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

Abstract

The application 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 a game control method. The application solves the problems that the calculation of an overall control quantity depends on a central unit and the constraint processing of a micro-satellite control moment size is not accurate in the prior art. The method comprises the following steps: S1, obtaining a state-dependent coefficient model by modeling and pseudo-linearizing an attitude dynamics of a combined space vehicle; S2, obtaining a local optimal control strategy of each satellite in the combined space vehicle by a model predictive control method according to the state-dependent coefficient model, a dynamics model in a prediction time domain and a flywheel constraint condition; and S3, obtaining a distributed Nash equilibrium solution by a distributed iteration and global coordination method according to the local optimal control strategy of each satellite and communication topology information. The application is suitable for efficient cooperative tasks of a large-scale satellite group and a micro-satellite system.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically involving satellite attitude control and game theory control methods. Background Technology

[0002] With the rapid development of satellite technology, especially the widespread application of multi-satellite collaborative control technology in the aerospace field, the importance of satellite attitude control in various missions is becoming increasingly prominent. Particularly in the construction of large-scale satellite constellations and microsatellite systems, achieving precise and efficient attitude control and collaborative operation among satellites has become a key technical challenge. Traditional satellite attitude control methods mainly rely on centralized control systems, where a central control unit calculates the control inputs for each satellite and directly transmits this control information to each execution unit. The advantage of this method is its simple control algorithm and ease of implementation. When the number of satellites is small and the system structure is relatively simple, centralized control can effectively achieve global coordination, ensuring the accuracy and stability of attitude control. However, as the number of satellites increases and system complexity rises, the limitations of centralized control methods gradually become apparent.

[0003] First, centralized control methods rely entirely on a single central control unit. If this unit fails, the entire satellite constellation's control system will immediately fail, potentially causing mission interruption. This single point of failure is particularly dangerous in critical missions, especially when high attitude control accuracy is required. Second, maintaining stable communication links is challenging due to the large distances between satellites and limited communication bandwidth. 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 demands rise sharply, often exceeding the capacity of existing communication systems, thus affecting the transmission speed and accuracy of real-time control commands. Furthermore, centralized control methods often suffer from some accuracy loss when calculating global control variables, especially in microsatellites or small satellite constellations. Small control torques can lead to error accumulation, further impacting the overall system accuracy.

[0004] To overcome the shortcomings of centralized control methods, distributed game theory control has gradually become one of the mainstream technologies for multi-satellite collaborative control in recent years. In distributed game theory control, each satellite makes decisions based on local information, without relying on a single central control unit. In this way, satellites can update control variables through communication and information exchange, thereby achieving collaborative completion of attitude control tasks. Distributed game theory control transforms the control problem between multiple satellites into a local information game problem. This method consists of a total control variable calculation 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, thereby allocating less torque to flywheels with higher saturation. In the total control variable calculation layer, constraints on the magnitude of the control torque of each satellite are achieved through multi-satellite total control variable calculation based on model predictive control methods.

[0005] Despite the excellent performance of distributed game theory control methods in various aspects, several problems remain to be solved in practical applications. For example, patent document CN118890083A—"A Multi-Satellite On-Orbit Cooperative Dynamic Scheduling Method and System under Satellite Resource Failure"—although employs a distributed method at the torque allocation layer, the overall control quantity calculation still relies on a central unit. If this unit fails, the entire system may still face the risk of collapse. Secondly, the constraint processing on the magnitude of the control torque for microsatellites is not precise enough during the overall control quantity calculation process, which may lead to a decrease in control performance. Furthermore, while the saturation of flywheel speed is considered during control torque allocation, the flywheel speed is not limited to a defined range, which may result in the flywheel speed failing to output the allocated torque after saturation, thus affecting control performance. These problems need to be further addressed in future research to improve the reliability and accuracy of distributed game theory control methods in practical applications. Summary of the Invention

[0006] To address some shortcomings of distributed game control methods in practical applications, this invention proposes the following solution:

[0007] A multi-star collaborative distributed game control method, the method comprising:

[0008] S1. The steps to obtain the state-dependent coefficients (SDC) model based on the attitude dynamics model of the combined spacecraft and pseudo-linearization.

[0009] S2. Based on the state dependence coefficient model combined with the predictive time domain dynamic model and flywheel constraints, the steps to obtain the local optimal control strategy for each satellite in the combined spacecraft through model predictive control methods.

[0010] S3. The steps to obtain a distributed Nash equilibrium solution by combining the local optimal control strategy of each satellite with communication topology information and through distributed iteration and global coordination methods.

[0011] Furthermore, S1 includes: introducing an error quaternion q e and error angular velocity ω e Based on the principles of attitude dynamics, kinematic and dynamic equations for attitude error are established, and the SDC model is obtained through pseudo-linearization.

[0012]

[0013] Where A(x) is the state dependency matrix; x is the variable representing the motion state of the combined spacecraft; N is the number of sub-spacecraft contained in the combined spacecraft; B i U is the control matrix for the i-th satellite. i It is the control vector of the i-th satellite.

[0014] Further, S2 includes:

[0015] S21. Discretization of the SDC model:

[0016]

[0017] Where, x k It is the system state at the current time k; x k+1 It is the system state at the next moment; It is the discretized state transition matrix; It is the discretized control action matrix; u i,k It is the control quantity of the i-th satellite at the current time k and in the subsequent time period;

[0018] S22. Obtain the dynamic model in the prediction time domain:

[0019]

[0020] Among them, U i,k X is the sequence of control variables for the i-th satellite in the prediction time domain; k It is the system state sequence in the prediction time domain; Λ is the state transition matrix in the prediction time domain; Θ i It is the control input matrix of the i-th satellite in the prediction time domain;

[0021] S23. Select the local objective function in the finite time domain for all satellites:

[0022]

[0023] Among them, J iQ is the local objective function of the i-th satellite; i,k It is the state weight matrix in the prediction time domain; R i,k It is the control weight matrix in the prediction time domain; W i,k It is the weighting matrix for predicting flywheel speed in the time domain; Ω i,k It is the sequence of flywheel rotation speeds contained in the i-th satellite within the prediction time domain;

[0024] S24. Set flywheel constraint conditions, including flywheel torque amplitude constraint and speed constraint:

[0025]

[0026] in, This indicates a flywheel torque amplitude constraint; It is the upper limit of the flywheel torque amplitude constraint;

[0027] Indicates flywheel speed constraint; It is the upper limit of the flywheel speed constraint; ε i For identity matrix Let be a block-shaped lower triangular matrix of elements. N represents the Kronecker product. p It is the control sequence U i,k and state quantity sequence X k Length, N represents p A column vector whose elements are all 1s;

[0028] S25, X k and Ω i,k Combining the flywheel constraints, we obtain the quadratic programming problem:

[0029]

[0030]

[0031] Among them, M i,2 It is the quadratic coefficient matrix; M i,1 It is a matrix of coefficients for the first-order terms.

[0032] Further, S3 includes:

[0033] S31. Initialize the estimation vector. Set the initial estimation vector for the i-th satellite as follows:

[0034] μ i (0)=T i =Θ i U i,k ,

[0035] Where, μ i(0) is the initial estimation vector for the i-th satellite; T i =Θ i U i,k It is the actual effect of the i-th satellite on the system; U i,k It is the control input sequence of the i-th satellite in the prediction time domain;

[0036] S32, Pre-iteration loop:

[0037] S321. All satellites operate in parallel. The i-th satellite obtains the estimated vector μ of its neighboring satellites through the communication topology. j (t-1), and update its estimated vector according to the following rules:

[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 estimated vector of the i-th satellite; γ is the iteration step size; V(i) is the set of satellites connected to satellite i;

[0040] 322. When all satellites meet the tolerance conditions of the pre-iteration cycle:

[0041] ||μ i (t)-μ i (t-1)‖<ε p ,

[0042] Or when the maximum number of iterations in the pre-iteration loop is reached:

[0043] t p =t p,max ,

[0044] If so, proceed with the subsequent iterations; otherwise, return to S321.

[0045] S33, Subsequent Loop Iterations:

[0046] S331. All satellites operate in parallel, and the i-th satellite is based on μ. i (t) is used as a global and information estimate.

[0047]

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

[0049]

[0050] in, It is the local optimal control strategy for the i-th satellite at the t-th iteration;

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

[0052]

[0053] S334, Change the strategy amount Added to the estimation vector μ i ;

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

[0055]

[0056] Or when the maximum number of total iterations is reached:

[0057] t = t max ,

[0058] The iteration then ends, yielding an approximate solution to the Nash equilibrium. Otherwise, return to S331;

[0059] S34. Obtain the actual control output and take... The first N i Each element represents the actual output of each flywheel in the i-th satellite at the next control time k.

[0060] Furthermore, the local optimal control strategy is the solution that minimizes the local objective function of the i-th satellite while keeping the total amount of action of other satellites constant.

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

[0062]

[0063] The control vector μ of the i-th satellite i Iterative approximation can yield global and information estimates.

[0064] Where, d max It is the maximum degree of a vertex in the communication topology graph.

[0065] A multi-star collaborative distributed game control device, the device comprising:

[0066] Based on the attitude dynamics modeling of the combined spacecraft and pseudo-linearization processing, the modules of the SDC model are obtained;

[0067] Based on the state dependence coefficient model combined with the predictive time-domain dynamics model and flywheel constraints, a module is used to obtain the local optimal control strategy for each satellite in the combined spacecraft through model predictive control methods.

[0068] Based on the local optimal control strategies of each satellite and the communication topology information, a module obtains the distributed Nash equilibrium solution through distributed iteration and global coordination methods.

[0069] Based on the same inventive concept, the present invention also provides a computer storage medium for storing a computer program, which, when read by a computer, executes the method described in 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, wherein when the processor reads a computer program stored in the storage medium, the computer executes the method described in any one of the present invention.

[0071] Based on the same inventive concept, the present invention also provides a computer program product, which, when read, implements the method described in any one of the present invention.

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

[0073] This invention addresses the shortcomings of existing distributed game theory control methods in multi-star cooperative attitude control, and proposes an improved multi-star cooperative distributed game theory control method, device, computer program, and storage medium. Through the following technical means and creative efforts, this invention achieves significant technical effects, which are specifically categorized and described below:

[0074] (1) Based on the distributed game theory control method, this invention further optimizes the control architecture and adopts a fully distributed control strategy, avoiding the dependence on a single central unit in traditional methods. By introducing local information interaction and global coordination mechanisms, each satellite can make independent decisions based on local information, and exchange information with neighboring satellites through communication topology to achieve distributed calculation of global control quantities. During the research and development process, a distributed iterative algorithm based on model predictive control (MPC) was designed, combined with the Nash equilibrium principle in game theory, to achieve efficient calculation of multi-satellite collaborative control. By introducing a two-layer loop structure of pre-iteration and subsequent iteration, the rapid convergence and global consistency of control quantities 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 collapse problem caused by single point failure in traditional centralized control methods.

[0075] (2) In the process of calculating the control quantity, this invention accurately considers the torque amplitude constraint and speed constraint of the flywheel. By introducing a flywheel speed weight matrix and constraint conditions, the flywheel speed is limited to a reasonable range, avoiding the control performance degradation caused by flywheel saturation. An optimization algorithm based on quadratic programming is designed, integrating the flywheel constraint conditions into the solution of the local objective function, ensuring the accuracy and feasibility of control torque allocation. At the same time, by introducing a dynamic constraint mechanism for flywheel speed, the utilization efficiency of the flywheel is further optimized. This method significantly improves the control performance of the flywheel, avoids the problem of not being able to output allocated torque 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) This invention designs a local objective function for each satellite, and combines the state weight matrix, control quantity weight matrix, and flywheel speed weight matrix to achieve multi-objective optimization of satellite attitude control. Through distributed iteration and global coordination mechanisms, it ensures that the local optimal control strategies of each satellite converge to the global Nash equilibrium solution. A distributed iterative algorithm based on communication topology is proposed, which achieves fast calculation of the local objective function and global coordination through a two-layer structure of pre-iteration loop and subsequent loop iteration. Simultaneously, by introducing step size parameters and tolerance conditions, the convergence and computational efficiency of the algorithm are ensured. This method significantly improves the efficiency and accuracy of multi-satellite collaborative control, enabling rapid calculation and allocation of global control quantities under limited computing resources and communication bandwidth, and is suitable for efficient collaborative control of large-scale satellite constellations.

[0077] (4) This invention combines Model Predictive Control (MPC) with flywheel dynamic constraints, achieving dynamic optimization of satellite attitude control by predicting the dynamic model and constraints in the time domain. The real-time performance and adaptability of the control algorithm are ensured through discretization and the application of the State Dependency Coefficient (SDC) model. During the development process, a pseudo-linearization method based on the SDC model was designed to transform the nonlinear attitude dynamic equations into a linear form, simplifying the solution process for the control quantities. Simultaneously, by introducing flywheel constraints in the prediction time domain, the robustness and adaptability of the control algorithm are further improved. This method significantly enhances the real-time performance and adaptability of the control algorithm, enabling high-precision attitude control in complex dynamic environments, and is particularly suitable for the high-dynamic mission requirements of microsatellite systems.

[0078] (5) This invention achieves flexible information exchange among multiple satellites by introducing communication topology information. Each satellite only needs to exchange information with its neighboring satellites, without needing to establish 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 was designed to solve the global control variables through local information exchange. At the same time, by introducing iteration step size and tolerance conditions, the convergence and computational efficiency of the algorithm are ensured. This method significantly reduces the communication bandwidth requirements, improves the scalability of the system, and is suitable for efficient collaborative control of large-scale satellite constellations.

[0079] (6) This invention significantly improves the robustness, accuracy, and efficiency of multi-satellite collaborative control by optimizing the distributed control architecture, accurately handling flywheel constraints, designing local objective functions, combining model predictive control with dynamic constraints, and introducing flexible communication topologies. The combination of these technical means and creative efforts enables this invention to effectively address the shortcomings of existing distributed game theory control methods in practical applications, providing reliable technical support for the efficient collaborative control of large-scale satellite constellations and microsatellite systems.

[0080] This invention belongs to the field of aerospace technology and is specifically applicable to scenarios of multi-satellite collaborative control, especially for large-scale satellite constellations, microsatellite systems, and aerospace missions that require high-precision attitude coordination. Attached Figure Description

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

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

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

[0084] Figure 4 This is the communication topology diagram described in Embodiment Seven of the present invention, with reference numerals 1-5 corresponding to Star 1-Star 5, respectively;

[0085] Figure 5 The combined spacecraft error angular velocity described in Embodiment 7 of the present invention reflects the changes in the angular velocity error of the system in three axes;

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

[0087] Figure 7 The output torque of each flywheel of Star 1 as described in Embodiment 7 of the present invention;

[0088] Figure 8 It refers to the rotational speed of each flywheel in Star 1 as described in Embodiment 7 of the present invention;

[0089] Figure 9 The output torque of each flywheel of Star 2 as described in Embodiment 7 of the present invention;

[0090] Figure 10 It refers to the rotational speed of each flywheel in Star 2 as described in Embodiment 7 of the present invention;

[0091] Figure 11 The output torque of each flywheel of Star 3 as described in Embodiment 7 of the present invention;

[0092] Figure 12 It refers to the rotational speed of each flywheel in Star 3 as described in Embodiment 7 of the present invention;

[0093] Figure 13 The output torque of each flywheel of Star 4 as described in Embodiment 7 of the present invention;

[0094] Figure 14 It refers to the rotational speed of each flywheel in Star 4 as described in Embodiment 7 of the present invention;

[0095] Figure 15 The output torque of each flywheel of Star 5 as described in Embodiment 7 of the present invention;

[0096] Figure 16 It refers to the rotational speed of each flywheel in Star 5 as described in Embodiment 7 of the present invention;

[0097] Figure 17 These are all the flywheel speeds described in Embodiment Seven of this invention, reflecting the optimization effect of this control method on flywheel speed.

[0098] Figure 18 This refers to the number of algorithm iterations described in Embodiment 7 of this invention. Through multiple iterations and updates, the system response gradually stabilizes, achieving the expected control effect. Implementation

[0099] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0100] Implementation Method 1

[0101] Combination Figure 1 This embodiment describes a multi-star collaborative distributed game control method, the method comprising:

[0102] S1. The steps to obtain the SDC model by modeling the attitude dynamics of the combined spacecraft and performing pseudo-linearization.

[0103] S2. Based on the state dependence coefficient model combined with the predictive time domain dynamic model and flywheel constraints, the steps to obtain the local optimal control strategy for each satellite in the combined spacecraft through model predictive control methods.

[0104] S3. The steps to obtain a distributed Nash equilibrium solution by combining the local optimal control strategy of each satellite with communication topology information and through distributed iteration and global coordination methods.

[0105] This implementation introduces error quaternions and error angular velocities, establishing attitude error kinematics and dynamic equations based on attitude dynamics principles, and obtaining the SDC model through pseudo-linearization. This method simplifies the complex nonlinear attitude dynamic equations, transforming them into a linear form, which facilitates subsequent control variable calculation. 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.

[0106] Implementation Method 2

[0107] This embodiment is a further explanation of embodiment one.

[0108] Furthermore, S1 includes: introducing an error quaternion. With error angular velocity ω e =ω-Rω T Where R is the direction cosine matrix of the combined spacecraft body coordinate system relative to the desired coordinate system. Based on attitude dynamics principles, the kinematic and dynamic equations for attitude error are obtained, and after pseudo-linearization, state variables are defined. Then we have the following state equation in SDC form:

[0109]

[0110] Where A(x) is the state dependency matrix; x is the variable that combines the motion states of the spacecraft;

[0111] A 11 =-(Rω) T ) × +J -1 (Jω e +JRω T ) × -J -1 (Rω T ) × J is the state matrix related to the error angular velocity ω. eThe relevant part describes the dynamic behavior of the error angular velocity. J is the inertia matrix, × denotes the matrix cross product, R is the direction cosine matrix, and ω... T It is the desired angular velocity;

[0112] A 12 =-G1+J -1 (JRω T ) × G2 is the state matrix and the error quaternion q. e The relevant part describes the effect of the error quaternion on the rate of change of the error angular velocity;

[0113] It is to calculate A 12 Time and Relevant intermediate quantities;

[0114] It is to calculate A 12 Time and ω T Relevant intermediate quantities;

[0115] It is the state matrix and the error angular velocity ω e The relevant part describes the effect of the error angular velocity on the rate of change of the error quaternion;

[0116] It is the state matrix and the error quaternion q e The relevant part is used to describe the dynamic behavior of error quaternions;

[0117] N is the number of sub-spacecraft contained in the combined spacecraft;

[0118] It is the control matrix of the i-th satellite;

[0119] It is the control vector of the i-th satellite, where N i It is the dimension of the control quantity of the i-th satellite, that is, the number of flywheels contained in the i-th satellite;

[0120] It is the direction cosine matrix, used to describe the attitude relationship between the combined spacecraft body coordinate system and the desired coordinate system, q e0 It is the scalar part of the error quaternion, q e1 q e2 q e3 It is the vector part of the error quaternion.

[0121] This implementation further optimizes the discretization of the SDC model, achieving accurate prediction of the system state through the discretized state transition matrix and control action matrix. By predicting the dynamic model in the time domain, the system can achieve dynamic optimization of satellite attitude under limited computing resources and communication bandwidth. This method significantly improves the real-time performance and adaptability of the control algorithm, making it particularly suitable for highly dynamic mission requirements.

[0122] Implementation Method 3

[0123] This embodiment is a further explanation of embodiment one.

[0124] Further, S2 includes:

[0125] S21. Discretization of the SDC model:

[0126]

[0127] Where, x k It is the system state at the current time k, x k+1 It refers to the system state at the next moment. It is the discretized state transition matrix. It is the discretized control action matrix, μ i,k It is the control quantity of the i-th satellite at the current time k and in the subsequent time period τ;

[0128] τ is the control time interval. This represents the discretization of a continuous system;

[0129] N i It is the dimension of the control quantity of the i-th satellite;

[0130] S22. Obtain the dynamic model in the prediction time domain:

[0131]

[0132] in, It is the sequence of control quantities for the i-th satellite in the prediction time domain;

[0133] It predicts the system state sequence in the time domain;

[0134] It is the state transition matrix in the prediction time domain;

[0135] It is the control input matrix of the i-th satellite in the prediction time domain;

[0136] S23. Select the local objective function in the finite time domain for all satellites:

[0137]

[0138] in,

[0139] J i It is the local objective function of the i-th satellite;

[0140] Q i,k It is the state weight matrix in the prediction time domain;

[0141] R i,k It is the control quantity weight matrix in the prediction time domain;

[0142] W i,k It is the weight matrix for predicting flywheel speed in the time domain;

[0143] It is the sequence of flywheel rotation speeds contained in the i-th satellite within the prediction time domain, which can be expressed by the formula... get.

[0144] S24. Set flywheel constraint conditions, including flywheel torque amplitude constraint and speed constraint:

[0145]

[0146] in, This indicates a flywheel torque amplitude constraint; It is the upper limit of the flywheel torque amplitude constraint;

[0147] Indicates flywheel speed constraint; This is the upper limit of the flywheel speed constraint, expressed as:

[0148]

[0149] ε i For identity matrix Let be a block-shaped lower triangular matrix of elements. N represents the Kronecker product. p It is the control sequence U i,k and state quantity sequence X k Length, N represents p A column vector whose elements are all 1s;

[0150] S25, The time-domain dynamic model X k The rotational speed sequence Ω of the flywheel contained in the i-th satellite in the prediction time domain. i,k Combining the flywheel constraints and simplifying them, omitting those not containing U... i,kFor items that cannot be optimized, and considering flywheel torque amplitude constraints and speed constraints, the quadratic programming problem is obtained:

[0151]

[0152] Among them, M i,2 It is the quadratic coefficient matrix; M i,1 It is a matrix of coefficients for the first-order terms.

[0153] This implementation introduces flywheel constraints, including flywheel torque amplitude constraints and speed constraints, ensuring that the flywheel speed remains within a reasonable range and avoiding control performance degradation caused by flywheel saturation. Through solving a quadratic programming problem, the system can precisely allocate control torque, ensuring the accuracy and stability of attitude control. This method is particularly suitable for the high-precision control requirements of microsatellite systems.

[0154] Implementation Method 4

[0155] This embodiment is a further explanation of embodiment one, combined with... Figure 2 Description of this implementation method:

[0156] Further, S3 includes:

[0157] For a given system and a fixed objective function, a policy set is formed if the following inequality holds. Reaching Nash equilibrium

[0158]

[0159] in, This is the Nash equalization control strategy for the i-th satellite;

[0160] u i The control strategy for the i-th satellite is defined as follows:

[0161] u i ∈U i ,

[0162] U i It is the set of all possible controls for the i-th satellite, defined as follows:

[0163]

[0164] Where k is the current time, x k This is the current system state, N. i It is the dimension of the control quantity of the i-th satellite.

[0165] The communication network of each satellite can be represented by a topological graph, where each subsatellite is regarded as a vertex in the graph and the data interface is regarded as an edge of the graph. The entire undirected graph can be described by the Laplace matrix L.

[0166] The following distributed game control strategy is designed and implemented within the control interval τ:

[0167] S31. Initialize the estimation vector. Set the initial estimation vector for the i-th satellite as follows:

[0168] μ i (0)=T i =Θ i U i,k ,

[0169] Where, μ i (0) is the initial estimation vector for the i-th satellite; T i =Θ i U i,k It is the actual effect of the i-th satellite on the system; U i,k It is the control input sequence of the i-th satellite in the prediction time domain;

[0170] S32, Pre-iteration loop: Let the next control time be k, and the current iteration number be t;

[0171] S321. All satellites operate in parallel. The i-th satellite obtains the estimated vector μ of its neighboring satellites through the communication topology. j (t-1), and update its estimated vector according to the following rules:

[0172] μ i (t)=μ i (t-1)+γ∑ j∈V(i) (μ j (t-1)-μ i (t-1)),

[0173] Where, μ i (t) is the update of the estimated vector of the i-th satellite; γ is the iteration step size; V(i) is the set of satellites connected to satellite i;

[0174] 322. When all satellites meet the tolerance conditions of the pre-iteration cycle:

[0175] ||μ i (t)-μ i (t-1)‖<ε p , ε p It is the pre-iteration tolerance.

[0176] Or when the maximum number of iterations in the pre-iteration loop is reached:

[0177] t p =tp,max , t p,max It is the upper limit of the number of iterations.

[0178] If so, proceed with the subsequent iterations; otherwise, return to S321.

[0179] S33. Subsequent iterations: Let the current iteration number be t;

[0180] S331. All satellites operate in parallel, and the update μ of the i-th satellite is based on the estimated vector of the i-th satellite. i (t) is used as a global and information estimate.

[0181] S332. Solve the quadratic programming problem to obtain the locally optimal control strategy:

[0182]

[0183] in, It is the local optimal control strategy for the i-th satellite at the t-th iteration;

[0184] S333, Introduce step size parameter ξ and update the control strategy:

[0185]

[0186] S334, Change the strategy amount Added to the estimation vector μ i ;

[0187] S335. When all satellites meet the termination condition:

[0188]

[0189] Or when the maximum number of total iterations is reached:

[0190] t = t max ,

[0191] The iteration then ends, yielding an approximate solution to the Nash equilibrium. Otherwise, return to S331;

[0192] S34. Obtain the actual control output and take... The first N i Each element represents the actual output of each flywheel in the i-th satellite at the next control time k.

[0193] This is the final control quantity, which serves as the actual output torque of each flywheel at the start of the next control moment k.

[0194] This implementation achieves flexible information exchange among multiple satellites through a distributed game theory control program combined with communication topology information. A two-level loop structure of pre-iteration and subsequent iterations ensures rapid convergence and global consistency of the control variables. This method significantly improves the system's robustness and fault tolerance; even if some satellites or communication links fail, the system can continue to operate through local information exchange, avoiding the system collapse problem caused by single-point failures in traditional centralized control methods.

[0195] Implementation Method 5

[0196] This embodiment is a further explanation of embodiment four.

[0197] Furthermore, the local optimal control strategy is the solution that minimizes the local objective function of the i-th satellite while keeping the total amount of action of other satellites constant.

[0198] This approach, through the design of locally optimal control strategies, ensures that each satellite makes optimal decisions based on local information. Simultaneously, a global coordination mechanism ensures that the locally optimal control strategies of each satellite converge to a global Nash equilibrium solution. This method significantly improves the efficiency and accuracy of multi-satellite cooperative control, enabling rapid calculation and allocation of global control variables with limited computing resources and communication bandwidth. It is suitable for efficient cooperative control of large-scale satellite constellations.

[0199] Implementation Method Six

[0200] This embodiment is a further explanation of embodiment four.

[0201] Furthermore, the iteration step size satisfies the following condition:

[0202]

[0203] The control vector μ of the i-th satellite i Iterative approximation can yield global and information estimates.

[0204] Where, d max It represents the maximum degree of a vertex in the communication topology graph. Furthermore, when the optimization step size ξ is sufficiently small, the above iterative process can approximate the Nash equilibrium solution.

[0205] This implementation ensures the convergence and computational efficiency of the algorithm by introducing iteration step size and tolerance conditions. By optimizing the choice of step size, the system can quickly approximate the Nash equilibrium solution, ensuring accurate allocation of control variables. This method significantly reduces communication bandwidth requirements, improves system scalability, and is suitable for efficient collaborative control of large-scale satellite constellations.

[0206] Through the above six implementation methods, this invention achieves significant improvements in multi-satellite cooperative control, including enhancing system robustness, accuracy, and efficiency, optimizing flywheel constraints, designing local objective functions, combining model predictive control with dynamic constraints, and introducing flexible communication topologies. The combination of these techniques enables this invention to effectively address the shortcomings of existing distributed game theory control methods in practical applications, providing reliable technical support for the efficient cooperative control of large-scale satellite constellations and microsatellite systems.

[0207] Implementation Method Seven

[0208] This embodiment integrates the technical solutions described in embodiments one through six. Combined with practical situations, it further verifies and explains the technical effects of the present invention through numerical simulation examples. This includes demonstrating the effects achieved when certain parameters in the algorithm reach their optimal range or optimal values.

[0209] Without loss of generality, the moment of inertia of the combined spacecraft is defined as:

[0210]

[0211] There are 5 serving satellites, and their communication topology is as follows: Figure 4 As shown in the attached diagram, reference numerals 1-5 correspond to stars 1-5 respectively, where stars 1, 2, and 3 include three flywheels, and stars 4 and 5 include four flywheels.

[0212] Treating each subsatellite as a vertex in the graph and the data interface as an edge, the entire topology can be described by a Laplace matrix L, which is:

[0213]

[0214] In this matrix, the diagonal elements represent the degree of each vertex, i.e., the number of edges connected to that vertex; the off-diagonal elements represent the connection relationships between vertices, i.e., -1 for two connected vertices and 0 otherwise.

[0215] The number of each star wheel, its direction, and the control parameter settings are given in the table below:

[0216]

[0217]

[0218] Furthermore, the control parameter matrix Q of each satellite is the same, and is an identity matrix E. 6×6 Let the diagonal matrix W be...

[0219] All flywheels have an initial rotational speed of 0. Assume the initial attitude of the combined spacecraft is:

[0220] q0 = [0 0 0 1] T ,

[0221] The initial angular velocity is:

[0222] ω0 = [0 0 0] T rad / s,

[0223] The desired posture is:

[0224] q T =[0.5 -0.2 0.2 0.8185] T ,

[0225] The desired angular velocity is:

[0226] ω T =[0 0 0] T rad / s,

[0227] Take N p =40,

[0228] The sampling and control step size is set to τ = 0.1s, and the tolerance for pre-iteration stopping is set to ε. P =0.001,

[0229] The maximum number of pre-iterations is t P,max =15, The tolerance ε is taken in subsequent iterations. t =0.001,

[0230] Iteration upper limit t max =10,

[0231] Simulation results are as follows Figure 5-18 As shown:

[0232] according to Figure 5 The curve showing the change in error angular velocity indicates that the spacecraft's angular velocity tends to stabilize after about 40 seconds.

[0233] according to Figure 6 The error quaternion curve shown indicates that the spacecraft's attitude stabilizes in about 40 seconds.

[0234] The results show that the combined spacecraft reached the expected attitude around 50 seconds, and the output torque and speed of each flywheel were precisely constrained.

[0235] Observe the output torque curves of each flywheel, and according to Figure 7 , 9As shown in curves 11, 13, and 15, the output torque of each flywheel exhibits significant fluctuations around 25 seconds. This is because the iteration upper limit has been reached, resulting in inaccurate control strategies obtained during this period. This can be avoided by increasing the iteration upper limit, but it has little impact on the overall control effect. After this, each flywheel quickly enters a stable state, stabilizing the entire system. Once the system stabilizes, the rotational speed of each flywheel does not strictly return to zero. This is due to the iteration tolerance. Reducing the tolerance can improve this situation, but it will increase the computational and communication burden on each satellite, requiring a trade-off.

[0236] Observe the speed curves of each flywheel, see [reference]. Figure 8 , 10 As shown in curves 12, 14, and 16, the speeds of each flywheel are significantly reduced while maintaining good attitude control performance. This indicates that while performing attitude control, each star achieves optimized distribution of flywheel speeds overall through "idling" without total control torque.

[0237] Observing the number of iterations, we can see that both the pre-iteration and subsequent solution iterations are limited to a reasonable range. Therefore, the computational and communication load for solving this distributed game control strategy is not large, and it can be solved quickly online. Furthermore, it can be seen that as the system stabilizes, the number of pre-iteration and subsequent solution iterations decreases significantly, further reducing the computational and communication load for each star.

[0238] The above detailed description of the technical solution provided by the present invention is intended to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above detailed embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0239] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0240] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A distributed game control method for multi-star collaboration, characterized in that, The method includes: S1. The step of obtaining the SDC model by modeling the attitude dynamics of the combined spacecraft and performing pseudo-linearization processing, wherein the combined spacecraft includes... One satellite; S2. Based on the state dependence coefficient model combined with the predictive time domain dynamic model and flywheel constraints, the steps to obtain the local optimal control strategy for each satellite in the combined spacecraft through model predictive control methods. The flywheel constraints include flywheel torque amplitude constraints and speed constraints: , in, Indicates the first Flywheel torque amplitude constraints for each satellite; It is the first The upper limit of the flywheel torque amplitude constraint for each satellite; Indicates the first Flywheel speed constraints for each satellite; It is the first The upper limit of the flywheel speed constraint for each satellite; For the first Unit matrix of satellites Let be a block-shaped lower triangular matrix of elements. Indicates the Kronecker product. It is a control quantity sequence and state quantity sequence Length, express A column vector whose elements are all 1s; S3. The steps to obtain a distributed Nash equilibrium solution by combining the local optimal control strategy of each satellite with communication topology information and through distributed iteration and global coordination methods.

2. The distributed game control method according to claim 1, characterized in that, S1 includes: introducing an error quaternion. and error angular velocity Based on the principles of attitude dynamics, kinematic and dynamic equations for attitude error are established, and the SDC model is obtained through pseudo-linearization. ， in, It is a state dependency matrix; These are variables that combine the motion states of the spacecraft; It is the number of satellites contained in the combined spacecraft; Yes, yes, the first Control matrix of each satellite It is the first Control vectors for each satellite.

3. The distributed game control method according to claim 1, characterized in that, S2 includes: S21. Ignoring the changes in the state transition matrix in the prediction time domain, the sampling and control time interval is set to... Discretization of the SDC model: ， in, It is the current moment. The system status; It is the system state at the next moment; It is the discretized state transition matrix; It is the discretized control action matrix; It is the first Each satellite at the current moment and afterwards Control volume within a time period; S22. Obtain the dynamic model in the prediction time domain: ， in, It is the first The sequence of control quantities for each satellite in the prediction time domain; It predicts the system state sequence in the time domain; It is the state transition matrix in the prediction time domain; It is the first The control input matrix of each satellite in the prediction time domain; S23. Select the local objective function in the finite time domain for all satellites: ， in, It is the first Local objective functions for each satellite; It predicts the time within the time domain. No. The state weight matrix of each satellite; It predicts the time within the time domain. No. The control weight matrix for each satellite; It predicts the time within the time domain. No. The flywheel speed weight matrix for each satellite; It is a moment No. The rotational speed sequence of the flywheels contained in each satellite within the prediction time domain; S24. Set flywheel constraint conditions, including flywheel torque amplitude constraint and speed constraint; S25, will and Combining the flywheel constraints, we obtain the quadratic programming problem: ， ， in, It is a quadratic coefficient matrix; It is a linear coefficient matrix, where the subscript i represents the satellite number.

4. The distributed game control method according to claim 1, characterized in that, S3 includes: S31. Initialize the estimation vector. Set the initial estimation vector for the i-th satellite as follows: ， in, It is the first Initial estimated vectors for each satellite; It is the first The actual impact of each satellite on the system; It is the first The control input sequence of each satellite in the prediction time domain; S32, Pre-iteration loop: S321, All satellites operate in parallel, the... Each satellite obtains the estimated vectors of its neighboring satellites through the communication topology. It updates its estimated vector according to the following rules: ， in, It is the first Update of the estimated vectors for each satellite; It is the iteration step size; It is with satellite A collection of connected satellites; S322. When all satellites meet the tolerance conditions of the pre-iteration cycle: ， Or when the maximum number of iterations in the pre-iteration loop is reached: ， If so, proceed with the next iteration; otherwise, return to S321 and continue iterating. S33, Subsequent Loop Iterations: S331, All satellites operate in parallel, the... Each satellite is based on Use it as a global and informational estimate ; S332. Solve the quadratic programming problem to obtain the locally optimal control strategy: ， in, It is in the During the nth iteration, the 1st Local optimal control strategy for each satellite; S333, Introducing step size parameter Update control policy: ； S334, Change the strategy Added to the estimated vector ; S335. When all satellites meet the termination condition: ， Or when the maximum number of total iterations is reached: ， The iteration then ends, yielding an approximate solution to the Nash equilibrium. Otherwise, return to S331; S34. Obtain the actual control output and take... The former An element, as the next control moment No. Actual output of each flywheel in each satellite .

5. The distributed game control method according to claim 4, characterized in that, The locally optimal control strategy is to ensure that, with the total effect of other satellites remaining constant, the first... The solution that minimizes the local objective function of each satellite.

6. The distributed game control method according to claim 4, characterized in that, The iteration step size satisfies the following condition: ， No. Control vector of each satellite Iterative approximation can yield global and information estimates. ; in, It is the maximum degree of a vertex in the communication topology graph.

7. A multi-star collaborative distributed game control device, characterized in that, The device includes: Based on the attitude dynamics modeling of the combined spacecraft and pseudo-linearization processing, the modules of the SDC model are obtained; Based on the state dependence coefficient model combined with the predictive time-domain dynamics model and flywheel constraints, a module is used to obtain the local optimal control strategy for each satellite in the combined spacecraft through model predictive control methods. The flywheel constraints include flywheel torque amplitude constraints and speed constraints: , in, Indicates the first Flywheel torque amplitude constraints for each satellite; It is the first The upper limit of the flywheel torque amplitude constraint for each satellite; Indicates the first Flywheel speed constraints for each satellite; It is the first The upper limit of the flywheel speed constraint for each satellite; For the first Unit matrix of satellites Let be a block-shaped lower triangular matrix of elements. Indicates the Kronecker product. It is a control quantity sequence and state quantity sequence Length, express A column vector whose elements are all 1s; Based on the local optimal control strategies of each satellite and the communication topology information, a module obtains the distributed Nash equilibrium solution through distributed iteration and global coordination methods.

8. A computer storage medium for storing computer programs, characterized in that, When the computer program is read by the 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, is characterized by: When the computer program is read, the method described in any one of claims 1 to 6 is implemented.

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