A trajectory-oriented underactuated satellite incomplete information pursuit-evasion game control method

Abstract

The application discloses a kind of trace underactuated satellite incomplete information pursuit game control method, it belongs to satellite close-range orbit pursuit game technical field.The application solves the problem that three-dimensional pursuit game control of trace underactuated satellite cannot be realized using existing method.The application first derives the dynamics constraint imposed on tracker satellite and escape satellite by trace thrust loss through underactuated nonlinear and linear relative orbit dynamics, secondly derives trace underactuated three-dimensional pursuit game strategy under complete information using differential game theory, finally proposes an online calculation method based on differential Riccati equation control parameter, and derives trace underactuated pursuit game control strategy under incomplete information based on the same.The method of the application can be applied to trace underactuated satellite pursuit game control under incomplete information.

Description

Technical Field

[0001] This invention relates to the field of satellite near-orbit pursuit and escape game technology, specifically to a tracking underactuated satellite incomplete information pursuit and escape game control method. Background Technology

[0002] The satellite chase-escape game originates from the satellite interception problem, aiming to gain a dominant position and information control in space, evading or intercepting non-cooperative targets such as threatening satellites, meteorites, and space debris. With the development of autonomous satellite decision-making technology, escape satellites can perceive the space situation through various sensors and maneuver to evade trackers, thus increasing the difficulty of satellite interception. This autonomous scenario can be described as a conflict of interest between the tracker and the escape satellite, constituting a chase-escape game. Differential game theory, proposed by Isaacs in 1965, is mainly used to study dynamic game problems. Players' decisions affect the evolution of a dynamic system over time, and each player's goal is to optimize their own objective function under the constraints of system dynamics and the actions of other players. Recent research on spacecraft pursuit-escape game theory has focused on the following five aspects: 1) Linear quadratic differential games with state constraints; 2) Obtaining analytical solutions to differential games using direct, indirect, and semi-direct methods; 3) Quantitatively answering whether and when a tracking satellite can intercept an escape satellite, based on the game boundary and interception time in differential games; 4) In addition to two-player games, actual game situations may be more complex, such as those involving obstacles and multiple players; 5) In actual game processes, due to the non-cooperation of the escape satellite, the tracker may not be able to fully obtain game information such as the escape satellite's position, velocity, and control parameters. Typically, relative position can be measured using laser or Doppler effect sensors installed in the tracker; based on the difference between these measurements over time steps, the tracker can calculate the relative velocity using an inertial measurement unit. Furthermore, in research on non-cooperative target interception, some scholars have proposed filter-based methods to estimate the target's maneuvering acceleration, providing technical support for pursuit-escape games with incomplete information.

[0003] Current research on satellite pursuit-escape games is based on fully driven game dynamics. It is known that radially underdriven closed-loop systems are controllable, but track-driven underdriven systems are uncontrollable. Therefore, fully driven game strategies are not applicable to game scenarios where track drive is missing. There is also no research on three-dimensional pursuit-escape games for track-driven underdriven satellites. The main reasons are: first, constructing underdriven game dynamics from the controllable subspace of an uncontrollable system is the first challenge; second, verifying the feasibility of track-driven underdriven pursuit-escape games and deriving dynamic constraints based on nonlinear and linear relative orbit dynamics is the second challenge; third, deriving the game control law under underdriven conditions using differential game theory is the third challenge; and finally, obtaining the escaper's control parameters under incomplete information and deriving the game strategy under incomplete information is the fourth challenge.

[0004] In summary, existing methods cannot control the three-dimensional pursuit and escape game of track-underactuated satellites, making it essential to design a control method for the pursuit and escape game of track-underactuated satellites. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that existing methods cannot achieve control of three-dimensional pursuit and escape game of track-underactuated satellites, and to propose a pursuit and escape game control method for track-underactuated satellites with incomplete information.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a game-theoretic control method for tracking and escaping incomplete information of a trajectory-underdriven satellite, the method specifically including the following steps:

[0007] Step S1: Construct the relative dynamic equations for the pursuit-escape game of tracked underactuated satellites, and obtain the dynamic constraints on the tracker satellite and the escape satellite during the pursuit-escape game based on the constructed relative dynamic equations.

[0008] Step S2: Use differential game theory to derive the control law of the three-dimensional pursuit-escape game with complete information and underactuated tracking, and the control law satisfies the dynamic constraints in step S1.

[0009] Step S3: Based on the control law of the three-dimensional pursuit and escape game with underactuated trajectory under complete information, derive the control law of the three-dimensional pursuit and escape game with underactuated trajectory under incomplete information.

[0010] The beneficial effects of this invention are:

[0011] This invention first derives the dynamic constraints imposed on tracker and escape satellites by the absence of directional thrust through underactuated nonlinear and linear relative orbital dynamics. Second, it uses differential game theory to derive a three-dimensional pursuit-escape game strategy under complete information with underactuated directional thrust. Finally, it proposes an online calculation method for control parameters based on the differential Riccati equation, and uses this as a basis to derive a control strategy for pursuit-escape game with incomplete information with underactuated directional thrust. This invention expands the theory and engineering applications of underactuated satellite control and explores the feasibility of close-range three-dimensional orbital games when satellites lose directional thrust. Attached Figure Description

[0012] Figure 1 This is a flowchart of a tracking-based underactuated satellite incomplete information pursuit-escape game control method according to the present invention;

[0013] Figure 2 A schematic diagram of the trajectory in a trail-driven, under-driven pursuit-escape game;

[0014] Figure 3 The time history of the relative distance between the tracker and the escape vehicle;

[0015] Figure 4 For the control parameters of the tracker and the escape device;

[0016] Figure 5(a) shows the control acceleration of the radial channel tracker and escaper under complete information;

[0017] Figure 5(b) shows the control acceleration of the normal channel tracker and escaper under full information;

[0018] Figure 5(c) shows the control acceleration of the radial channel tracker and escape device under incomplete information;

[0019] Figure 5(d) shows the control acceleration of the normal channel tracker and escaper under incomplete information. Detailed Implementation

[0020] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a game-theoretic control method for tracking and escaping incomplete information from a track-underactuated satellite. The method specifically includes the following steps:

[0021] Step S1: Construct the relative dynamic equations for the pursuit-escape game of tracked underactuated satellites, and obtain the dynamic constraints on the tracker satellite and the escape satellite during the pursuit-escape game based on the constructed relative dynamic equations.

[0022] Step S2: Use differential game theory to derive the control law of the track underactuated three-dimensional pursuit-escape game under complete information (complete information means that the tracker and escaper can obtain each other's real-time state information and control parameters during the game), and the control law satisfies the dynamic constraints in step S1.

[0023] Step S3: Based on the control law of the three-dimensional pursuit and escape game with underactuated trajectory under complete information, derive the control law of the three-dimensional pursuit and escape game with underactuated trajectory under incomplete information.

[0024] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the relative dynamic equations for the trajectory-underactuated satellite pursuit-escape game are constructed in step S1. The specific process is as follows:

[0025] Given a pursuit-escape game scenario: A virtual navigator satellite is known to be orbiting in a near-Earth circular orbit (a near-Earth circular orbit is defined as an orbital radius of 160 km to 2000 km). A local-vertical-local-horizontal coordinate system is constructed with the navigator satellite's center of mass as the origin. The radial direction of this coordinate system is from the Earth's center of mass to the navigator satellite's center of mass; the normal direction is the direction of the navigator satellite's orbital angular momentum; and the track direction is determined using a right-handed Cartesian coordinate system. A tracker satellite and an escape satellite engage in a relative orbital pursuit-escape game near the navigator satellite. The positions and velocities of the tracker satellite and the escape satellite relative to the navigator satellite are expressed as follows: and ;

[0026] Among them, subscript Indicates tracker satellite, subscript Indicates an escape satellite, that is, when hour, Indicates the position of the tracker satellite relative to the navigator. This indicates the speed of the tracker satellite relative to the navigator;

[0027] The relative dynamic equations for the trajectory-underactuated satellite pursuit game are:

[0028] (1)

[0029] in, for The second time derivative represents the player's... The acceleration relative to the leader; , Indicates satellite Control of acceleration, For satellite Radial control acceleration, Indicates satellite Normal acceleration control; The second-order relative dynamics are specifically expressed as:

[0030]

[0031] In the formula, For the latitudinal amplitude of the Navigator satellite, and These are the angular velocity and angular acceleration of the Navigator satellite, respectively. The radius of the Navigator satellite's Earth orbit. , For satellite Earth's orbital radius, , This is Earth's gravitational constant.

[0032] The other steps and parameters are the same as in Specific Implementation Method 1.

[0033] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that, in step S1, the dynamic constraints experienced by the tracker satellite and the escape satellite during the pursuit-escape game are obtained based on the constructed relative dynamic equations; the specific process is as follows:

[0034] Linearizing equation (1) into:

[0035]

[0036] In the formula, for The first derivative, The superscript T indicates transpose. ;

[0037] , It is the identity matrix. , ,

[0038] ;

[0039] According to linear system theory, the system is decomposed into a controllable subspace. and uncontrollable subspace :

[0040] (2)

[0041] in, , , , for The first time derivative;

[0042] When the Navigator satellite is flying in a circular orbit , Equation (1) can be simplified to:

[0043] (3)

[0044] Based on equation (3), the nonlinear dynamic constraints of equation (4) are derived:

[0045] (4)

[0046] In close-range pursuit and escape games, the relative distance between the tracker and the escape vehicle is approximately several hundred meters to several kilometers, much smaller than the orbital radius of the virtual navigator in the inertial coordinate system. When it holds true, the solution to equation (4) is: and ;

[0047] Known Then the dynamic constraints on the tracker satellite and the escape satellite during the pursuit-escape game are:

[0048] (5)

[0049] In the formula, , It is the 2-norm of the vector;

[0050] Due to the uncontrollability of the system in the underactuated tracking scenario, the uncontrollable state variables impose linear dynamic constraints on the tracker satellite and the escape satellite as follows:

[0051] (6)

[0052] Equations (4) to (6) represent the dynamic constraints imposed on the tracker satellite and the escape satellite during the pursuit-escape game. Furthermore, these constraints are independent of the initial values ​​of the tracker satellite and the escape satellite.

[0053] Other steps and parameters are the same as in specific implementation method one or two.

[0054] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the specific process of step S2 is as follows:

[0055] Step S21: Define the relative error between the tracker and the escaper. for: ,in, , , , , ;

[0056] The error dynamics model for the trajectory-underactuated satellite pursuit game is then constructed as follows:

[0057] (7)

[0058] in, Yes First time derivative, For the control acceleration of the tracker satellite, For the radial control acceleration of the tracker satellite, The control acceleration representing the normal direction of the tracker satellite, For the control acceleration of the escape satellite, For the radial control acceleration of the escape satellite, This indicates the control acceleration in the direction normal to the escape satellite;

[0059] In a zero-sum game, the tracker's goal is to capture the escapee at the minimum cost, while the escapee's goal is to slow down the tracker's pursuit at the minimum cost. Therefore, a linear quadratic cost function is defined for the track-based underdriven chase-escape game. for:

[0060] (8)

[0061] In the formula, and It is a positive definite matrix. , , Represents real numbers, and For the control parameter matrix, , , Indicates the initial time of the pursuit and escape game. Indicates the deadline for the manhunt;

[0062] Step S22: Use differential game theory to solve the control law for the path-directed underdriven saddle point strategy pair in the three-dimensional pursuit-escape game;

[0063] Based on the linear quadratic cost function Constructing an underdriven Hamiltonian function and terminal conditions They are respectively:

[0064]

[0065]

[0066] in, As an accompanying variable, ;

[0067] According to differential game theory, the saddle point strategy satisfies the stability condition: The accompanying equation and terminal boundary conditions , yes The first time derivative;

[0068] For a linear quadratic game, the accompanying variables and error state conform to a linear feedback strategy: ,in, It is a positive semi-definite symmetric matrix. , satisfy: and ;

[0069] Substituting equation (7) into the time derivative of the above linear feedback strategy, we can construct the underdriven differential Riccati equation, that is, the trace underdriven differential Riccati equation can be constructed according to equation (7):

[0070] (9)

[0071] in, for The first derivative of the matrix, where the superscript -1 represents the inverse of the matrix;

[0072] Based on differential game theory, the saddle point strategy pairs in the trace-oriented, underdriven three-dimensional pursuit-escape game are solved:

[0073] (10)

[0074] Equation (10) is the saddle point solution under the underactuated track condition, and it is also the control law of the three-dimensional pursuit-escape game under the complete information condition. The tracker and the escaper are subject to the dynamic constraints of Equations (4) to (6) during the game.

[0075] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0076] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the specific process of step S3 is as follows:

[0077] Step S31, in equation (10) Substituting into equation (7), we obtain a new fifth-order error dynamics model:

[0078] (11)

[0079] in, , The escapement satellite control parameters to be calculated;

[0080] definition The observation equation of the system in equation (11), after discretization, is obtained as follows:

[0081] (12)

[0082] in, for The relative error in time, for The relative error in time, for The control acceleration of the time-tracking satellite, and All are white Gaussian noise. , , and Both represent the variance of the noise and are positive definite matrices. From Time's up The state transition matrix at each time step. ,in Sampling time, for The observation results at that time It is the base of the natural logarithm;

[0083] The relative error of the discrete system in equation (12) is estimated using a Kalman filter, and the estimated relative error is expressed as follows: ;

[0084] Step S32: Assuming the escape vehicle has sufficient knowledge of the tracker's real-time motion state and control parameters to explore the impact of incomplete information game theory on the tracker's game strategy and interception performance, the escape vehicle's game strategy under incomplete information is the same as the game control law under complete information. That is, the game control law of the escape vehicle satellite under incomplete information is:

[0085] (19)

[0086] Based on the first term of the game strategy formula (10) for the tracker under complete information, the game control law for the tracker satellite under incomplete information is designed as follows:

[0087] (20)

[0088] in, Let be the state matrix of the Riccati equation, and it is positive semi-definite.

[0089] In this embodiment, for At time , the Kalman filter is used to estimate Relative error of time Afterwards, according to Calculate Moment and ; and then according to and Calculate Relative error of time And then according to Calculate Moment and The process continues iteratively until the relative distance between the tracker and the escape device approaches the capture distance.

[0090] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0091] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that it uses a Kalman filter to estimate the relative error of the discrete system in equation (12); the specific process is as follows:

[0092]

[0093] in, , It is a fifth-order identity matrix. This is a one-step prediction of relative error. for Relative error estimation at time, for The control acceleration of the time-tracking satellite, for Gain matrix at time step , for One-step prediction of the state covariance matrix at each time step. , for The predicted state covariance matrix at time t. for The predicted state covariance matrix at time t. It is the identity matrix. for Momentary white Gaussian noise variance for Momentary white Gaussian noise The variance.

[0094] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0095] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the escaper satellite control parameters are... The calculation process is as follows:

[0096] According to equations (11) and (12) and the Kalman filter, it can be seen that only when the escaper control parameters are known... Only then can one obtain Relative state at any moment Therefore, an online parameter calculation method based on the differential Riccati equation was designed.

[0097] Similar to the observation equation, let Then equation (9) is multiplied on the right. get:

[0098] (13)

[0099] Assumption The estimated value of the escape satellite control acceleration obtained by the time step tracker through a filter method. satisfy:

[0100] (14)

[0101] To facilitate matrix operations, Expand to :

[0102] (15)

[0103] In the formula, Radial control acceleration for escape satellite The estimated value, For escape satellite normal control acceleration The estimated value;

[0104] Substituting equations (14) and (15) into equation (13), we get:

[0105] (16)

[0106] Let equation (16) be multiplied on the right. We obtain a new differential Riccati equation:

[0107] (17)

[0108] In equation (17), according to and Solve the state matrix of the new Riccati equation. , yes The first time derivative;

[0109] make In equation (14) and Given, defined Then the parameters can be solved using equation (14). and ;

[0110] Again The control parameters of the escape satellite are then recalculated as follows:

[0111] (18)

[0112] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0113] Specific Implementation Method Eight: This implementation method differs from one of Specific Implementation Methods One to Seven in that the... It can be obtained from the following differential Riccati equation:

[0114]

[0115] in, yes The first time derivative.

[0116] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0117] Experimental Section

[0118] The orbital parameters of the virtual navigator satellite are shown in Table 1, while the differential game parameters are set as follows: , , , , , , .

[0119] The initial states of the tracker satellite and the escape satellite are set as follows:

[0120]

[0121] Set when the relative distance between the tracker and the escape vehicle approaches the capture range. The pursuit and maneuver was completed in a short time.

[0122] Table 1: Track Elements of the Virtual Navigator

[0123] orbital elements numerical values unit semi-long shaft 6878137 m Eccentricity 0 - track inclination 42 deg Right ascension of ascending node -60 deg Latitude Aspect 30 deg

[0124] The trajectory of a three-dimensional pursuit game in the case of underdriven tracking is as follows: Figure 2 As shown in the figure and Trajectories under complete and incomplete information, respectively. This represents the trajectory of the escape vehicle under complete information. This represents the tracker's trajectory under complete information. This represents the trajectory of the escape vehicle under incomplete information. The symbol represents the tracker's trajectory under incomplete information. and These represent the initial positions of the tracker and the escape device, respectively. Figure 3 The time history of the relative positions of the tracker and the escaper is given. The game time is 244s under complete information and 297s under incomplete information. This result shows that the lack of accurate state information and control parameters of the escaper by the tracker will lead to a longer capture time. Figure 4 These are the control parameters for the tracker and the escape device, where The escapement control parameters are obtained through an online parameter calculation method based on the differential Riccati equation. Since it is assumed that the escapement acceleration estimated by the tracker follows a normal distribution, therefore... Similar jitter occurred. Furthermore, it can be estimated that... The amplitude is in the range within, that is In the range According to equation (14), The values ​​are much smaller than those of other variables, indicating that even if the estimated control parameters fluctuate, it will not affect the effectiveness of the control law in the pursuit-escape game. Figure 5(a) shows the control acceleration of the radial channel tracker and the escaper under complete information. It can be seen that the tracker provides a larger control input than the escaper to reduce the relative distance. Similarly, Figure 5(b) shows the control acceleration of the normal channel under complete information. Figure 5(c) shows the control acceleration of the radial channel tracker and the escaper under incomplete information, where... The radial control acceleration of the escapement is estimated by the tracker using a filter method, while This represents the actual control acceleration of the escape vehicle. Figure 5(d) shows the control acceleration of the normal channel tracker and the escape vehicle under incomplete information. Similarly, The normal control acceleration of the escaper is estimated by the tracker using a filter method. It can be observed that incomplete information prevents the tracker from acquiring accurate information about the escaper, thus prolonging the capture time.

[0125] Therefore, by employing the trajectory-underactuated satellite incomplete information pursuit-escape game control method of the present invention, the tracker satellite and the escaper satellite can complete the three-dimensional relative orbit pursuit-escape game even in the absence of trajectory thrust. In the simulation, the tracker will gradually approach the escaper.

[0126] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A game-theoretic control method for tracking and escaping an underactuated satellite with incomplete information, characterized in that, The method specifically includes the following steps: Step S1: Construct the relative dynamic equations for the pursuit-escape game of tracked underactuated satellites, and obtain the dynamic constraints on the tracker satellite and the escape satellite during the pursuit-escape game based on the constructed relative dynamic equations. The specific process for constructing the relative dynamic equations for the trajectory-based underactuated satellite pursuit game is as follows: Given a pursuit-escape game scenario: A virtual navigator satellite is orbiting in a near-Earth circular orbit. A local-vertical-local-horizontal coordinate system is constructed with the navigator satellite's center of mass as the origin. The radial direction of this coordinate system is from the Earth's center of mass to the navigator satellite's center of mass; the normal direction is the direction of the navigator satellite's orbital angular momentum; and the track direction is determined using a right-handed Cartesian coordinate system. A tracker satellite and an escape satellite engage in a relative orbital pursuit-escape game near the navigator satellite. The positions and velocities of the tracker satellite and the escape satellite relative to the navigator satellite are expressed as follows: and ; Among them, subscript Indicates tracker satellite, subscript Indicates an escape satellite, that is, when hour, Indicates the position of the tracker satellite relative to the navigator. This indicates the speed of the tracker satellite relative to the navigator; The relative dynamic equations for the trajectory-underactuated satellite pursuit game are: (1) in, for The second time derivative, , Indicates satellite Control of acceleration, For satellite Radial control acceleration, Indicates satellite Normal acceleration control; The second-order relative dynamics are specifically expressed as: In the formula, For the latitudinal amplitude of the Navigator satellite, and These are the angular velocity and angular acceleration of the Navigator satellite, respectively. The radius of the Navigator satellite's Earth orbit. , For satellite Earth's orbital radius, , This is Earth's gravitational constant; The dynamic constraints on the tracker satellite and the escape satellite during the pursuit-escape game are obtained based on the constructed relative dynamic equations; the specific process is as follows: Linearizing equation (1) into: In the formula, for The first derivative, The superscript T indicates transpose. ; , It is the identity matrix. , , ； According to linear system theory, the system is decomposed into a controllable subspace. and uncontrollable subspace : (2) in, , , , for The first time derivative; When the Navigator satellite is flying in a circular orbit , Equation (1) can be simplified to: (3) Based on equation (3), the nonlinear dynamic constraints of equation (4) are derived: (4) when When it holds true, the solution to equation (4) is: and ; Known Then the dynamic constraints on the tracker satellite and the escape satellite during the pursuit-escape game are: (5) In the formula, , It is the 2-norm of the vector; Due to the uncontrollability of the system in the underactuated tracking scenario, the uncontrollable state variables impose linear dynamic constraints on the tracker satellite and the escape satellite as follows: (6) Equations (4) to (6) represent the dynamic constraints imposed on the tracker satellite and the escape satellite during the pursuit-escape game. Step S2: Use differential game theory to derive the control law of the three-dimensional pursuit-escape game with complete information and underactuated tracking, and the control law satisfies the dynamic constraints in step S1. The specific process of step S2 is as follows: Step S21: Define the relative error between the tracker and the escaper. for: ,in, , , , , ; The error dynamics model for the trajectory-underactuated satellite pursuit game is then constructed as follows: (7) in, Yes First time derivative, For the control acceleration of the tracker satellite, For the radial control acceleration of the tracker satellite, The control acceleration representing the normal direction of the tracker satellite, For the control acceleration of the escape satellite, For the radial control acceleration of the escape satellite, This indicates the control acceleration in the direction normal to the escape satellite; Define the linear quadratic cost function for a trace-underdriven pursuit game. for: (8) In the formula, and It is a positive definite matrix. , , Represents real numbers, and For the control parameter matrix, Indicates the initial time of the pursuit and escape game. Indicates the deadline for the manhunt; Step S22: Use differential game theory to solve the control law for the path-directed underdriven saddle point strategy pair in the three-dimensional pursuit-escape game; Based on the linear quadratic cost function Constructing an underdriven Hamiltonian function and terminal conditions They are respectively: in, As an accompanying variable, ; According to differential game theory, the saddle point strategy satisfies the stability condition: The accompanying equation and terminal boundary conditions , yes The first time derivative; For a linear quadratic game, the accompanying variables and error state conform to a linear feedback strategy: ,in, It is a positive semi-definite symmetric matrix. , satisfy: and ; Based on equation (7), the trace underactuated differential Riccati equation is constructed as follows: (9) in, for The first derivative of the matrix, where the superscript -1 represents the inverse of the matrix; Based on differential game theory, the saddle point strategy pairs in the trace-oriented, underdriven three-dimensional pursuit-escape game are solved: (10) Step S3: Based on the control law of the three-dimensional pursuit and escape game with underactuated track under complete information, derive the control law of the three-dimensional pursuit and escape game with underactuated track under complete information. The specific process of step S3 is as follows: Step S31, in equation (10) Substituting into equation (7), we obtain a new fifth-order error dynamics model: (11) in, , The escapement satellite control parameters to be calculated; definition The observation equation of the system in equation (11), after discretization, is obtained as follows: (12) in, for The relative error in time, for The relative error in time, for The control acceleration of the time-tracking satellite, and All are white Gaussian noise. From Time's up The state transition matrix at each time step. ,in Sampling time, for The observation results at that time It is the base of the natural logarithm; The relative error of the discrete system in equation (12) is estimated using a Kalman filter, and the estimated relative error is expressed as follows: ; Step S32: The game strategy of the escaper under incomplete information is the same as the game control law under complete information, that is, the game control law of the escaper satellite under incomplete information is: (19) The game-theoretic control law for the tracker satellite under incomplete information is designed as follows: (20) in, Let be the state matrix of the Riccati equation, and it is positive semi-definite.

2. The method for controlling the pursuit and escape of an underactuated satellite with incomplete information according to claim 1, characterized in that, The relative error of the discrete system in equation (12) is estimated using a Kalman filter; the specific process is as follows: in, , It is a fifth-order identity matrix. This is a one-step prediction of relative error. for Relative error estimation at time, for The control acceleration of the time-tracking satellite, for Gain matrix at time step , for One-step prediction of the state covariance matrix at each time step. , for The predicted state covariance matrix at time t. for The predicted state covariance matrix at time t. It is the identity matrix. for Momentary white Gaussian noise variance for Momentary white Gaussian noise The variance.

3. The method for controlling the pursuit and escape of an underactuated satellite with incomplete information according to claim 2, characterized in that, The escape satellite control parameters The calculation process is as follows: make Then equation (9) is multiplied on the right. get: (13) Estimates of escape satellite control acceleration satisfy: (14) Will Expand to : (15) In the formula, Radial control acceleration for escape satellite The estimated value, For escape satellite normal control acceleration The estimated value; Substituting equations (14) and (15) into equation (13), we get: (16) Let equation (16) be multiplied on the right. We obtain a new differential Riccati equation: (17) In equation (17), according to and Solve the state matrix of the new Riccati equation. , yes The first time derivative; make In equation (14) and Given, defined Then the parameters can be solved using equation (14). and ; Again The control parameters of the escape satellite are then recalculated as follows: (18)。 4. The method for controlling the pursuit and escape of an underactuated satellite with incomplete information according to claim 3, characterized in that, The It can be obtained from the following differential Riccati equation: in, yes The first time derivative.

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