel constraint conditions within the prediction horizon;

[0105] S3. Steps to obtain the distributed Nash equilibrium solution through the distributed iteration and global coordination method according to the local optimal control strategy of each satellite and combining the communication topology information.

[0106] In this embodiment, by introducing the error quaternion and error angular velocity, the attitude error kinematic and dynamic equations are established based on the principle of attitude dynamics, and the SDC model is obtained through pseudo-linear processing. This method simplifies the complex non-linear attitude dynamics equation and transforms it into a linear form, facilitating the subsequent calculation of the control quantity. In this way, the system can perform attitude control more efficiently, especially in multi-satellite cooperative control, significantly improving the real-time performance and adaptability of the control algorithm.

[0107] Embodiment 2

[0108] This embodiment is a further explanatory description of Embodiment 1.

[0109] Further, the S1 includes: introducing the error quaternion and the error angular velocity ω e = ω - Rω T , where R is the direction cosine matrix of the body coordinate system of the combined spacecraft relative to the desired coordinate system. According to the principle of attitude dynamics, the attitude error kinematic and dynamic equations are obtained and pseudo-linearly processed. Defining the state variable Then there is a state equation in the following SDC form,

[0110]

[0111] where, A(x) is the state-dependent matrix; x is the variable of the motion state of the combined spacecraft;

[0112] A 11 = -(Rω T ) × + J -1 (Jω e + JRω T ) × - J -1 (Rω T ) × J, is the part related to the error angular velocity ω in the state matrix eThe relevant part for describing the dynamic behavior of the error angular velocity, J is the inertia matrix, × represents the matrix cross product operation, R is the direction cosine matrix, ω T is the desired angular velocity;

[0113] A 12 = -G1 + J -1 (JRω T ) × G2, which is the part in the state matrix related to the error quaternion q e and is used to describe the influence of the error quaternion on the change rate of the error angular velocity;

[0114] is the intermediate quantity related to 12 when calculating A ;

[0115] is the intermediate quantity related to ω 12 when calculating A T ;

[0116] is the part in the state matrix related to the error angular velocity ω e and is used to describe the influence of the error angular velocity on the change rate of the error quaternion;

[0117] is the part in the state matrix related to the error quaternion q e and is used to describe the dynamic behavior of the error quaternion;

[0118] N is the number of subsatellites included in the combined spacecraft;

[0119] is the control action matrix of the i-th satellite;

[0120] is the control quantity vector of the i-th satellite, where N i is the dimension of the control quantity of the i-th satellite, that is, the number of flywheels included in the i-th satellite;

[0121] is the direction cosine matrix used to describe the attitude relationship of the body coordinate system of the combined spacecraft relative to the desired coordinate system, q e0 is the scalar part of the error quaternion, q e1 q e2 q e3 is the vector part of the error quaternion.

[0122] This embodiment further optimizes the discretization of the SDC model. Through the discretized state transition matrix and control action matrix, accurate prediction of the system state is achieved. Through the dynamic model within the prediction time domain, the system can achieve dynamic optimization of the satellite attitude with limited computing resources and communication bandwidth. This method significantly improves the real-time performance and adaptability of the control algorithm, especially suitable for high-dynamic task requirements.

[0123] Embodiment 3

[0124] This embodiment is a further explanatory description of Embodiment 1.

[0125] Furthermore, the S2 includes:

[0126] S21. Discretize the SDC model:

[0127]

[0128] where x k is the system state at the current time k, and x k+1 is the system state at the next time. is the discretized state transition matrix, is the discretized control action matrix, and μ i,k is the control quantity of the i-th satellite within the time period τ after the current time k;

[0129] τ is the control time interval, represents the discretization based on the continuous system;

[0130] N i is the dimension of the control quantity of the i-th satellite;

[0131] S22. Obtain the dynamic model within the prediction time domain:

[0132]

[0133] where is the control quantity sequence of the i-th satellite within the prediction time domain;

[0134] is the system state sequence within the prediction time domain;

[0135] is the state transition matrix within the prediction time domain;

[0136] is the control input matrix of the i-th satellite within the prediction time domain;

[0137] S23. Select the local objective functions of all satellites in the finite time domain:

[0138]

[0139] where,

[0140] J i is the local objective function of the i-th satellite;

[0141] Q i,k is the state weight matrix in the prediction time domain;

[0142] R i,k is the control input weight matrix in the prediction time domain;

[0143] W i,k is the flywheel speed weight matrix in the prediction time domain;

[0144] is the sequence of flywheel speeds of the flywheels contained in the i-th satellite in the prediction time domain, which can be obtained by Equation as follows.

[0145] S24. Set the flywheel constraint conditions, where the constraint conditions include flywheel torque amplitude constraints and speed constraints:

[0146]

[0147] where, represents the flywheel torque amplitude constraint; is the upper limit of the flywheel torque amplitude constraint;

[0148] represents the flywheel speed constraint; is the upper limit of the flywheel speed constraint, and the expression is:

[0149]

[0150] ε i is a block lower triangular matrix with the identity matrix as its elements, represents the Kronecker product, N p is the length of the control input sequence U i,k and the state sequence X k ; represents N p column vectors with all elements equal to 1;

[0151] S25. Incorporate the dynamic model X k in the time domain and the sequence of flywheel speeds Ω i,k of the flywheels contained in the i-th satellite in the prediction time domain into the flywheel constraint conditions and simplify, omitting the terms that do not contain U i,kItems that cannot be optimized are considered, and considering the flywheel torque amplitude constraint and speed constraint, a quadratic programming problem is obtained:

[0152]

[0153] Among them, M i,2 is the quadratic term coefficient matrix; M i,1 is the linear term coefficient matrix.

[0154] In this embodiment, by introducing flywheel constraint conditions, including flywheel torque amplitude constraint and speed constraint, the flywheel speed is ensured to be within a reasonable range, and the decline of control performance caused by flywheel saturation is avoided. Through the solution of the quadratic programming problem, the system can accurately distribute the control torque to ensure the accuracy and stability of attitude control. This method is particularly suitable for the high-precision control requirements of microsatellite systems.

[0155] Embodiment 4

[0156] This embodiment is a further explanatory description of Embodiment 1. Combining Figure 2 to illustrate this embodiment:

[0157] Furthermore, the S3 includes:

[0158] For a determined system and a fixed objective function, if the following inequality holds, then the strategy set reaches the Nash equilibrium state

[0159]

[0160] Among them, is the Nash equilibrium control strategy of the i-th satellite;

[0161] u i is the control strategy of the i-th satellite, defined as follows:

[0162] u i ∈U i ,

[0163] U i is the set of all possible controls of the i-th satellite, defined as follows:

[0164]

[0165] Among them, k is the current time, x k is the current system state, N i is the dimension of the control quantity of the i-th satellite.

[0166] The communication network of each satellite can be represented by a topological graph. Regarding each subsatellite as a vertex in the graph and the data interface as an edge, the entire undirected graph can be described by the Laplace matrix L.

[0167] The following distributed game control strategy is designed and carried out within the control interval τ:

[0168] S31. Initialize the estimation vector, and set the initial estimation vector of the i-th satellite as:

[0169] μ i (0) = T i = Θ i U i,k ,

[0170] where μ i (0) is the initial estimation vector of the i-th satellite; T i = Θ i U i,k is the actual action of the i-th satellite on the system; U i,k is the control input sequence of the i-th satellite within the prediction time domain;

[0171] S32. Pre-iteration loop: Let the next control moment be k, and let the current iteration number be t;

[0172] S321. All satellites run in parallel. The i-th satellite obtains the estimation vector μ j (t - 1) of its neighbor satellites through the communication topology, and updates its own estimation vector according to the following rule:

[0173] μ i (t) = μ i (t - 1) + γ∑ j∈V(i) (μ j (t - 1) - μ i (t - 1)),

[0174] where μ i (t) is the update of the estimation vector of the i-th satellite; γ is the iteration step size; V(i) is the set of satellites connected to satellite i;

[0175] 322. When all satellites meet the tolerance condition of the pre-iteration loop:

[0176] ‖μ i (t) - μ i (t - 1)‖ < ε p , ε p is the pre-iteration tolerance,

[0177] or when the upper limit of the number of times of the pre-iteration loop is reached:

[0178] t p = tp,max , t p,max is the upper limit of the number of iterations,

[0179] then proceed to the subsequent iterative loop, otherwise return to S321;

[0180] S33. Subsequent loop iteration: Let the current iteration number be t;

[0181] S331. All satellites run in parallel. The i-th satellite updates μ i (t) of the i-th satellite's estimated vector and uses it as the global sum information estimate value

[0182] S332. Solve the quadratic programming problem to obtain the local optimal control strategy:

[0183]

[0184] where, is the local optimal control strategy of the i-th satellite at the t-th iteration;

[0185] S333. Introduce the step size parameter ξ and update the control strategy:

[0186]

[0187] S334. Add the strategy change amount to the estimated vector μ i ;

[0188] S335. When all satellites meet the termination condition:

[0189]

[0190] or reach the upper limit of the total number of iterations:

[0191] t = t max ,

[0192] then end the iteration and obtain an approximate solution of the Nash equilibrium solution otherwise return to S331;

[0193] S34. Obtain the actual control quantity output. Take the first N elements of i as the actual output quantities of each flywheel in the i-th satellite at the next control moment k

[0194] Here is the final control quantity, which is used as the actual output torque of each flywheel at the beginning of the next control moment k.

[0195] In this embodiment, through a distributed game control program and combined with communication topology information, flexible information interaction between multiple satellites is achieved. Through a double-layer loop structure of pre-iteration and subsequent iteration, the rapid convergence and global consistency of the control quantity are ensured. This method significantly improves the robustness and fault tolerance of the system. Even if some satellites or communication links fail, the system can still continue to operate through local information interaction, avoiding the system crash problem caused by single-point failures in traditional centralized control methods.

[0196] Embodiment 5

[0197] This embodiment is a further explanatory description of Embodiment 4.

[0198] Furthermore, the local optimal control strategy is the solution that minimizes the local objective function of the i-th satellite under the condition that the sum of the action quantities of other satellites remains unchanged.

[0199] In this embodiment, through the design of the local optimal control strategy, it is ensured that each satellite makes an optimal decision based on local information. At the same time, through the global coordination mechanism, it is ensured that the local optimal control strategies of each satellite can converge to the global Nash equilibrium solution. This method significantly improves the efficiency and accuracy of multi-satellite cooperative control, and can achieve the rapid calculation and allocation of global control quantities under limited computing resources and communication bandwidth, and is applicable to the efficient cooperative control of large-scale satellite groups.

[0200] Embodiment 6

[0201] This embodiment is a further explanatory description of Embodiment 4.

[0202] Furthermore, when the iteration step size satisfies the following conditions:

[0203]

[0204] The control quantity vector μ of the i-th satellite i Can be iteratively approximated to the global sum information estimate

[0205] Where, d max Is the maximum degree of vertices in the communication topology graph. At the same time, when the optimization step size ξ is taken small enough, the above iterative process can approximate the Nash equilibrium solution.

[0206] In this embodiment, by introducing the iteration step size and tolerance conditions, the convergence and computational efficiency of the algorithm are ensured. Through the selection of the optimization step size, the system can quickly approximate the Nash equilibrium solution and ensure the accurate allocation of the control quantity. This method significantly reduces the communication bandwidth requirements and improves the scalability of the system, and is applicable to the efficient cooperative control of large-scale satellite groups.

[0207] Through the above six embodiments, the present invention has achieved significant improvements in multi-satellite cooperative control, including enhancing the robustness, accuracy, and efficiency of the system, optimizing the flywheel constraint conditions, designing local objective functions, combining model predictive control with dynamic constraints, and introducing flexible communication topologies. The combination of these technical means enables the present invention to effectively address the deficiencies of existing distributed game control methods in practical applications, providing reliable technical support for the efficient cooperative control of large-scale satellite constellations and microsatellite systems.

[0208] Embodiment Seven

[0209] This embodiment combines the technical solutions described in Embodiments One to Six, and through numerical simulation examples, further verifies and explains the technical effects of the present invention in light of the actual situation. It includes the effects that can be achieved when certain parameters in the algorithm take optimal ranges or optimal values.

[0210] Without loss of generality, define the moment of inertia of the combined spacecraft as

[0211]

[0212] Suppose there are 5 service satellites, and its communication topology diagram is as Figure 4 shown, where the reference numerals 1 - 5 respectively correspond to Satellite 1 - Satellite 5. Among them, Satellite 1, Satellite 2, and Satellite 3 include three flywheels, and Satellite 4 and Satellite 5 include four flywheels.

[0213] Regarding each subsatellite as a vertex in the graph and the data interface as an edge of the graph, the entire topology graph can be described by the Laplace matrix L, and the Laplace matrix is:

[0214]

[0215] Among them, the diagonal elements of the matrix represent the degree of each vertex, that is, the number of edges connected to this vertex; the non - diagonal elements represent the connection relationship between vertices, that is, if two vertices are connected, it is - 1, otherwise it is 0.

[0216] The number, direction of the flywheel of each satellite, and the set values of the control parameters are given in the following table:

[0217]

[0218]

[0219] In addition, the control parameter matrix Q of each satellite is the same and is the identity matrix E 6×6 , and the diagonal matrix W is set as

[0220] The initial rotational speed of all flywheels is 0, and the initial attitude of the combined spacecraft is set as:

[0221] q0 = [0 0 0 1] T ,

[0222] The initial angular velocity is:

[0223] ω0 = [0 0 0] T rad / s,

[0224] The desired attitude is:

[0225] q T = [0.5 -0.2 0.2 0.8185] T ,

[0226] The desired angular velocity is:

[0227] ω T = [0 0 0] T rad / s,

[0228] Take N p = 40,

[0229] The sampling and control step is taken as τ = 0.1 s, and the tolerance for pre-iteration stop is set as ε P = 0.001,

[0230] The maximum number of pre-iterations is t P,max = 15, For subsequent iterations, the tolerance ε t = 0.001,

[0231] The iteration upper limit t max = 10,

[0232] The simulation results are as Figures 5 - 18 shown:

[0233] According to Figure 5 the change curve of the error angular velocity shown, the angular velocity of the spacecraft tends to be stable around 40 s;

[0234] According to Figure 6 the change curve of the error quaternion shown, the attitude of the spacecraft tends to be stable around 40 s;

[0235] The results show that the combined spacecraft reaches the expected attitude around 50 s, and the output torques and speeds of each flywheel are precisely constrained.

[0236] Observing the output torque curves of each flywheel, according to Figure 7 , 9As shown by the curves in Figures 11, 13, and 15, around 25 s, the output torques of each flywheel exhibit significant fluctuations. This is because the iteration limit is reached, resulting in an inaccurate control strategy obtained during this period. This can be avoided by increasing the iteration limit, but it has little impact on the overall control effect. After that, each flywheel quickly enters a stable state, making the entire system stable. When the system is stable, the rotational speeds of the flywheels do not strictly return to zero, which is caused by the iteration tolerance. Reducing the tolerance can improve this situation, but it will increase the computational and communication burdens of each satellite, and a trade-off is needed.

[0237] Observing the rotational speed curves of each flywheel, see Figure 8 、 10 As shown by the curves in Figures 12 and 14, while ensuring good attitude control performance, the magnitudes of the rotational speeds of the flywheels are significantly reduced. This indicates that while performing attitude control, each satellite realizes an optimized distribution of the flywheel rotational speeds overall through the "idle rotation" without the total control torque.

[0238] Observing the number of iterations, it can be seen that both the pre-iteration and subsequent solution iteration counts are limited within a reasonable range. Therefore, the computational and communication volumes for solving this distributed game control strategy are not large, and it can be solved quickly online. At the same time, it can be seen that as the system stabilizes, both the pre-iteration and subsequent solution iteration counts decrease significantly, further reducing the computational and communication volumes of each satellite.

[0239] The technical solutions provided by the present invention are further described in detail through the above several specific embodiments to highlight the advantages and beneficial effects of the technical solutions provided by the present invention. However, the above several specific embodiments are not used as limitations on the present invention. Any reasonable modifications, improvements, combinations of embodiments, and equivalent replacements based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0240] Those skilled in the art can understand that the above is only the preferred embodiment of the present invention. The features recorded in each embodiment and / or claim of the present disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly recorded in the present disclosure. It is not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0241] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once they learn the basic creative concept. Therefore, the appended claims are intended to be interpreted to include the preferred embodiments as well as all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art can make various changes and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A distributed game control method for multi-satellite collaboration, where the combined spacecraft includes N satellites, characterized in that The method includes: S1. The step of obtaining the SDC model by modeling and pseudo-linearizing the attitude dynamics of the combined spacecraft; S2. The step of obtaining the local optimal control strategy for each satellite in the combined spacecraft by the model predictive control method according to the state-dependent coefficient model, combining the dynamic model and the flywheel constraint conditions within the prediction horizon; S3. The step of obtaining the distributed Nash equilibrium solution by the distributed iteration and global coordination method according to the local optimal control strategy of each satellite and combining the communication topology information.

2. The distributed game control method according to claim 1, wherein S1 includes: introducing the error quaternion q e and error angular velocity ω e , the attitude error kinematics and dynamics equations are established based on the attitude dynamics principle, and the SDC model is obtained through pseudo-linearization: Among them, A(x) is the state-dependent matrix; x is the variable of the combined spacecraft's motion state; N is the number of satellites included in the combined spacecraft; B i is the control action matrix of the i-th satellite, u i is the control quantity vector of the i-th satellite.

3. The distributed game control method according to claim 1, characterized in that, The S2 includes: S21. Ignoring the change of the state transition matrix within the prediction horizon, setting the sampling and control time interval as τ, and discretizing the SDC model; where, x k is the system state at the current time k; x k+1 is the system state at the next time; is the discretized state transition matrix; is the discretized control action matrix; u i,k is the control quantity of the i-th satellite within the time period τ after the current time k; S22. Obtaining the dynamic model within the prediction horizon; where U i,k is the control quantity sequence of the i-th satellite within the prediction horizon; X k is the system state sequence within the prediction horizon; Λ is the state transition matrix within the prediction horizon; Θ i is the control input matrix of the i-th satellite within the prediction horizon; S23. Selecting the local objective function of all satellites for a finite horizon; Among them, J i is the local objective function of the i-th satellite; Q i,k is the state weight matrix of the i-th satellite at time k within the prediction horizon; R i,k is the control input weight matrix of the i-th satellite at time k within the prediction horizon; W i,k is the flywheel speed weight matrix of the i-th satellite at time k within the prediction horizon; Ω i,k is the flywheel speed sequence of the i-th satellite within the prediction horizon at time k; S24. Setting the flywheel constraint conditions, where the constraint conditions include the flywheel torque amplitude constraint and the rotational speed constraint. Among them, represents the flywheel torque amplitude constraint of the i-th satellite; is the upper limit of the flywheel torque amplitude constraint of the i-th satellite; Denote the flywheel speed constraint of the \(i\)th satellite; is the upper limit of the flywheel speed constraint of the \(i\)th satellite; ε i For the \(i\)th satellite, with the identity matrix as the element of the block lower triangular matrix, denote the Kronecker product, \(N\) p is the control sequence \(U\) i,k and the state sequence \(X\) k length of; denote \(N\) p column vector with all elements equal to 1; S25. Combine X k with the flywheel constraint condition to obtain a quadratic programming problem: i,k and Ω Among them, M i,2 is the quadratic coefficient matrix; M i,1 is the linear coefficient matrix, and the subscript i represents the satellite number.

4. The distributed game control method according to claim 1, wherein The S3 includes: S31. Initializing the estimation vector, and setting the initial estimation vector of the i-th satellite as: μ i (0) = T i = Θ i U i,k , where, μ i (0) is the initial estimated vector of the i-th satellite; T i is the true action of the i-th satellite on the system; U i,k is the control input sequence of the i-th satellite within the prediction time domain; S32. Pre-iteration loop: S321. All satellites operate in parallel. The i-th satellite obtains the estimated vector μ j (t - 1) of its neighboring satellites through the communication topology and updates its own estimated vector according to the following rules: μ i μ(t) = μ i (t - 1)+γ∑ j∈V(i) (μ j (t - 1)-μ i (t - 1)), where μ i (t) is the update of the i-th satellite estimation vector; γ is the iteration step size; V(i) is the set of satellites connected to satellite i; 322. When all satellites satisfy the tolerance condition of the pre-iteration loop: ‖μ i (t) - μ i (t - 1)‖ < ε p , Or reach the upper limit of the number of pre-iteration loop times: t p = t p,max , Then perform the subsequent iteration loop, otherwise return to S321 and continue the iteration; S33. Subsequent loop iteration: S331. All satellites operate in parallel. The i-th satellite uses μ i (t) as the global sum information estimate value S332. Solving the quadratic programming problem to obtain the local optimal control strategy; Among them, is the local optimal control strategy of the i-th satellite at the t-th iteration; S333. Introducing the step size parameter ξ to update the control strategy; S334. Add the policy change amount to the estimated vector μ i ; S335. When all satellites satisfy the termination condition: Or reach the upper limit of the total number of iteration times: t = t max , Then the iteration ends and an approximate solution of the Nash equilibrium solution is obtained. Otherwise, return to S331; S34. Obtain the actual control quantity output, and take the first N i elements as the actual output quantity of each flywheel in the i-th satellite at the next control moment k 5. The distributed game control method according to claim 4, wherein The local optimal control strategy is the solution that minimizes the local objective function of the i-th satellite when the total action of other satellites remains unchanged.

6. The distributed game control method according to claim 4, characterized in that When the iteration step size satisfies the following conditions: The control quantity vector μ of the i-th satellite i can be iteratively approximated to a global sum information estimate where d max is the maximum degree of vertices in the communication topology graph.

7. A distributed game control device for multi-satellite collaboration, characterized in that The device includes: A module for modeling and pseudo-linearizing the attitude dynamics of the combined spacecraft to obtain the SDC model; A module for obtaining the local optimal control strategy for each satellite in the combined spacecraft by the model predictive control method according to the state-dependent coefficient model, combining the dynamic model and the flywheel constraint conditions within the prediction horizon; A module for obtaining the distributed Nash equilibrium solution by the distributed iteration and global coordination method according to the local optimal control strategy of each satellite and combining the communication topology information.

8. A computer storage medium for storing a computer program, characterized in that, When the computer program is read by a computer, the computer executes the method according to any one of claims 1 to 6.

9. A computer, comprising a processor and a storage medium, characterized in that, When the processor reads the computer program stored in the storage medium, the computer executes the method according to any one of claims 1 to 6.

10. A computer program product, as a computer program, characterized in that, When the computer program is read, the method according to any one of claims 1 to 6 is implemented.

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