A Predictive Control Method Based on a Distributed Model of Cooperative Game Theory in Defense Satellites

Abstract

This invention discloses a distributed model predictive control method for cooperative game theory of defensive satellites, belonging to the field of cooperative control technology for defensive satellites. It includes establishing a relative motion model based on the Clohessy-Wiltshire equations, recursively predicting future trajectories through target prediction to achieve dynamic cooperative encirclement; comprehensively considering multiple constraints such as control input saturation, communication range, collision avoidance, and obstacle avoidance, it adopts a distributed architecture and synchronous update mechanism to optimize computational efficiency; and evaluates encirclement performance through position and velocity cost functions. This application can significantly reduce computational complexity, meet real-time requirements, and ensure efficient cooperative encirclement in complex environments.

Description

Technical Field

[0001] This invention belongs to the field of satellite cooperative control technology, specifically, it relates to a distributed model predictive control method for defensive satellite cooperative game. Background Technology

[0002] Distributed model predictive control for collaborative game among defensive satellites is a core technology for building satellite constellation operational capabilities. As the space security situation becomes increasingly complex and competition for orbital resources intensifies, defensive satellite constellations are gradually moving from static deployment to possessing dynamic response and autonomous game-playing capabilities. In typical missions such as orbital confrontation, target tracking, resource blockade, and defensive interception, defensive constellations must achieve rapid decision-making and collaborative control in highly uncertain orbital environments. Facing challenges such as complex lighting conditions, orbital congestion, sudden threats, and non-cooperative targets, they must demonstrate excellent organization, cooperation, stability, and environmental adaptability.

[0003] Current research on distributed model predictive control of defensive satellite cooperative game at home and abroad mainly focuses on differential game, formation tracking and deep reinforcement learning methods, but there are still shortcomings in practical applications: (1) When the number of defensive satellites increases, the orbital game control based on differential game is difficult to achieve rapid decision-making and control calculation, and it is difficult to quickly generate game trajectories that meet the constraints in complex lighting or environments with obstacles; (2) The defensive satellite group cooperative game method based on formation tracking is difficult to simultaneously take into account the complex constraints such as game performance optimization and thrust saturation, collision avoidance and limited flight time; (3) The defensive satellite game control method based on deep reinforcement learning has a complex network structure and a large number of parameters, making it difficult to guarantee the online computing speed of the onboard equipment. Summary of the Invention

[0004] The purpose of this invention is to provide a predictive control method for a distributed model of cooperative game theory of defense satellites, which mainly solves the technical problems in the prior art such as unknown target satellite maneuverability, difficulty in handling multiple constraints, high computational complexity, and difficulty in guaranteeing real-time performance.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A predictive control method for a distributed model of cooperative game theory in defense satellites includes the following steps:

[0007] S1, Establish a relative motion model to describe the relative motion relationship between defensive satellites or between a defensive satellite and a target satellite;

[0008] S2, the relative motion model is discretized to obtain a discrete-time state-space model of the relative motion of the defense satellite or the target satellite;

[0009] S3, the cost function for predictive control of a cooperative game-theoretic distributed model for constructing defense satellites;

[0010] S4, Establish the conditional constraints of the cost function in the cooperative game control of defensive satellites;

[0011] S5, combining cost function and condition constraints, transforms the predictive control problem of the distributed model of cooperative game of defense satellites into an objective function optimization problem;

[0012] S6 defines the assumed state of the defense satellite at the current time k, and models and predicts the control behavior of the target satellite in the prediction time domain based on the current centroid position of the defense satellite.

[0013] S7 constructs and solves a target satellite optimization problem under multiple constraints, providing a basis for decision-making for defense satellites, thereby achieving dynamic and coordinated encirclement of target satellites.

[0014] Further, in step S1, the expression for the relative motion model is:

[0015]

[0016] In the formula, , and These represent the coordinate components of the target satellite or defense satellite constellation in the LVLH coordinate system of the reference satellite. For reference satellite orbital angular velocity; , and This represents the acceleration component acting on the target satellite or the defense satellite; , and express , and The corresponding second derivative; , and express , and The corresponding first derivative;

[0017] Define state variables and control of acceleration variables Then equation (1) can be rewritten as:

[0018]

[0019] In the formula,

[0020] .

[0021] Furthermore, in step S2, the discrete-time state-space model is:

[0022]

[0023] In the formula, and They represent the first The state vector and control acceleration input at each sampling time, Indicates the first The location of each sampling time. Indicates the first The velocity at each sampling moment; matrix and The state transition matrix and input matrix obtained from discretization, respectively, are defined as follows:

[0024]

[0025] In the formula, Indicates the sampling time.

[0026] Furthermore, the expression for the cost function is:

[0027]

[0028] in, The cost function for the capture location is expressed as follows:

[0029]

[0030] In the formula, It is the step index within the prediction interval. It predicts the length of the time domain. For the first A defense satellite at any time The capture position error vector, For the first Position vectors of each defense satellite in the LVLH coordinate system It is the position vector of the target satellite in the same coordinate system. It is the expected relative displacement, i.e., the first... The ideal offset position of each defensive satellite relative to the target satellite in the encirclement formation;

[0031] Let the capture speed cost function be... Here are the weighting coefficients for the capture speed cost function, which is expressed as follows:

[0032]

[0033] In the formula, No. A defense satellite at any time The capture speed error vector, No. The velocity vector of a defense satellite in the LVLH coordinate system It is the velocity vector of the target satellite in the same coordinate system.

[0034] Furthermore, in step S4, the constraints on the defensive satellite cooperative game control include:

[0035] Control input constraints:

[0036]

[0037] In the formula, It is the first A defensive satellite in Make predictions constantly, targeting the future. The control input vector for the step; It is the maximum acceleration limit allowed by the defense satellite controller;

[0038] Communication distance constraints:

[0039]

[0040] In the formula, and These are defense satellites and At any moment Predicted future Step position; It is the maximum distance at which defensive satellites can communicate with each other.

[0041] Safety distance constraints:

[0042]

[0043] In the formula, It is the maximum distance at which defensive satellites can communicate with each other.

[0044] Safety constraints:

[0045]

[0046] In the formula, It refers to the location of spatial obstacles. It is the minimum safe distance between a defensive satellite and an obstacle.

[0047] Further, in step S5, the expression for the objective function optimization problem is:

[0048]

[0049] In the formula, C11–C18 represent: the dynamic constraints of the defensive satellite, the predictive dynamic constraints of the target satellite, the initial state constraints of the defensive satellite, the initial state constraints of the target satellite, the control input constraints of the defensive satellite, the maximum communication distance constraints, the minimum safe distance constraints, and the minimum safe distance constraints between the defensive satellite and obstacles, respectively. Indicates at time Predicted defense satellites In the future The state at any given moment; Indicates at time Based on model predictions, the target satellite will be in the future. The state at any given moment; Indicates at time The predicted target satellite in the future Predictive control input at specific times; Indicates defense satellite At any moment Predicted state Equal to its true state ; Indicates defense satellite At any moment Predicted status of the target satellite Equal to its true state ; Indicates from neighboring satellites The satellite obtained in the future The location at any given moment.

[0050] Furthermore, in step S6, the expression for the assumed state of the defense satellite at the current time k is:

[0051]

[0052] in, Based on Constantly defending against satellites The optimal state.

[0053] Furthermore, in step S7, the target satellite optimization problem under multiple constraints is as follows:

[0054]

[0055] In the formula, C21 and C23 represent the dynamic constraints of the predicted state of the defense satellite from the perspective of the target satellite and the initial state velocity; C22 and C24 represent the dynamic constraints of the predicted state of the target satellite and the initial state constraints; and C25 represents the maximum thrust constraint of the target satellite's control input. Is the target satellite in the prediction step? The control input is the optimization variable; Enemy satellite at time For the future Predicted position of the step This indicates that during the enemy satellite prediction process, defensive satellites... In the prediction step The estimation of the location; It is the number of defense satellites. To protect the satellite's center of mass. This indicates that during the calculation of the target satellite's control input, the defensive satellite... future Estimation of the state at any given time; Indicates the target satellite at time Defense satellites Predicted initial state value The target satellite can observe the defense satellite. Real state Consistent; This represents the initial value of the target satellite's predicted state. Equal to its true state ; The predicted target satellite in the future The control input at any given time, its infinite norm The maximum control input cannot be exceeded. .

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] (1) The present invention is based on dynamic cooperative encirclement of the target based on target prediction: In the prediction time domain, the future trajectory of the target satellite is recursively derived using the discrete dynamics model of the target satellite to obtain the state evolution information of the target satellite. Based on this, the defense satellite cluster determines its own control input through a cooperative game strategy, taking into account both its own optimal response and the actions of other satellites, thereby achieving dynamic encirclement of the target.

[0058] (2) In the design of the control strategy, the present invention comprehensively considers multiple constraints such as control input saturation, communication range limitation, inter-satellite collision avoidance and obstacle avoidance, and addresses the problems of high computational complexity and difficulty in ensuring real-time performance through distributed control architecture and synchronous execution mechanism, so as to realize real-time collaborative optimization of defense satellites. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method of the present invention;

[0060] Figure 2 A diagram showing the motion trajectories of the target satellite and each defense satellite in the LVLH;

[0061] Figure 3 This refers to the positional error between the target satellite and each defense satellite during the encirclement and suppression process.

[0062] Figure 4 This refers to the capture speed error between the target satellite and each defense satellite. Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments.

[0064] Example

[0065] like Figure 1 As shown, this invention discloses a distributed model predictive control (DMPC) method for cooperative game theory among defensive satellites. To describe the relative motion relationships between defensive satellites, this invention uses the classic Clohessy–Wiltshire (C–W) equations to establish a relative motion model, the specific form of which is as follows:

[0066]

[0067] In the formula, , and These represent the coordinate components of the target satellite or defense satellite constellation in the reference satellite LVLH (Local Vertical Local Horizontal) coordinate system. For reference satellite orbital angular velocity; , and This represents the acceleration component acting on the target satellite or the defense satellite; , and express , and The corresponding second derivative; , and express , and The corresponding first derivative.

[0068] Define state variables and control of acceleration variables Then equation (1) can be rewritten as:

[0069]

[0070] In the formula,

[0071]

[0072] Furthermore, to meet the real-time requirements of the distributed predictive control model in the cooperative game of defense satellites, the above continuous-time dynamic equations are discretized, and a discrete-time state-space model is derived:

[0073]

[0074] In the formula, and They represent the first The state vector and control acceleration input at each sampling time, Indicates the first The location of each sampling time. Indicates the first The velocity at each sampling time point. Matrix and The state transition matrix and input matrix obtained from discretization, respectively, are defined as follows:

[0075]

[0076] In the formula, Indicates the sampling time.

[0077] After establishing a discrete dynamic model of the relative motion of satellites, a cost function can be constructed for the predictive control of a distributed model of cooperative game theory for defense satellites. The cost function for the capture position of a single defense satellite can be defined as follows:

[0078]

[0079] In the formula, It is the step index within the prediction interval. It predicts the length of the time domain. No. A defense satellite at any time The capture position error vector, No. Position vectors of each defense satellite in the LVLH coordinate system It is the position vector of the target satellite (the satellite being captured) in the same coordinate system. It is the expected relative displacement, i.e., the first... The ideal offset position of each defense satellite relative to the target satellite in the encirclement formation.

[0080] No. The capture rate cost function for a single defense satellite is defined as:

[0081]

[0082] In the formula, No. A defense satellite at any time The capture speed error vector, No. The velocity vector of a defense satellite in the LVLH coordinate system It is the velocity vector of the target satellite in the same coordinate system.

[0083] The cost function in this embodiment includes two parts: position error cost and velocity error cost, which are used to comprehensively evaluate the control performance of the defense satellite in the process of capturing the target.

[0084]

[0085] In the formula, The weighting coefficient represents the speed cost.

[0086] In defending against satellite cooperative game control, the following constraints must also be met.

[0087] Control input constraints:

[0088]

[0089] In the formula, It is the first A defensive satellite in Make predictions constantly, targeting the future. The control input vector for each step. It is the maximum acceleration limit allowed by the defense satellite controller.

[0090] Communication distance constraints:

[0091]

[0092] In the formula, and These are defense satellites and At any moment Predicted future Step position. It is the maximum distance at which defensive satellites can communicate with each other.

[0093] Safety distance constraints:

[0094]

[0095] In the formula, It is the maximum distance at which defensive satellites can communicate with each other.

[0096] Safety constraints:

[0097]

[0098] In the formula, It refers to the location of spatial obstacles. It is the minimum safe distance between a defensive satellite and an obstacle.

[0099] In summary, for the scenario of predictive control using a distributed model in a cooperative game among defense satellites, the problem can be formulated as the following optimization problem:

[0100]

[0101] In the formula, C11–C18 represent: defensive satellite dynamics constraints (C11), target satellite prediction dynamics (C12), defensive satellite initial state (C13), target satellite initial state (C14), defensive satellite control input constraints (C15), maximum communication distance constraints (C16), minimum safe distance constraints (C17), and minimum safe distance constraints between defensive satellite and obstacles (C18), respectively. Indicates at time Predicted defense satellites In the future The state at any given moment; Indicates at time Based on model predictions, the target satellite will be in the future. The state at any given moment; Indicates at time The predicted target satellite in the future Predictive control input at specific times; Indicates defense satellite At any moment Predicted state Equal to its true state ; Indicates defense satellite At any moment Predicted status of the target satellite Equal to its true state ; Indicates from neighboring satellites The satellite obtained in the future The location at any given moment.

[0102] In the synchronous update scheme, each defense satellite can simultaneously optimize at each time step, transmitting the hypothetical state rather than the actual state. (Based on time...) Constantly defending against satellites optimal state It can be placed at the current moment. hypothetical state The definition is as follows:

[0103]

[0104] When a defensive satellite calculates its own control input, it needs to model and predict the control behavior of the target satellite in the prediction time domain. Specifically, it is assumed that the target satellite, when planning its motion, does not consider the control input of the defensive satellite, but only determines its own motion trend based on the current position of the defensive satellite's center of mass, i.e., it tries to move as far away from the defensive satellite's center of mass as possible. Therefore, the prediction optimization problem of the target satellite can be formulated as follows:

[0105]

[0106] In the formula, C21–C25 represent: the predicted state dynamics (C21) and initial state (C23) of the defense satellite from the perspective of the target satellite, the predicted state dynamics (C22) and initial state (C24) of the target satellite itself, and the maximum thrust constraint of the target satellite control input (C25), respectively. Is the target satellite in the prediction step? The control input is the optimization variable. Enemy satellite at time For the future Predicted position of the step This indicates that during the enemy satellite prediction process, defensive satellites... In the prediction step The location is estimated. It is the number of defense satellites. To protect the satellite's center of mass. This indicates that during the calculation of the target satellite's control input, the defensive satellite... future Estimation of the state at any given time; Indicates the target satellite at time Defense satellites Predicted initial state value The target satellite can observe the defense satellite. Real state Consistent; This represents the initial value of the target satellite's predicted state. Equal to its true state ; The predicted target satellite in the future The control input at any given time, its infinite norm The maximum control input cannot be exceeded. .

[0107] The following simulation experiments were conducted using the above method in the Matlab 2018a simulation environment. Fmincon was used to solve the predictive control problem of the distributed model of cooperative game between defense satellites and the predictive optimization problem of the target satellite. The specific values ​​of each performance parameter and optimization problem parameter in the simulation case are shown in Table 1.

[0108] Table 1 Parameters of the Optimization Problem

[0109] Parameter values significance Prediction Time Domain Sampling time Weighting coefficient Maximum control input safe distance between satellites Maximum communication distance Reference satellite orbital altitude

[0110] The initial states of the defense satellite and the target satellite are set as shown in Table 2.

[0111] Table 2 Parameters for the Optimization Problem

[0112] state Defense Satellite 1 Defense Satellite 2 Defense Satellite 3 Target satellite -10.8 -9.5 -10.25 -10 -2.9 -3.1 -3.2 -3 -4.85 -4.5 -5.95 -5 2 2 2 0 0 0 0 -2 0 0 0 0

[0113] The coordinates of the obstacles and the safe distances are shown in Table 3.

[0114] Table 3 Obstacle Coordinates and Safety Distance

[0115] Obstacle number coordinate safe distance 1 0.2 2 0.3

[0116] The expected positional deviation between each defensive satellite and the target satellite is: , , .

[0117] Figure 2 The motion trajectories of the target satellite and the defense satellite in the LVLH coordinate system are shown, and the results show that the defense satellite can still achieve cooperative encirclement even in the presence of obstacles. Figure 3 The capture position error between the target satellite and each defense satellite is given. Figure 4The encirclement velocity error between the target satellite and each defense satellite is shown. This demonstrates that the proposed distributed model predictive control method based on cooperative game theory of defense satellites can effectively guide defense satellites to the desired encirclement position, achieving cooperative encirclement control of the target satellite.

[0118] The above embodiments are merely one of the preferred embodiments of the present invention and should not be used to limit the scope of protection of the present invention. Any modifications or refinements made to the main design concept and spirit of the present invention that are not of substantial significance, but solve the same technical problem as the present invention, should be included within the scope of protection of the present invention.

Claims

1. A predictive control method for a distributed model of cooperative game theory in defense satellites, characterized in that, Includes the following steps: S1, Establish a relative motion model to describe the relative motion relationship between defensive satellites or between a defensive satellite and a target satellite; S2, the relative motion model is discretized to obtain a discrete-time state-space model of the relative motion of the defense satellite or the target satellite; S3, Construct the cost function for predictive control of the collaborative game-theoretic distributed model of the defense satellite; wherein, the expression of the cost function is: in, The cost function for the capture location is expressed as follows: In the formula, It is the step index within the prediction interval. It predicts the length of the time domain. For the first A defense satellite at any time The capture position error vector, For the first Position vectors of each defense satellite in the LVLH coordinate system It is the position vector of the target satellite in the same coordinate system. It is the expected relative displacement, i.e., the first... The ideal offset position of each defensive satellite relative to the target satellite in the encirclement formation; Let the capture speed cost function be... Here are the weighting coefficients for the capture speed cost function, which is expressed as follows: In the formula, No. A defense satellite at any time The capture speed error vector, No. The velocity vector of a defense satellite in the LVLH coordinate system It is the velocity vector of the target satellite in the same coordinate system; S4, Establish the conditional constraints of the cost function in the cooperative game control of defensive satellites; S5, combining cost function and condition constraints, transforms the predictive control problem of the distributed model of cooperative game of defense satellites into an objective function optimization problem; S6 defines the assumed state of the defense satellite at the current time k, and models and predicts the control behavior of the target satellite in the prediction time domain based on the current centroid position of the defense satellite. S7 constructs and solves a target satellite optimization problem under multiple constraints, providing a basis for decision-making for defense satellites, thereby achieving dynamic and coordinated encirclement of target satellites.

2. The predictive control method for a distributed model of cooperative game theory in defense satellites according to claim 1, characterized in that, In step S1, the expression for the relative motion model is: In the formula, , and These represent the coordinate components of the target satellite or defense satellite constellation in the LVLH coordinate system of the reference satellite. For reference satellite orbital angular velocity; , and This represents the acceleration component acting on the target satellite or the defense satellite. , and express , and The corresponding second derivative; , and express , and The corresponding first derivative; Define state variables and control of acceleration variables Then equation (1) can be rewritten as: In the formula, 。 3. The predictive control method for a distributed model of cooperative game theory in defense satellites according to claim 2, characterized in that, In step S2, the discrete-time state-space model is: In the formula, and They represent the first The state vector and control acceleration input at each sampling time, Indicates the first The location of each sampling time. Indicates the first The velocity at each sampling moment; matrix and The state transition matrix and input matrix obtained from discretization, respectively, are defined as follows: In the formula, Indicates the sampling time.

4. The predictive control method for a distributed model of cooperative game theory in defense satellites according to claim 3, characterized in that, In step S4, the constraints for the defensive satellite cooperative game control include: Control input constraints: In the formula, It is the first A defensive satellite in Make predictions constantly, targeting the future. The control input vector for the step; It is the maximum acceleration limit allowed by the defense satellite controller; Communication distance constraints: In the formula, and These are defense satellites and At any moment Predicted future Step position; It is the maximum distance at which defensive satellites can communicate with each other. Safety distance constraints: In the formula, It is the minimum safe distance between defensive satellites; Safety constraints: In the formula, It refers to the location of spatial obstacles. It is the minimum safe distance between a defensive satellite and an obstacle.

5. The predictive control method for a distributed model of cooperative game theory in defense satellites according to claim 4, characterized in that, In step S5, the expression for the objective function optimization problem is: In the formula, C11–C18 represent: the dynamic constraints of the defensive satellite, the predictive dynamic constraints of the target satellite, the initial state constraints of the defensive satellite, the initial state constraints of the target satellite, the control input constraints of the defensive satellite, the maximum communication distance constraints, the minimum safe distance constraints, and the minimum safe distance constraints between the defensive satellite and obstacles, respectively. Indicates at time Predicted defense satellites In the future The state at any given moment; Indicates at time Based on model predictions, the target satellite will be in the future. The state at any given moment; Indicates at time The predicted target satellite in the future Predictive control input at specific times; Indicates defense satellite At any moment Predicted state Equal to its true state ; Indicates defense satellite At any moment Predicted status of the target satellite Equal to its true state ; Indicates from neighboring satellites The satellite obtained in the future The position at any given moment.

6. The predictive control method for a distributed model of cooperative game theory in defense satellites according to claim 5, characterized in that, In step S6, the expression for the assumed state of the defense satellite at the current time k is: in, Based on Constantly defending against satellites The optimal state.

7. The predictive control method for a distributed model of cooperative game theory in defense satellites according to claim 6, characterized in that, In step S7, the target satellite optimization problem under multiple constraints is as follows: In the formula, C21 and C23 represent the dynamic constraints of the predicted state of the defense satellite from the perspective of the target satellite and the initial state velocity; C22 and C24 represent the dynamic constraints of the predicted state of the target satellite and the initial state constraints; and C25 represents the maximum thrust constraint of the target satellite's control input. Is the target satellite in the prediction step? The control input is the optimization variable; Enemy satellite at time For the future Predicted position of the step This indicates that during the enemy satellite prediction process, defensive satellites... In the prediction step The estimation of the location; It refers to the number of defense satellites. To protect the location of the satellite's center of mass; This indicates that during the calculation of the target satellite's control input, the defensive satellite... future Estimation of the state at any given time; Indicates the target satellite at time Defense satellites Predicted initial state value The target satellite can observe the defense satellite. Real state Consistent; This represents the initial value of the target satellite's predicted state. Equal to its true state ; The predicted target satellite in the future The control input at any given time, its infinite norm The maximum control input cannot be exceeded. .

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