Spacecraft pursuit-evasion anti-game control method with upper bound of thrust

Abstract

The application discloses a spacecraft pursuit-escape defense game control method with thrust upper limit and belongs to the technical field of spacecrafts. The control method comprises the following steps: acquiring spacecraft pursuit-escape defense game parameters of a pursuit star and a defense star; using the acquired spacecraft pursuit-escape defense game parameters of the pursuit star and the defense star to establish a spacecraft pursuit-escape defense game problem model with thrust upper limit; solving the spacecraft pursuit-escape defense game problem model with thrust upper limit to obtain optimal control laws of both sides of the pursuit star and the defense star; converting the spacecraft pursuit-escape defense game problem with thrust upper limit into a two-point boundary value problem through the optimal control laws of both sides; using a solving tool to solve the two-point boundary value problem to obtain state trajectories of the pursuit star and the defense star; and adjusting a motion trajectory of the defense star according to the state trajectories of the pursuit star and the defense star. The method can timely adjust the running path of the defense star, so that the defense star has stronger maneuverability and is more accurate in intercepting the pursuit star.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft technology, specifically relating to a spacecraft pursuit and escape anti-game control method with a thrust upper limit. Background Technology

[0002] Spacecraft in orbit are vulnerable to attacks and close approaches from non-cooperative targets. Due to their high value and the need for fuel for on-orbit operations, they cannot autonomously evade threats and must deploy companion satellites as defensive satellites to engage in a chase-escape-defense game. The competition for position between the companion and the adversary satellites over the host satellite is known as the spacecraft chase-escape-defense game problem. The adversary satellite aims to approach the host satellite while ensuring it is not intercepted or destroyed by the companion satellite; the adversary satellite aims to prevent the adversary satellite from approaching the host satellite as much as possible.

[0003] Currently, most modeling of the spacecraft pursuit-escape game problem is based on dynamic models without upper control constraints. This often results in very large control accelerations after solving, exceeding the capabilities of real spacecraft. Introducing upper control constraints, however, leads to model complexity and difficulty in solving. This can result in the inability to control the trajectory of the defensive satellite in a timely manner, making it impossible for defensive satellites located around the primary satellite to prevent the pursuing satellite from approaching the primary satellite. Consequently, the spacecraft in orbit can be attacked or approached by non-cooperative targets. Summary of the Invention

[0004] Existing technologies for modeling spacecraft pursuit and escape game-theoretic problems based on dynamic models without upper control constraints often fail to accurately reflect the capabilities of real spacecraft, making it difficult to promptly demonstrate the actual performance of a spacecraft. Introducing upper control constraints further complicates the model, making it harder to solve and hindering the defense satellite's ability to prevent the pursuing satellite from approaching the host satellite. This invention provides a spacecraft pursuit and escape game-theoretic control method with a thrust upper limit. By introducing upper control constraints on the participants in the pursuit and escape game-theoretic problem, the problem is transformed into a zero-sum differential game problem. This makes the model more realistic, enhances the defense satellite's maneuverability, and improves the accuracy of intercepting the pursuing satellite.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A spacecraft pursuit and escape anti-game control method with a thrust limit includes:

[0007] Acquire spacecraft pursuit, escape, and defense game parameters for both the pursuing and defending satellites;

[0008] Using the spacecraft pursuit-escape-defense game parameters obtained from the pursuing and defending satellites, a spacecraft pursuit-escape-defense game problem model with a thrust upper limit is established.

[0009] The optimal control laws for both the pursuing and defending satellites are obtained by solving a game-theoretic problem model of a spacecraft with a thrust limit.

[0010] By using the optimal control laws of both parties, the spacecraft pursuit and escape game problem with thrust limit is transformed into a two-point boundary value problem.

[0011] The two-point boundary value problem is solved using a solver to obtain the state trajectories of the pursuing and defending stars.

[0012] Adjust the trajectory of the defensive star based on the status and trajectory of the pursuing and defensive stars.

[0013] As a further improvement of the present invention, the spacecraft pursuit-escape-defense game parameters of the pursuing star and the defending star include:

[0014] The initial position of the pursuing star, the initial position of the defensive star, the speed of the pursuing star, and the speed of the defensive star.

[0015] As a further improvement of the present invention, the step of establishing a spacecraft pursuit-escape-defense game problem model with a thrust upper limit using the acquired spacecraft pursuit and defense satellite game parameters includes:

[0016] Establish an LVLH coordinate system with the position of the primary star t as the origin, and design a cost function based on the game objectives of the pursuing star and the defensive star in combination with the LVLH coordinate system.

[0017] Based on the CW equations, we determine the differential equations of the dynamic constraints that need to be satisfied by the pursuing and defending stars in space orbits.

[0018] Based on the above process, a spacecraft pursuit and escape defense game model with thrust upper limit based on differential games is established.

[0019] As a further improvement of the present invention, the establishment of an LVLH coordinate system with the position of the primary star t as the origin, and the design of a cost function based on the game objective of the pursuing star and the defensive star in combination with the LVLH coordinate system, includes:

[0020]

[0021] Among them, J a The cost function for the tracking star; J d The cost function for the defense star; x a x is the state vector of the tracking star. d The state vector of the defense star; t f Q1 represents the terminal moment of the game; Q2 represents the weight matrix of the terminal distance term between the pursuing star and the main star; Q3 represents the weight matrix of the terminal distance term between the defensive and pursuing stars.

[0022] As a further improvement of the present invention, the method of solving the game-theoretic problem model of spacecraft pursuit, escape, and defense with a thrust upper limit to obtain the optimal control law for the pursuing and defending satellites includes:

[0023] By introducing costate variables based on the Lagrange multiplier method, the bilateral optimization problem with differential equation equality constraints is transformed into an unconstrained bilateral optimization problem, and the auxiliary cost function is obtained by processing the cost function.

[0024] The optimal control law for both parties is obtained by partially integrating the auxiliary cost function.

[0025] As a further improvement of the present invention, the method of introducing costate variables based on the Lagrange multiplier method transforms the bilateral optimization problem with differential equation equality constraints into an unconstrained bilateral optimization problem, and processes the cost function to obtain an auxiliary cost function, including:

[0026]

[0027] Where, x a x is the state vector of the tracking star. d The state vector of the defense star; t f Q1 represents the terminal moment of the game; Q2 represents the weight matrix of the terminal distance term between the pursuing star and the main star; Q3 represents the weight matrix of the terminal distance term between the defensive and pursuing stars; and λ and ν are costate variables.

[0028] As a further improvement of the present invention, the step of obtaining the optimal control law for both parties by performing partial integration on the auxiliary cost function includes:

[0029] Perform partial integration on the auxiliary function:

[0030]

[0031] in:

[0032]

[0033] H(x a ,y,u a ,u d ,t)=λ T (Ax a +BT a )+ν T (Ay+BT d -BT a )

[0034] Variational analysis of the auxiliary cost function:

[0035]

[0036] Since a necessary condition for solving this problem using the variational method is that the variation of the auxiliary cost function is 0, i.e., , we obtain the following necessary condition:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] The optimal control laws for both parties are derived from the latter two equations, namely:

[0044]

[0045]

[0046] Wherein: T a T represents the magnitude of the maximum thrust acceleration of the tracking star. d This represents the magnitude of the maximum thrust acceleration of the defense star; The optimal control rate for the tracking star; This is the optimal control law for the defensive star.

[0047] As a further improvement of the present invention, the game-theoretic problem of spacecraft pursuit and escape with thrust upper limit is transformed into a two-point boundary value problem through the optimal control law of both parties, including:

[0048] Substitute the optimal control laws of both parties into the dynamic constraint differential equations of both parties;

[0049]

[0050] Where: x a x is the state vector of the tracking star. d y is the state vector of the defense star; x is the radial position component of the orbit in the LVLH system; y is the directional position component of the flight in the LVLH system; v x ν represents the radial velocity component of the orbit in the LVLH system; λ and ν are costate variables.

[0051] As a further improvement of the present invention, the optimal control laws of both parties are substituted into the dynamic constraint differential equations of both parties, and then:

[0052] Substituting the optimal control laws of both sides into the differential equations of their dynamic constraints, and combining them with the differential equations of the dynamic constraints that the pursuing and defending stars need to satisfy, yields the two-point boundary value problem, including:

[0053]

[0054] Among them, t f This is the final moment of the game.

[0055] As a further improvement of the present invention, the two-point boundary value problem is solved using a solving tool to obtain the state trajectories of the pursuing star and the defending star, wherein:

[0056] The bvp4c function in MATLAB is used to solve the two-point boundary value problem.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] This invention discloses a spacecraft pursuit-escape game-theoretic control method with a thrust upper limit. By acquiring the spacecraft pursuit-escape game-theoretic parameters of the pursuing and defending satellites, a spacecraft pursuit-escape game-theoretic problem model with a thrust upper limit is established. The optimal control laws for both the pursuing and defending satellites are obtained, thus transforming the spacecraft pursuit-escape game-theoretic problem with a thrust upper limit into a two-point boundary value problem. A solution tool is then used to solve this problem, yielding the state trajectories of the pursuing and defending satellites. The spacecraft pursuit-escape game-theoretic problem model and solution method provided in this invention are as follows: The thrust-upper-limit spacecraft pursuit-escape game-theoretic problem model is a differential game-theoretic model based on linear CW equations, which has the advantages of model simplicity and small linearization error; a continuous control-based control mode is introduced, allowing for the design of the upper limit of thrust, making the model more realistic. Furthermore, the solution method of this invention transforms the spacecraft pursuit-escape game-theoretic problem into a zero-sum game problem, and further into a two-point boundary value problem, significantly improving the solution efficiency. Therefore, this invention can provide an effective threat solution for spacecraft that employ master-slave satellite coordination. By adjusting the orbital paths of the defense satellites around the master satellite in a timely manner, the pursuit satellites around the master satellite can be intercepted, thereby protecting the operational safety of the master satellite. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the specific implementation of the present invention for the anti-game theory problem of spacecraft pursuit and escape with a thrust limit;

[0060] Figure 2 This is a game scenario diagram for the pursuit and escape game problem of spacecraft with thrust limit to which this invention applies;

[0061] Figure 3 This is a simulation trajectory diagram from an embodiment of the present invention;

[0062] Figure 4 This is a simulation speed change graph from an embodiment of the present invention;

[0063] Figure 5 This is a simulation thrust angle variation diagram in an embodiment of the present invention;

[0064] Figure 6 This is a diagram showing the distances between the pursuing satellite and the defensive satellite, as well as the distances between the pursuing satellite and the primary satellite, in an embodiment of the present invention.

[0065] Figure 7 This is a schematic diagram of the structure of a spacecraft pursuit and escape anti-game control system with a thrust upper limit according to the present invention. Detailed Implementation

[0066] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0067] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0068] Current modeling of spacecraft pursuit-escape game-theoretic problems based on dynamic models without upper control constraints fails to accurately reflect the capabilities of real spacecraft and cannot promptly demonstrate the actual performance levels achievable by a real spacecraft. Introducing upper control constraints leads to model complexity and difficulty in solving, resulting in the defensive satellite's inability to promptly prevent the pursuing satellite from approaching the host satellite. This invention provides a 7-dimensional dynamic model with a thrust upper control constraint.

[0069] Spacecraft pursuit and escape prevention game-theoretic control methods, such as Figure 1 As shown, the method includes:

[0070] Acquire spacecraft pursuit, escape, and defense game parameters for both the pursuing and defending satellites;

[0071] Using the spacecraft pursuit-escape-defense game parameters obtained from the pursuing and defending satellites, a spacecraft pursuit-escape-defense game problem model with a thrust upper limit is established.

[0072] The optimal control laws for both the pursuing and defending satellites are obtained by solving a game-theoretic problem model of a spacecraft with a thrust limit.

[0073] By using the optimal control laws of both parties, the spacecraft pursuit and escape game problem with thrust limit is transformed into a two-point boundary value problem.

[0074] The two-point boundary value problem is solved using a solver to obtain the state trajectories of the pursuing and defending stars.

[0075] Adjust the trajectory of the defensive star based on the status and trajectory of the pursuing and defensive stars.

[0076] The present invention will now be described in further detail with reference to the accompanying drawings:

[0077] S1: Based on the spacecraft pursuit-escape-defense game parameters of the pursuing and defending satellites, establish a spacecraft pursuit-escape-defense game problem model with a thrust upper limit:

[0078] The spacecraft pursuit-escape-defense game parameters for the pursuing and defending satellites include the initial position of the pursuing satellite, the initial position of the defending satellite, the velocity of the pursuing satellite, and the velocity of the defending satellite.

[0079] S2: The process of establishing the game-theoretic model for the spacecraft pursuit and escape prevention problem with a thrust limit is as follows:

[0080] Establish an LVLH coordinate system with the position of the primary star t as the origin, and design the following cost function based on the game objectives of the pursuing star and the defensive star in combination with the LVLH coordinate system;

[0081]

[0082] The meaning of this cost function is the relative state between the pursuing satellite and the primary satellite at the terminal moment, and the relative state between the defending satellite and the primary satellite, t. f This is the final moment of the game.

[0083] In formula (1): matrix A represents the spacecraft relative motion dynamics constraint matrix;

[0084] Wherein, the symmetric positive semi-definite matrix Q1∈R 4×4 Q2∈R 4×4 satisfy:

[0085] Q1=k1I 4×4 Q2 = k2I 4×4 (2)

[0086] In formula (2):

[0087] k1 and k2 are weighting coefficients;

[0088] Based on the CW equations, we determine the differential equations of the dynamic constraints that need to be satisfied by the pursuing and defending stars in space orbits.

[0089]

[0090] u a =T a τ a ,‖τ a ||≤1

[0091] u d =T d τ d ,‖τ d ‖≤1 (3) The meanings of other symbols in formulas (1) to (3) are as follows:

[0092] a is the subscript of the pursuing star; d is the subscript of the defensive star; x a Let x be the state vector of the tracking star. a =[x a ,y a ,v ax ,v ay ] T ;x d Let x be the state vector of the defense star. d =[x d ,y d ,v dx ,v dy ] T x represents the radial position component of the orbit in the LVLH frame; y represents the directional position component of the flight in the LVLH frame; v x v represents the radial velocity component of the orbit in the LVLH system. y The velocity component in the orbital flight direction under the LVLH system; u a The control applied to the tracking satellite manifests as continuous control of the thrust angle; u d The control quantity applied to the defensive satellite is manifested as continuous control of the thrust angle; B is the control matrix for both the pursuing and defensive satellites, B = [0, 1, 2, 3]. 2×2 ,I 2×2 ] T J represents the cost function for both the pursuing and defending stars; T a T represents the magnitude of the maximum thrust acceleration of the tracking star. d This represents the magnitude of the maximum thrust acceleration of the defense star.

[0093] Based on the above process, a spacecraft pursuit and escape defense game model with thrust upper limit based on differential games is established.

[0094] Matrix A is constructed using the CW equation, as follows:

[0095]

[0096] in The value represents the angular velocity of the primary star's orbit around Earth, and μ is the Earth's gravitational field coefficient, μ = 3.986 × 10⁻⁶. 14 , where a0 is the semi-major axis of the main star's orbit.

[0097] S3: The process of obtaining the optimal control law for both sides by solving the established spacecraft pursuit-escape anti-game problem model with thrust upper limit is as follows:

[0098] Define the relative state difference between the defensive star and the pursuing star as: y = x d -x a The constraint differential equation is changed to:

[0099]

[0100] By introducing costate variables based on the Lagrange multiplier method, the bilateral optimization problem with differential equation equality constraints is transformed into an unconstrained bilateral optimization problem, and the auxiliary cost function is obtained by processing the cost function.

[0101]

[0102] Where λ and ν are costate variables.

[0103] To facilitate the variational calculation of the auxiliary cost function, we first perform integration by parts on the auxiliary cost function:

[0104]

[0105] in:

[0106]

[0107] H(x a ,y,u a ,u d ,t)=λ T (Ax a +BT a )+v T (Ay+BT d -BT a (9)

[0108] Variational analysis of the auxiliary cost function:

[0109]

[0110] Since a necessary condition for solving this problem using the variational method is that the variation of the auxiliary cost function is 0, i.e., , the following necessary condition can be obtained:

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] The optimal control laws for both parties are derived from the latter two equations, namely:

[0118]

[0119]

[0120] S4: The steps to transform the spacecraft pursuit and escape anti-game problem with a thrust limit into a two-point boundary value problem are as follows:

[0121] Substitute the optimal control laws of both parties into their dynamic constraint differential equations:

[0122]

[0123] Combining formula (19) with formulas (3)(11)(12), we obtain the following two-point boundary value problem:

[0124]

[0125] S5: Use the bvp4c function in MATLAB to solve the two-point boundary value problem, obtain the state trajectories of both parties, and finally complete the solution of the spacecraft pursuit and escape anti-game problem model with thrust upper limit.

[0126] S6: Based on the solution of the spacecraft pursuit-escape-defense game problem model with thrust upper limit, the state trajectories of the pursuing and defending stars are obtained, thereby adjusting the motion trajectory of the defending star.

[0127] In summary, this invention provides a spacecraft pursuit-escape anti-game control method with a thrust upper limit, which effectively solves the spacecraft pursuit-escape anti-game problem with a thrust upper limit. It represents an effective extension of existing models and methods for spacecraft pursuit-escape anti-game problems. This invention employs a differential game method described by a zero-sum cost function, thus simplifying the solution of the difficult-to-solve constrained weighted performance index pursuit-escape anti-game problem and improving the solution efficiency. Therefore, it can provide an effective threat solution for spacecraft employing master-slave satellite cooperation.

[0128] Example

[0129] See Figure 2 Suppose that at a certain initial time t0=0, there are 3 satellites near a circular orbit with an orbital radius of 500km, namely the main star m, the pursuing star a, and the defensive star d. The main star cannot maneuver, while the pursuing and defensive stars can maneuver in the plane. An LVLH coordinate system is established with the main star as the origin. Its initial state is shown in Table 1, which shows the initial position and velocity of the pursuing star a and the defensive star d.

[0130] Table 1

[0131]

[0132] S1: The spacecraft pursuit-escape-defense game parameters of the target satellite and the defense satellite are input. The spacecraft pursuit-escape-defense game parameters of the target satellite and the defense satellite include the initial position of the target satellite, the initial position of the defense satellite, the velocity of the target satellite, and the velocity of the defense satellite.

[0133] S2: Establish a game-theoretic model for spacecraft pursuit and escape prevention with a thrust upper limit. The establishment process is as follows:

[0134] Establish an LVLH coordinate system with the position of the primary star t as the origin, and design the following cost function based on the game objectives of the pursuing star and the defensive star in combination with the LVLH coordinate system;

[0135]

[0136] The meaning of this cost function is the relative state between the pursuing satellite and the primary satellite at the terminal moment, and the relative state between the defending satellite and the primary satellite, t. f =4000s is the end time of the game.

[0137] In formula (1): matrix A represents the spacecraft relative motion dynamics constraint matrix;

[0138] Wherein, the symmetric positive semi-definite matrix Q1∈R 4×4 Q2∈R 4×4 satisfy:

[0139] Q1=k1I 4×4 Q2 = k2I4×4 (2)

[0140] In formula (2):

[0141] k1 = 0.2, k2 = 0.2 are weighting coefficients;

[0142] Based on the CW equations, we determine the differential equations of the dynamic constraints that need to be satisfied by the pursuing and defending stars in space orbits.

[0143]

[0144] u a =T a τ a ,‖τ a ||≤1

[0145] u d =T d τ d ,‖τ d ‖≤1 (3)

[0146] Matrix A is constructed using the CW equation, as follows:

[0147]

[0148] in The value represents the angular velocity of the primary star's orbit around Earth, and μ is the Earth's gravitational field coefficient, μ = 3.986 × 10⁻⁶. 14 a0 = 6871.39 km is the semi-major axis of the main star's orbit.

[0149] The meanings of the other symbols in formulas (1) to (3) are as follows:

[0150] a is the subscript of the pursuing star; d is the subscript of the defensive star; x a Let x be the state vector of the tracking star. a =[x a ,y a ,v ax ,v ay ] T ;x d Let x be the state vector of the defense star. d =[x d ,y d ,v dx ,v dy ] T x represents the radial position component of the orbit in the LVLH frame; y represents the directional position component of the flight in the LVLH frame; v x v represents the radial velocity component of the orbit in the LVLH system. yThe velocity component in the orbital flight direction under the LVLH system; u a The control applied to the tracking satellite manifests as continuous control of the thrust angle; u d The control quantity applied to the defensive satellite is manifested as continuous control of the thrust angle; B is the control matrix for both the pursuing and defensive satellites, B = [0, 1, 2, 3]. 2×2 ,I 2×2 ] T J represents the cost function for both the pursuing and defending stars; T a =0.02 represents the magnitude of the maximum thrust acceleration of the tracking star; T d =0.02 represents the maximum thrust acceleration of the defense star.

[0151] Based on the above process, a spacecraft pursuit and escape defense game model with thrust upper limit based on differential games is established.

[0152] S3: The process of obtaining the optimal control law for both sides by solving the established spacecraft pursuit-escape anti-game problem model with thrust upper limit is as follows:

[0153] Define the relative state difference between the defensive star and the pursuing star as: y = x d -x a The constraint differential equation is changed to:

[0154]

[0155] By introducing costate variables based on the Lagrange multiplier method, the bilateral optimization problem with differential equation equality constraints is transformed into an unconstrained bilateral optimization problem, and the auxiliary cost function is obtained by processing the cost function.

[0156]

[0157] Where λ and ν are costate variables.

[0158] To facilitate the variational calculation of the auxiliary cost function, we first perform integration by parts on the auxiliary cost function:

[0159]

[0160] in:

[0161]

[0162] H(x a ,y,u a ,u d ,t)=λ T (Ax a +BT a )+v t (Ay+BT d -BTa (9) Find the variation of the auxiliary cost function:

[0163]

[0164] Since a necessary condition for solving this problem using the variational method is that the variation of the auxiliary cost function is 0, i.e., , the following necessary condition can be obtained:

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171] The optimal control laws for both parties are derived from the latter two equations, namely:

[0172]

[0173]

[0174] S4: The steps to transform the spacecraft pursuit and escape anti-game problem with a thrust limit into a two-point boundary value problem are as follows:

[0175] Substitute the optimal control laws of both parties into their dynamic constraint differential equations:

[0176]

[0177] Combining formula (19) with formulas (3)(11)(12), we obtain the following two-point boundary value problem:

[0178]

[0179] S5: Use the bvp4c function in MATLAB to solve the two-point boundary value problem, obtain the state trajectories of both parties, and finally complete the solution of the spacecraft pursuit and escape anti-game problem model with thrust upper limit.

[0180] S6: Based on the solution of the spacecraft pursuit-escape-defense game problem model with thrust upper limit, the state trajectories of the pursuing and defending stars are obtained, thereby adjusting the motion trajectory of the defending star.

[0181] Figure 3The simulation trajectory diagram shows that the pursuing star starts from [0, 20000m] and the defensive star starts from [0, 5000m], and both eventually converge near the main star; Figure 4 The simulated velocity change graph shows the velocity changes of the pursuing and defending satellites. Figure 5 The simulation thrust angle change diagram shows the change in thrust direction for both sides under maximum thrust. Figure 6 The diagram shows the distances between the pursuing and defending stars, as well as the changes in the distances between the pursuing and primary stars. Ultimately, the defending star successfully intercepted the pursuing star.

[0182] like Figure 7 As shown, the second objective of this invention is to propose a spacecraft pursuit and escape anti-game control system with a thrust upper limit, comprising:

[0183] Data acquisition module: used to acquire spacecraft pursuit, escape, and defense game parameters for the pursuing and defending satellites;

[0184] Model building module: Used to build a spacecraft pursuit-escape-defense game problem model with a thrust limit using the acquired spacecraft pursuit-escape-defense game parameters of the pursuing and defending satellites;

[0185] The control law solving module is used to solve the game problem model of spacecraft pursuit, escape, and defense with a thrust limit to obtain the optimal control laws for both the pursuing and defending satellites.

[0186] Transformation Equation Module: Used to transform the spacecraft pursuit and escape anti-game problem with thrust upper limit into a two-point boundary value problem through the optimal control law of both parties;

[0187] Complete the solution module: Used to solve two-point boundary value problems using solution tools to obtain the state trajectories of the pursuing and defending stars;

[0188] Track Adjustment Module: Adjusts the trajectory of the defensive star based on the status trajectories of the pursuing and defensive stars.

[0189] A third objective of this invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the aforementioned spacecraft pursuit and escape anti-game control method with a thrust upper limit.

[0190] The aforementioned spacecraft pursuit and escape anti-game control method with a thrust limit includes the following steps:

[0191] Acquire spacecraft pursuit, escape, and defense game parameters for both the pursuing and defending satellites;

[0192] Using the spacecraft pursuit-escape-defense game parameters obtained from the pursuing and defending satellites, a spacecraft pursuit-escape-defense game problem model with a thrust upper limit is established.

[0193] The optimal control laws for both the pursuing and defending satellites are obtained by solving a game-theoretic problem model of a spacecraft with a thrust limit.

[0194] By using the optimal control laws of both parties, the spacecraft pursuit and escape game problem with thrust limit is transformed into a two-point boundary value problem.

[0195] The two-point boundary value problem is solved using a solver to obtain the state trajectories of the pursuing and defending stars.

[0196] Adjust the trajectory of the defensive star based on the status and trajectory of the pursuing and defensive stars.

[0197] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the aforementioned spacecraft pursuit and escape anti-game control method with a thrust upper limit.

[0198] The aforementioned spacecraft pursuit and escape anti-game control method with a thrust limit includes the following steps:

[0199] Acquire spacecraft pursuit, escape, and defense game parameters for both the pursuing and defending satellites;

[0200] Using the spacecraft pursuit-escape-defense game parameters obtained from the pursuing and defending satellites, a spacecraft pursuit-escape-defense game problem model with a thrust upper limit is established.

[0201] The optimal control laws for both the pursuing and defending satellites are obtained by solving a game-theoretic problem model of a spacecraft with a thrust limit.

[0202] By using the optimal control laws of both parties, the spacecraft pursuit and escape game problem with thrust limit is transformed into a two-point boundary value problem.

[0203] The two-point boundary value problem is solved using a solver to obtain the state trajectories of the pursuing and defending stars.

[0204] Adjust the trajectory of the defensive star based on the status and trajectory of the pursuing and defensive stars.

[0205] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0206] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0207] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0208] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0209] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A spacecraft pursuit and escape anti-game control method with a thrust upper limit, characterized in that, include: Acquire spacecraft pursuit, escape, and defense game parameters for both the pursuing and defending satellites; Using the spacecraft pursuit-escape-defense game parameters obtained from the pursuing and defending satellites, a spacecraft pursuit-escape-defense game problem model with a thrust upper limit is established. The optimal control laws for both the pursuing and defending satellites are obtained by solving a game-theoretic problem model of a spacecraft with a thrust limit. By using the optimal control laws of both parties, the spacecraft pursuit and escape game problem with thrust limit is transformed into a two-point boundary value problem. The two-point boundary value problem is solved using a solver to obtain the state trajectories of the pursuing and defending stars. Adjust the trajectory of the defensive star based on the status and trajectory of the pursuing and defensive stars; The aforementioned method uses the acquired spacecraft pursuit-escape-defense game parameters from the pursuing and defending satellites to establish a spacecraft pursuit-escape-defense game problem model with a thrust upper limit, including: Establish an LVLH coordinate system with the position of the primary star t as the origin, and design a cost function based on the game objectives of the pursuing star and the defensive star in combination with the LVLH coordinate system. Based on the CW equations, we determine the differential equations of the dynamic constraints that need to be satisfied by the pursuing and defending stars in space orbits. Based on the above process, a spacecraft pursuit and escape defense game model with thrust upper limit based on differential game theory is established. The establishment of an LVLH coordinate system with the position of the primary star t as the origin, and the design of a cost function based on the game objectives of the pursuing and defending stars in conjunction with the LVLH coordinate system, includes: in, The cost function for the tracking star; The cost function for the defensive star; The state vector of the tracking star; The state vector of the defense star; The final moment of the game; The weight matrix for the terminal distance term between the tracking star and the primary star; This is the weight matrix for the defensive-targeting satellite terminal distance term.

2. The spacecraft pursuit and escape anti-game control method with thrust upper limit according to claim 1, characterized in that, The spacecraft pursuit-escape-defense game parameters for the pursuing and defending satellites include: The initial position of the pursuing star, the initial position of the defensive star, the speed of the pursuing star, and the speed of the defensive star.

3. The spacecraft pursuit and escape anti-game control method with thrust upper limit according to claim 1, characterized in that, The optimal control laws for the pursuing and defending satellites are obtained by solving the game-theoretic problem model of spacecraft pursuit, escape, and defense with a thrust limit, including: By introducing costate variables based on the Lagrange multiplier method, the bilateral optimization problem with differential equation equality constraints is transformed into an unconstrained bilateral optimization problem, and the auxiliary cost function is obtained by processing the cost function. The optimal control law for both parties is obtained by partially integrating the auxiliary cost function.

4. The spacecraft pursuit and escape anti-game control method with thrust upper limit according to claim 1, characterized in that, The method uses a solver to solve the two-point boundary value problem, obtaining the state trajectories of the pursuing and defending stars, where: The bvp4c function in MATLAB is used to solve the two-point boundary value problem.

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