Multi-satellite pursuit game method based on survival type differential game

Abstract

The invention discloses a multi-satellite pursuit game method based on a survival type differential game, and relates to a spaceflight pursuit satellite optimal method.The method comprises the steps that firstly, a particle swarm algorithm and a Newton iteration algorithm are combined, and a complex two-point boundary value problem is converted into a parameter optimization problem with constraints; and then solving a countermeasure saddle point corresponding to the game countermeasure for chasing the satellite. On the premise of considering the accuracy of the algorithm, shortening the calculation cost and ignoring the attitude problem of the satellite, the model is simplified, and the thrust direction angle of the satellite is used as the control quantity to realize the orbital maneuver of the satellite. Assuming that the satellites are all under the condition of continuous small thrust, taking terminal end time as a payment function by three game parties, taking a minimum function as a target by chasing the satellites, and contrarily taking the minimum function as the target by escaping the satellites. Simulation results show that the confrontation game of the pursuit satellites in the orbital plane is relatively intense, and the pursuit satellites with higher thrust acceleration have more advantages in confrontation.

Description

Technical Field

[0001] The invention relates to an optimal method for chasing and escaping a space satellite, and in particular to a multi-satellite chasing and escaping game method based on survival differential countermeasures. Background Art

[0002] With the continuous development of science and technology, the military value of space resources has been increasingly valued by countries around the world. Various space platforms, mainly low-Earth satellites, have become an important part of modern warfare due to their wide observation range and fast information transmission speed. They play an irreplaceable role in reconnaissance and communication, navigation and positioning, monitoring and early warning. With the development of autonomous rendezvous and docking technology, attacking spacecraft use rendezvous to approach target spacecraft to interfere with or attack them, which has become an important means of attack, especially in military warfare. It has shown great advantages and further reflects the important position of space warfare in modern warfare. Therefore, exploring the confrontation problem of spacecraft in the pursuit and escape game, especially solving the pursuit and escape game problem through differential game theory, and obtaining the optimal control strategy and pursuit and escape game law are of great significance to promoting the sustainable development of the aerospace industry.

[0003] At present, for the problem of spacecraft orbital pursuit. According to the transparency of information in the game process, it can be divided into two major research categories: complete information and incomplete information; according to the differential strategy to solve the saddle point of the pursuit spacecraft, it can be divided into fixed stay period differential strategy, infinite time domain differential strategy and survival differential strategy; according to the maneuvering method, it can be divided into pulse thrust and continuous thrust. However, most of the research is aimed at the pursuit game between two spacecraft. The space pursuit problem is an important issue in the field of aerospace engineering. In the past decade, it has attracted many scholars to conduct in-depth research and discussion on the pursuit game of multiple spacecraft.

[0004] The pursuit and escape game problem of multiple spacecraft is essentially a continuous dynamic confrontation problem controlled by multiple parties. The maneuvering strategy can be constructed by constructing a scoring function, and the overall interception efficiency is higher than that of a single spacecraft interception, but the maneuvering method of this design does not introduce movement in a composite direction, and the trajectory control is not flexible enough; the single pulse maneuvering method is used to change the track and complete the pursuit process. The hybrid algorithm shortens the interception time, but the single pulse propulsion method has the defect of a fixed number of maneuvers, and the thrust is large, which will consume a lot of fuel. There is still greater room for development in the research of the pursuit and escape game of multiple spacecraft, and it also has deeper research significance. Summary of the invention

[0005] The purpose of the present invention is to provide a multi-satellite pursuit and escape game method based on survival differential countermeasures. Under the condition of continuous small thrust, the method studies the pursuit and escape game of two pursuit satellites and one escape satellite based on survival differential countermeasures. The three parties in the game use the terminal end time as the payment function, the pursuit satellite takes the minimization function as the goal, and the escape satellite takes the opposite. The complex two-point boundary value problem is transformed into a constrained parameter optimization problem, and then the hybrid algorithm is used to solve the game saddle point corresponding to the game countermeasures of the pursuit satellite; reducing the defect of a fixed number of maneuvers in a single pulse propulsion method is the technical problem to be solved by the present invention, so as to achieve the completion of the pursuit task with the least fuel consumption, thereby significantly improving the pursuit efficiency and shortening the calculation cost, and providing a more efficient and accurate solution to the problem of pursuit and escape between satellites.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A multi-satellite pursuit and escape game method based on survival differential game, the method comprising the following steps:

[0008] S1, a mathematical model is established based on the CW equation, and the relationship between the transfer time and the analytical solution of the speed system is derived;

[0009] S2, establish a survival differential game model of three satellites, take terminal time as the variable to be determined, determine the game terminal set, motion state equation and payment function;

[0010] S3, based on the established model, construct Hamiltonian function and terminal constraint function to determine the optimal control strategy of the pursuit satellite;

[0011] S4, a method combining particle swarm optimization and Newton iteration algorithm is proposed to solve the saddle point of the game; the pursuit time of the optimal strategy is calculated through iterative solution;

[0012] The specific process is:

[0013] Firstly, the CW equation is established according to the claim, and basic assumptions and constraints are made on it to establish the orbital dynamics equation of the pursuit satellite in the LVLH coordinate system:

[0014] Basic assumptions and constraints

[0015] Assuming that during the confrontation process, the distance between the virtual reference satellite and the pursuit satellite is much smaller than the distance from the center of the earth to the center of mass of the virtual reference satellite, its dynamic model can ignore the second-order and higher-order small quantities; the reference orbit is a near-circular orbit, and ω is a constant:

[0016]

[0017] Although in actual space missions, factors such as the Earth's oblateness, atmospheric drag, solar radiation pressure, and the gravity of the third body may interfere with the orbit of the spacecraft, the optimization process of the interception mission requires multiple iterations. In order to ensure calculation efficiency and speed, only the Earth's gravity is taken as the main consideration; the orbital dynamics equation of the spacecraft under the two-body problem is

[0018]

[0019] Where μ is the Earth's gravitational constant; r is the spacecraft position vector; μ = 398600 (km 3 / s 2 );

[0020] S12, the orbital dynamics equations of the pursuit satellite in the LVLH coordinate system are:

[0021]

[0022] The thrust used for chasing satellites and escaping satellites is a continuous small thrust. By controlling the direction of the satellite thrust acceleration, that is, changing the size of the α and β angles, the three-axis component a of the satellite is changed. Px 、a Py 、a Pz The size of the satellite is used to realize the maneuver of the satellite, thereby carrying out pursuit or escape operations; the dynamic equations of the pursuit satellite are organized into the form of state space to obtain the analytical solution of the system; the relative state quantity of the satellite Thrust acceleration a P(t) =[a Px ,a Py ,a Pz ] T .

[0023]

[0024] When the initial state is known, the analytical solution in the state space formula can be obtained, and finally the specific form of the state transfer matrix Φ(t,t0) can be obtained

[0025]

[0026] τ=t-t0 is the state transition time. P(t) is a constant value P0 , find Ψ(τ); if the initial state of the pursuit satellite P is x P (t0) is known, and the analytical solution of the system can be obtained according to Φ(τ) and Ψ(τ), and the expression of the motion state equation of P can be obtained. Similar to the pursuit satellite, the motion state expression of the escape satellite E can be obtained:

[0027] x P(t) = Φ(τ)x P (t0)+Ψ(τ)a P0

[0028] x E (t) = Φ(τ)x E (t0)+Ψ(τ)a E0

[0029] Through the definition of the relative motion coordinate system and the derivation process of the motion state function of the pursuit satellite P and the escape satellite E in this coordinate system, it can be seen that in the satellite pursuit and escape game, the thrust acceleration of the satellite is controlled to change the motion state of the satellite, thereby performing orbital maneuvers and achieving the respective pursuit and escape missions of the satellites.

[0030] The multi-satellite pursuit and escape game method based on survival differential countermeasures, said S2, establishes a survival differential countermeasures model of three satellites, takes terminal time as the variable to be determined, determines the countermeasure terminal set, motion state equation and payment function;

[0031] S2, equation of motion:

[0032]

[0033] x(t0)=x0

[0034] Terminal set for countermeasures:

[0035] ∧={X|x=0,y=0,z=0}

[0036] Payment function:

[0037] J iP =t f

[0038] J E =-J iP

[0039] Among them, u P =[α p ,β P ] T 、u E =[α E ,β E ] T , are the control quantities of the chasing satellite and the escaping satellite, respectively, t f is the terminal end time, and i is the number of satellites.

[0040] The multi-satellite pursuit and escape game method based on survival differential game, S3 constructs Hamiltonian function and terminal constraint function on the basis of establishing a model, and determines the optimal control strategy of the pursuit and escape satellite:

[0041] H(x,u iP ,u E ,λ)=λ T [Ax+B(a E -a iP )]

[0042]

[0043] λ is the covariate variable, v is the Lagrange multiplier corresponding to the terminal constraint, where λ = [λ1,λ2,λ3,λ4,λ5,λ6] T ,v=[v1,v2,v3] T , is the relative position constraint of the terminal;

[0044] Co-state equation:

[0045]

[0046] The final value condition of the covariate variable:

[0047]

[0048] Write the co-state equation in state transfer form, where Φ λ (τ) is the state transfer matrix; the above formula is as follows:

[0049] λ(t)=Φ λ (τ)λ(t0)

[0050]

[0051] make The optimal control strategy for chasing satellites and escaping satellites can be obtained:

[0052]

[0053] This strategy needs to satisfy the transversality condition of the differential game, and finally can solve the open-loop saddle point of the survival differential game.

[0054] The multi-satellite pursuit and escape game method based on survival differential game, S4 proposes a method combining particle swarm algorithm and Newton iteration algorithm to solve the saddle point of the game; the pursuit time of the optimal strategy is calculated by iterative solution;

[0055] The optimal strategy hunting time is calculated through iterative solution; the design variables of the particle swarm optimization model are:

[0056] X PSO =[t f , v1, v2, v3] T

[0057] The objective function is:

[0058]

[0059] Among them, k i is the weighting coefficient, c i is the miss distance of the terminal constraint; the particle swarm algorithm is used to obtain a rough solution, and then combined with the Newton iteration algorithm to obtain an exact solution;

[0060] Newton's iterative algorithm finds the exact solution:

[0061] The Newton iteration method has fast convergence speed and small amount of calculation, which can increase the robustness and reliability of the algorithm;

[0062] For a general system of nonlinear equations:

[0063] F(x)=[f1(x)f2(x)…f n (x)] T =0

[0064] Formula (25) x = [x1, x2…, x n ] T is the independent variable to be determined. (k) Taylor expansion is performed at the position, and the approximate linear part is obtained:

[0065] F(x)≈F(x (k) )+F′(x (k) )(xx (k) )

[0066] Then we get the linear equation system:

[0067] F(x (k) )+F′(x (k) )(xx (k) )=0

[0068] The solution to the system of equations:

[0069] x (k+1) =x (k) -[F′(x (k ))] -1 F(x (k) ). BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 The three-dimensional space trajectory of the pursuit satellite in the multi-satellite pursuit-escape game based on the survival differential game in the embodiment of the present invention;

[0071] Figure 2 It is a trajectory curve on three coordinate axes based on the change of the positions of the three parties in pursuit and escape over time in the embodiment;

[0072] in: Figure 2 (a) Change pattern on the X-axis; Figure 2 (b) Variation pattern on the Y axis; Figure 2 (c) Variation pattern on the Z axis;

[0073] Figure 3 is a graph showing the change of relative distance over time in the embodiment;

[0074] Figure 4 is a diagram of relative speed changes in the embodiment;

[0075] Figure 5 This is the law diagram of the change of the optimal thrust direction angle of the pursuit satellite;

[0076] in: Figure 5 (a) Optimal control rate α; Figure 5 (b) Optimal control rate β. DETAILED DESCRIPTION

[0077] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0078] A multi-satellite pursuit and escape game method based on survival differential game comprises the following steps:

[0079] S1, a mathematical model is established based on the CW equation, and the relationship between the transfer time and the analytical solution of the speed system is derived;

[0080] S2, establish a survival differential game model of three satellites, take terminal time as the variable to be determined, determine the game terminal set, motion state equation and payment function;

[0081] S3, based on the established model, construct Hamiltonian function and terminal constraint function to determine the optimal control strategy of the pursuit satellite;

[0082] S4, a method combining particle swarm optimization and Newton iteration algorithm is proposed to solve the saddle point of the game. The pursuit time of the optimal strategy is calculated through iterative solution;

[0083] S5, using MATLAB to design simulation experiments, analyzes the changing rules in the pursuit and escape game process.

[0084] The relative motion state of the pursuit in step S1 is described using the CW equation:

[0085]

[0086] Where ρ = [x p ,yp , z p ] T , are the position and velocity vector of the satellite in the reference satellite LVLH coordinate system, respectively; is the average angular velocity of the reference orbit, μ is the gravitational constant of the Earth, a r is the reference orbit radius, where the reference orbit is a circular orbit; the above expression is to pursue satellite a P The expression of escape satellite a E That's also true.

[0087] a Px 、a Py 、a Pz They are the radial, track and normal thrust acceleration components of the satellite respectively; the control vector expression here is:

[0088] a Px =a T cosβsinα

[0089] a Py =a T cosβcosα

[0090] a Pz =a T sinβ

[0091] where a Px 、a Py 、a Pz is through a T The projection directly obtains the three-axis components in the coordinate system, where α represents the satellite P acceleration vector a T The angle at which the projection to the plane where X and Y are located intersects the X axis, and β represents the acceleration vector a T The angle between the planes of the X-axis and the Y-axis in the coordinate axis. Similarly, the vector acceleration of the escaping satellite is a E Here, the pursuit satellites all use continuous thrust control. a is the thrust direction angle, β is the thrust height angle, and the range of the two angles is [-π<α≤π], by changing the size of angle α and angle β, the satellite's orbital maneuvers can be realized, thereby carrying out pursuit.

[0092] The CW equations need to be converted into state space form:

[0093]

[0094] In step S2, a multi-satellite pursuit differential game model is established. The survival differential game models of the three satellites are:

[0095] Multi-satellite pursuit differential game model:

[0096]

[0097] x(t0)=x0

[0098] Among them, x(t) represents the relative state of the pursuit satellite, x t =x E(t) -x iP(t) , here u P1 (t),u P2 (t) respectively represent the input control quantities of P1 and P2 for chasing satellites, u E (t) represents the input control variable of the escape satellite, and x0 represents the initial state.

[0099] The survival differential game model of three satellites is:

[0100]

[0101] x(t0)=x0

[0102] The terminal time of the pursuit satellite is a variable to be determined. When the terminal distance between the two parties is less than a certain value, the strategy ends. The terminal set of the strategy is:

[0103] ∧={X|x=0,y=0,z=0}

[0104] Payment function:

[0105] J iP =t f

[0106] J E =-J iP

[0107] Among them, t f is the terminal end time, and i is the number of satellites.

[0108] In step S3, based on the established model, the Hamiltonian function and the terminal constraint function are constructed:

[0109] H(x,u iP ,u E ,λ)=λ T [Ax+B(a E -a iP )]

[0110]

[0111] λ is the covariate variable, v is the Lagrange multiplier corresponding to the terminal constraint, where λ = [λ1,λ2,λ3,λ4,λ5,λ6] T ,v=[v1,v2,v3] T , It is the relative position constraint of the terminal.

[0112] Co-state equation:

[0113]

[0114] The final value condition of the covariate variable:

[0115]

[0116] Write the co-state equation in state transfer form, where Φ λ (τ) is the state transfer matrix. The above formula is as follows:

[0117] λ(t)=Φ λ (τ)λ(t0)

[0118]

[0119] make The optimal control strategy for chasing satellites and escaping satellites can be obtained:

[0120]

[0121] This strategy needs to satisfy the transversality condition of the differential game, and finally can solve the open-loop saddle point of the survival differential game.

[0122] In step S4, a method combining the particle swarm algorithm and the Newton iteration algorithm is proposed to solve the saddle point of the game. The mathematical model of the particle swarm algorithm is as follows: Assume that in a D-dimensional target search space, there are N particles forming a colony, where the position of the i-th particle is represented as a D-dimensional vector, denoted as:

[0123] X i =(x i1 ,x i2 ,…x iD ),i=1,2,…N

[0124] The "flying" speed of the i-th particle is also expressed as a D-dimensional vector, denoted as:

[0125] V i =(v i1 ,v i2 ,…v iD ),i=1,2,…N

[0126] When the i-th particle of the t-th generation evolves to the t+1-th generation, it is updated according to the following relationship:

[0127]

[0128] Among them, ω is the inertia weight, which determines the degree of inheritance of the particle's previous motion trend, that is, the inertia of search flight; c1 and c2 are individual learning factors and social learning factors, respectively. C1 controls the self-cognition part and guides the particle to fly in the direction of its own historical optimal solution; c2 controls the social cognition part, reflecting the collaborative cooperation ability between particles and guiding the particle to fly in the direction of the historical optimal solution of the entire population; P best，i is the individual optimal position of the i-th particle, G best is the global optimal position, r1 and r2 are random factors, that is, random numbers in the interval [0, 1].

[0129] The basic process of particle swarm algorithm is as follows Figure 3 As shown in the figure, population initialization includes setting the particle swarm size, particle "flying" speed boundary, search space range, and designing the system's inertia weight coefficient and learning factor. Before each particle flight, first check whether the current particle speed value exceeds the preset speed boundary. If it exceeds this range, automatically adjust the current speed to the speed boundary value. After completing the flight, verify again whether the new position exceeds the preset maximum search space. If it exceeds this range, the system will adopt the same strategy as speed adjustment, that is, reset the current position to the boundary value of the search space to ensure that the particle always finds the optimal solution within the effective search space.

[0130] According to the change of fitness function value f, update the optimal position P of individuals in the system best，i and the global optimal position G best , the update equation is as follows:

[0131]

[0132] In the optimization process of solving practical problems, the global optimal solution reaching a predetermined fitness standard is usually used as the termination condition. However, in the experimental research of the present invention, in order to compare the performance of different algorithms more fairly and systematically, we set a fixed iteration termination condition, that is, when the preset maximum number of iterations is reached, the algorithm will stop iterating. In addition, considering that minimizing fuel consumption is the main optimization goal of the present invention, we selected the objective function J mentioned above as the fitness function to evaluate the performance of each optimization algorithm in finding the lowest fuel consumption solution.

[0133] 6. The method of multi-satellite pursuit and escape game strategy based on survival differential game according to claim 2 is characterized in that step S5 uses MATLAB to design a simulation experiment to analyze the changing rules in the pursuit and escape game process.

[0134] The design contents of the simulation analysis are as follows: the present invention adopts a circular orbit as the reference orbit, the orbit altitude is 36000km, the orbit semi-major axis is 42378.137km, the orbit angular velocity is 7.237×10-5rad / s, g=9.78m / s2, the earth's gravitational constant is 3.986×1014m3 / s2, the continuous thrust accelerations of the pursuit satellite 1, pursuit satellite 2 and escape satellite are 0.001g, 0.0009g, 0.0004g respectively, and the initial motion state of the pursuit satellite is shown in Table 1. When the particle swarm algorithm is used to solve the initial rough solution, the population size is set to 50, the number of evolutionary iterations is 100, the integration step is 10s, c1 is 1, c2 is 2, and the upper and lower bounds of the design variables are shown in Table 2.

[0135] Table 1 Initial relative motion states of the chasing satellite and the escaping satellite

[0136] Tab.1 The initial relative motion state of the satellite being pursued and the escaping satellite ite

[0137]

[0138] Tab.2 Upper and lower bounds of design variables in PSO algorithm

[0139] Design variables <![CDATA[t f / s]]> <![CDATA[v1]]> <![CDATA[v2]]> <![CDATA[v3]]> Upper Bound 2000 -200 -200 -200 The Nether 20000 200 200 200

[0140] The present invention solves the saddle point of the game of two chasing satellites and one escaping satellite based on the survival differential game theory. First, a rough solution is obtained by particle swarm algorithm, and then the precise solution of the survival differential game that meets the constraint conditions is obtained by Newton iteration method. In the process of chasing and escaping game, the satellite with large thrust acceleration has better chasing effect. When two satellites chase one escaping satellite, the escape strategy of the escaping satellite can be interfered, effectively reducing the escape efficiency of the escaping satellite, thereby improving the overall pursuit success rate.

Claims

1. A multi-satellite pursuit and escape game method based on survival differential game, characterized in that: The method comprises the following steps: S1, a mathematical model is established based on the CW equation, and the relationship between the transfer time and the analytical solution of the speed system is derived; S2, establish a survival differential game model of three satellites, take terminal time as the variable to be determined, determine the game terminal set, motion state equation and payment function; S3, based on the established model, construct Hamiltonian function and terminal constraint function to determine the optimal control strategy of the pursuit satellite; S4, a method combining particle swarm optimization and Newton iteration algorithm is proposed to solve the saddle point of the game; the pursuit time of the optimal strategy is calculated through iterative solution; The specific process is: Firstly, the CW equation is established according to the claim, and basic assumptions and constraints are made on it to establish the orbital dynamics equation of the pursuit satellite in the LVLH coordinate system: Basic assumptions and constraints Assuming that during the confrontation process, the distance between the virtual reference satellite and the pursuit satellite is much smaller than the distance from the center of the earth to the center of mass of the virtual reference satellite, its dynamic model can ignore the second-order and higher-order small quantities; the reference orbit is a near-circular orbit, and ω is a constant: Although in actual space missions, factors such as the Earth's oblateness, atmospheric drag, solar radiation pressure, and the gravity of the third body may interfere with the orbit of the spacecraft, the optimization process of the interception mission requires multiple iterations. In order to ensure calculation efficiency and speed, only the Earth's gravity is taken as the main consideration; the orbital dynamics equation of the spacecraft under the two-body problem is Where μ is the Earth's gravitational constant; r is the spacecraft position vector; μ = 398600 (km 3 / s 2 ); S12, the orbital dynamics equations of the pursuit satellite in the LVLH coordinate system are: The thrust used for chasing satellites and escaping satellites is a continuous small thrust. By controlling the direction of the satellite thrust acceleration, that is, changing the size of the α and β angles, the three-axis component a of the satellite is changed. Px 、a Py 、a Pz The size of the satellite is used to realize the maneuver of the satellite, thereby carrying out pursuit or escape operations; the dynamic equations of the pursuit satellite are organized into the form of state space to obtain the analytical solution of the system; the relative state quantity of the satellite Thrust acceleration a P(t) =[a Px ,a Py ,a Pz ] T . When the initial state is known, the analytical solution in the state space formula can be obtained, and finally the specific form of the state transfer matrix Φ(t,t0) can be obtained τ=t-t0 is the state transition time; when a P(t) is a constant value P0 , find Ψ(τ); if the initial state of the pursuit satellite P is x P (t0) is known, and the analytical solution of the system can be obtained according to Φ(τ) and Ψ(τ), and the expression of the motion state equation of P can be obtained. Similar to the pursuit satellite, the motion state expression of the escape satellite E can be obtained: x P (t)=Φ(τ)x P (t0)+Ψ(τ)a P0 # x E (t)=Φ(τ)x E (t0)+Ψ(τ)a E0 Through the definition of the relative motion coordinate system and the derivation process of the motion state function of the pursuit satellite P and the escape satellite E in this coordinate system, it can be seen that in the satellite pursuit and escape game, the thrust acceleration of the satellite is controlled to change the motion state of the satellite, thereby performing orbital maneuvers and achieving the respective pursuit and escape missions of the satellites.

2. The multi-satellite pursuit and escape game method based on survival differential strategy according to claim 1 is characterized in that: S2, establishing a survival differential game model of three satellites, taking terminal time as the variable to be determined, determining the game terminal set, motion state equation and payment function; S2, equation of motion: x(t0)=x0 Terminal set for countermeasures: ∧={X|x=0,y=0,z=0} Payment function: J iP =t f I E =-J iP Among them, u P =[α p ,β P ] T 、u E =[α E ,β E ] T , are the control quantities of the chasing satellite and the escaping satellite, respectively, t f is the terminal end time, and i is the number of satellites.

3. The multi-satellite pursuit and escape game method based on survival differential strategy according to claim 1 is characterized in that: The S3 constructs the Hamiltonian function and the terminal constraint function on the basis of the established model to determine the optimal control strategy of the pursuit satellite: H(x,u iP ,her E ,λ)=λ T [Ax+B(a E -your iP )] λ is the covariate variable, v is the Lagrange multiplier corresponding to the terminal constraint, where λ = [λ1,λ2,λ3,λ4,λ5,λ6] T ,v=[v1,v2,v3] T , is the relative position constraint of the terminal; Co-state equation: The final value condition of the covariate variable: Write the co-state equation in state transfer form, where Φ λ (τ) is the state transfer matrix; the above formula is as follows: λ(t)=Φ λ (t)λ(t0) make The optimal control strategy for chasing satellites and escaping satellites can be obtained: This strategy needs to satisfy the transversality condition of the differential game, and finally can solve the open-loop saddle point of the survival differential game.

4. The multi-satellite pursuit and escape game method based on survival differential strategy according to claim 1 is characterized in that: S4 proposes a method combining particle swarm algorithm and Newton iteration algorithm to solve the saddle point of the strategy; the pursuit time of the optimal strategy is calculated through iterative solution; The optimal strategy hunting time is calculated through iterative solution; the design variables of the particle swarm optimization model are: X PSO =[t f ,v1,v2,v3] T The objective function is: Among them, k i is the weighting coefficient, c i is the miss distance of the terminal constraint; the particle swarm algorithm is used to obtain a rough solution, and then combined with the Newton iteration algorithm to obtain an exact solution; Newton's iterative algorithm finds the exact solution: The Newton iteration method has fast convergence speed and small amount of calculation, which can increase the robustness and reliability of the algorithm; For a general system of nonlinear equations: F(x)=[f1(x) f2(x)…f n (x)] T =0 Formula (25) x=[x1,x2,…,x n ] T is the independent variable to be determined; let F(x) be (k) Taylor expansion is performed at the position, and the approximate linear part is obtained: F(x)≈F(x (k) )+F'(x (k) )(x-x (k) ) Then we get the linear equation system: F(x (k) )+F'(x (k) )(x-x (k) )=0 The solution to the system of equations: x (k+1) =x (k) -[F'(x (k) )] -1 F(x (k) )。

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