Spacecraft pursuit game robust control method under non-complete information based on non-zero sum game

Abstract

The invention discloses a spacecraft pursuit game robust control method under non-complete information based on a non-zero sum game, and the method mainly comprises the following steps: 1, building a spacecraft non-zero sum game control model containing uncertainty according to the dynamics; 2, designing a control gain adaptive estimator of the target spacecraft under incomplete information; step 3, based on the adaptive estimator, establishing an improved Riccati equation of spacecraft non-zero sum game control; 4, designing a value iteration algorithm of the spacecraft control strategy based on the improved Riccati equation; according to the control method, the adverse effect of uncertainty in a pursuit game system is overcome, the problem that the cost function and the control strategy of the target spacecraft are unknown is solved, and the effectiveness and the control precision of the pursuit strategy of the spacecraft are ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of space vehicle intelligent control, and in particular to a robust control method for a space vehicle pursuit-escape game under incomplete information based on a non-zero-sum game. Background Art

[0002] As the main carrier of the future space environment, spacecraft is of great significance to the future national space security and development. The pursuit and escape game of aircraft has always been a key topic in space game confrontation and is widely used in space operation tasks, such as space target reconnaissance and non-cooperative target detection.

[0003] When designing a spacecraft control strategy, it is easily affected by various uncertainties such as external environmental perturbations, which will seriously reduce the control accuracy of the spacecraft. Therefore, it is necessary to incorporate the influence of external environmental uncertainties into the control performance indicators. However, due to the unknown characteristics of uncertainty, the design of spacecraft controllers is more difficult.

[0004] A variety of control methods have been proposed for the pursuit and escape game confrontation control problem of spacecraft. For example, the discrete-time fault-tolerant zero-sum game, the event-triggered nonlinear zero-sum game problem, etc. However, in the actual confrontation environment, it is difficult for the two parties to obtain the other party's cost function and the control strategy of the target spacecraft. In this case, the zero-sum game is not suitable for modeling the pursuit and escape game problem under incomplete information, while the non-zero-sum game theory does not require the cost functions of the two parties to be completely opposite, and is more suitable for the pursuit and escape game scenario of spacecraft with incomplete information. Therefore, for the pursuit and escape control problem of spacecraft, how to design a non-zero-sum game pursuit and escape control method under incomplete information is a difficult problem. Summary of the invention

[0005] Aiming at the spacecraft pursuit and escape game control problem under the condition of partially unknown information, a robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game was proposed to overcome the shortcomings of the existing technology and make full use of the non-zero-sum game theory.

[0006] In order to solve the above technical problems, the present invention proposes a robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game, comprising the following steps:

[0007] Step 1: Based on dynamics, establish a non-zero-sum game control model of spacecraft with uncertainty;

[0008] Step 2: Design a control gain adaptive estimator for the target space vehicle under incomplete information;

[0009] Step 3: Based on the adaptive estimator, the improved Riccati equation for non-zero-sum game control of spacecraft is established;

[0010] Step 4: Based on the improved Riccati equation, design a value iteration algorithm for the space vehicle control strategy;

[0011] Among them, step 1 is specifically divided into the following steps:

[0012] Step 1.1:

[0013] Establish a non-zero-sum game control model for spacecraft:

[0014]

[0015] in, is the vector of the spacecraft's position and velocity; A is the state matrix; B is the coefficient matrix of the control input; u is the control input of the spacecraft. The specific forms of A and B are as follows:

[0016]

[0017] in, a0 is the reference orbit radius, μ is the gravitational constant;

[0018] Step 1.2:

[0019] Using the Euler discretization method, a discrete control model of the spacecraft is established:

[0020] η k+1 =A d η k +B d u k

[0021] Among them, A d =e Aτ , τ is the sampling period, η k is the value of the spacecraft state at the kth moment, u k Enter the value of the spacecraft at time k.

[0022] Step 1.3:

[0023] Establish discrete control models for spacecraft of the pursuer and the escaper

[0024] η p,k+1 =A d η p,k +B d u p,k

[0025] η e,k+1 =A d ηe,k +B d u e,k

[0026] Among them, u p,k and u e,k are the control inputs of the pursuer and the escaper at the kth moment, η p,k and η p,k are the states of the pursuer and the escaper at the kth moment respectively.

[0027] Therefore, the pursuit-escape game control model between two spacecraft is:

[0028]

[0029] in, B p =-B d , B e =B d .

[0030] Step 1.4:

[0031] Building a discrete control model for spacecraft with uncertainty

[0032]

[0033] in, is the uncertainty term of the spacecraft control system and satisfies the following inequality:

[0034]

[0035] Among them, Φ is a known positive definite matrix.

[0036] In the non-zero-sum game framework, the control cost function of the pursuing spacecraft is set as:

[0037]

[0038] Among them, the matrix Q p ,R p is an adjustable known positive definite constant matrix.

[0039] The control cost function of the escaping spacecraft is set as:

[0040]

[0041] Among them, the matrix Q e ,R e is an adjustable known positive definite constant matrix.

[0042] Controller p,k ,ue,k The design goal is to minimize the control cost function and Where K p is the control gain of the pursuing aircraft, K e is the control gain of the escaping aircraft;

[0043] Among them, step 2 is specifically as follows:

[0044] Under incomplete information, the pursuing spacecraft cannot know the control input of the escaping spacecraft, so a control gain adaptive estimator is designed;

[0045] First, assume that the escaping spacecraft adopts the optimal control strategy, that is, Among them, K e * is the optimal control strategy of the escaping spacecraft, and satisfies the following equation:

[0046]

[0047] Among them, P e is a positive definite matrix and satisfies the following equation:

[0048]

[0049] Among them, β1 and β3 are preset positive constants and satisfy λ max {P e} represents the matrix P e The maximum eigenvalue of

[0050] The state equation can be written as:

[0051]

[0052] The pursuit state equation estimated by the pursuer can be written as:

[0053]

[0054] Therefore, the following equation can be obtained:

[0055]

[0056] Multiply both sides by (B e T B e ) -1 B e T , we can get

[0057]

[0058] in,

[0059]

[0060] Control gain of the escaping spacecraft The adaptive estimator of is designed as:

[0061]

[0062] Among them, Γ is a positive definite matrix and κ is a positive constant.

[0063] From the above adaptive estimator, we can see that there is a time constant T>0, Gain Estimation Error satisfy:

[0064]

[0065] in,

[0066] Based on the estimated control gain The system state space model can be written as:

[0067]

[0068] in,

[0069] Because the estimation error and relative state error The mutual coupling further increases the difficulty of designing the optimal control strategy for the pursuing spacecraft. To solve this problem, first, assume that the value of the control gain estimator after working for a period of time T is The pursuing spacecraft uses this estimate to design its own control strategy. The state space equation of the game system is:

[0070]

[0071] in,

[0072] Among them, step 3 is specifically: based on the above-mentioned adaptive control gain estimator, the following improved Riccati equation is established:

[0073]

[0074] and

[0075]

[0076] Among them, ρ1=σ1+γ1+1, ρ2=σ2+γ2+1, Here, σ1, σ2, σ3, γ1, γ2 are all positive constants;

[0077] Specifically, step 4 is as follows: Based on the above Riccati equation, the following value iteration algorithm is designed:

[0078] Step 4.1: First choose an initial value And meet And initialize the calculation error threshold ò>0.

[0079] Step 4.2: For iteration number j = 1, 2, 3, ..., iterate the matrix Calculate according to the following equation:

[0080]

[0081] Step 4.3: Calculate the control strategy norm error for two consecutive times If e i,k >ò, then go to step 4.2, otherwise, the calculation ends and the optimal value is output

[0082] Step 4.4: Calculate the optimal control strategy u p,k :

[0083]

[0084] The beneficial effects of the present invention are as follows: it overcomes the adverse effects of uncertainty in the pursuit-escape game system, solves the problem of unknown cost function and control strategy of the target aircraft, and ensures the effectiveness and control accuracy of the space aircraft pursuit strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is the overall flow chart of the method of the present invention;

[0086] Figure 2 It is a position error curve diagram of the pursuing party's space vehicle and the escaping party;

[0087] Figure 3 is the velocity error curve between the vehicle and the desired trajectory. DETAILED DESCRIPTION

[0088] The present invention proposes a robust control method for a space vehicle pursuit-escape game under incomplete information based on a non-zero-sum game. The specific implementation mode of the present invention is further explained below in conjunction with the accompanying drawings.

[0089] It should be noted that the embodiments described in the present invention are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative work are all within the scope of protection of the present invention.

[0090] A robust control method for a spacecraft pursuit-escape game under incomplete information based on a non-zero-sum game comprises the following steps:

[0091] Step 1: Based on dynamics, establish a non-zero-sum game control model of spacecraft with uncertainty;

[0092] Step 2: Design a control gain adaptive estimator for the target space vehicle under incomplete information;

[0093] Step 3: Based on the adaptive estimator, the improved Riccati equation for non-zero-sum game control of spacecraft is established;

[0094] Step 4: Based on the improved Riccati equation, design a value iteration algorithm for the space vehicle control strategy;

[0095] In a specific embodiment 1, the above four steps are described in detail:

[0096] Among them, step 1 is specifically divided into the following steps:

[0097] Step 1.1:

[0098] Establish a non-zero-sum game control model for spacecraft:

[0099]

[0100] in, is the vector of the spacecraft's position and velocity; A is the state matrix; B is the coefficient matrix of the control input; u is the control input of the spacecraft. The specific forms of A and B are as follows:

[0101]

[0102] in, a0 is the reference orbit radius, μ is the gravitational constant;

[0103] Step 1.2:

[0104] Using the Euler discretization method, a discrete control model of the spacecraft is established:

[0105] η k+1 =A d η k +B d u k

[0106] Among them, A d =e Aτ , τ is the sampling period, η k is the value of the spacecraft state at the kth moment, u k Enter the value of the spacecraft at time k.

[0107] Step 1.3:

[0108] Establish discrete control models for spacecraft of the pursuer and the escaper

[0109] η p,k+1 =A d η p,k +B d u p,k

[0110] η e,k+1 =A d η e,k +B d u e,k

[0111] Among them, u p,k and u e,k are the control inputs of the pursuer and the escaper at the kth moment, η p,k and η p,k are the states of the pursuer and the escaper at the kth moment respectively.

[0112] Therefore, the pursuit-escape game control model between two spacecraft is:

[0113]

[0114] in, B p =-B d , B e =B d .

[0115] Step 1.4:

[0116] Building a discrete control model for spacecraft with uncertainty

[0117]

[0118] in, is the uncertainty term of the spacecraft control system and satisfies the following inequality:

[0119]

[0120] Among them, Φ is a known positive definite matrix.

[0121] In the non-zero-sum game framework, the control cost function of the pursuing spacecraft is set as:

[0122]

[0123] Among them, the matrix Q p ,R p is an adjustable known positive definite constant matrix.

[0124] The control cost function of the escaping spacecraft is set as:

[0125]

[0126] Among them, the matrix Q e ,R e is an adjustable known positive definite constant matrix.

[0127] Controller p,k ,u e,k The design goal is to minimize the control cost function and Where K p is the control gain of the pursuing aircraft, K e is the control gain of the escaping aircraft;

[0128] Among them, step 2 is specifically as follows:

[0129] Under incomplete information, the pursuing spacecraft cannot know the control input of the escaping spacecraft, so a control gain adaptive estimator is designed;

[0130] First, assume that the escaping spacecraft adopts the optimal control strategy, that is, Among them, K e * is the optimal control strategy of the escaping spacecraft, and satisfies the following equation:

[0131]

[0132] Among them, P e is a positive definite matrix and satisfies the following equation:

[0133]

[0134] Among them, β1 and β3 are preset positive constants and satisfy λ max {P e} represents the matrix P e The maximum eigenvalue of

[0135] The state equation can be written as:

[0136]

[0137] The pursuit state equation estimated by the pursuer can be written as:

[0138]

[0139] Therefore, the following equation can be obtained:

[0140]

[0141] Multiply both sides by (B e T B e ) -1 B e T , we can get

[0142]

[0143] in,

[0144]

[0145] Control gain of the escaping spacecraft The adaptive estimator of is designed as:

[0146]

[0147] Among them, Γ is a positive definite matrix and κ is a positive constant.

[0148] From the above adaptive estimator, we can see that there is a time constant T>0, Gain Estimation Error satisfy:

[0149]

[0150] in,

[0151] Based on the estimated control gain The system state space model can be written as:

[0152]

[0153] in,

[0154] Because the estimation error and relative state error The mutual coupling further increases the difficulty of designing the optimal control strategy for the pursuing spacecraft. To solve this problem, first, assume that the value of the control gain estimator after working for a period of time T is The pursuing spacecraft uses this estimate to design its own control strategy. The state space equation of the game system is:

[0155]

[0156] in,

[0157] Among them, step 3 is specifically: based on the above-mentioned adaptive control gain estimator, the following improved Riccati equation is established:

[0158]

[0159] and

[0160]

[0161] Among them, ρ1=σ1+γ1+1, ρ2=σ2+γ2+1, Here, σ1, σ2, σ3, γ1, γ2 are all positive constants;

[0162] Specifically, step 4 is as follows: Based on the above Riccati equation, the following value iteration algorithm is designed:

[0163] Step 4.1: First choose an initial value And meet And initialize the calculation error threshold ò>0.

[0164] Step 4.2: For iteration number j = 1, 2, 3, ..., iterate the matrix Calculate according to the following equation:

[0165]

[0166] Step 4.3: Calculate the control strategy norm error for two consecutive times If e i,k >ò, then go to step 4.2, otherwise, the calculation ends and the optimal value is output

[0167] Step 4.4: Calculate the optimal control strategy u p,k :

[0168]

[0169] In specific embodiment 1, due to the estimation error in step 2 and relative state error The mutual coupling further increases the difficulty of designing the optimal control strategy for the pursuing space vehicle.

[0170] In order to solve this problem, a specific embodiment 2 is proposed as follows, which mainly improves the state space equation of the game system in step 2. Specific embodiment 2:

[0172] A robust control method for a spacecraft pursuit-escape game under incomplete information based on a non-zero-sum game comprises the following steps:

[0173] Step 1: Based on dynamics, establish a non-zero-sum game control model of spacecraft with uncertainty;

[0174] Step 2: Design a control gain adaptive estimator for the target space vehicle under incomplete information;

[0175] Step 3: Based on the adaptive estimator, the improved Riccati equation for non-zero-sum game control of spacecraft is established;

[0176] Step 4: Based on the improved Riccati equation, design a value iteration algorithm for the space vehicle control strategy;

[0177] Among them, step 1 is specifically divided into the following steps:

[0178] Step 1.1:

[0179] Establish a non-zero-sum game control model for spacecraft:

[0180]

[0181] in, is the vector of the spacecraft's position and velocity; A is the state matrix; B is the coefficient matrix of the control input; u is the control input of the spacecraft. The specific forms of A and B are as follows:

[0182]

[0183] in, a0 is the reference orbit radius, μ is the gravitational constant;

[0184] The specific initial state parameter values ​​are as follows:

[0185] a0=8×10 6 , μ=3.986×10 14 , τ=0.1s, α1=0.1, α2=0.5, α3=0.5, β1=0.1,

[0186] β2=0.1,β3=0.1,Q p =I, R p=I,Q e =I, R e =I, ε=0.01,

[0187]

[0188] Step 1.2:

[0189] Using the Euler discretization method, a discrete control model of the spacecraft is established:

[0190] η k+1 =A d η k +B d u k

[0191] Among them, A d =e Aτ , τ is the sampling period, η k is the value of the spacecraft state at the kth moment, u k Enter the value of the spacecraft at time k. In this example, τ = 0.1;

[0192] Step 1.3:

[0193] Establish discrete control models for spacecraft of the pursuer and the escaper

[0194] η p,k+1 =A d η p,k +B d u p,k

[0195] η e,k+1 =A d η e,k +B d u e,k

[0196] Among them, u p,k and u e,k are the control inputs of the pursuer and the escaper at the kth moment, η p,k and η p,k are the states of the pursuer and the escaper at the kth moment respectively.

[0197] Therefore, the pursuit-escape game control model between two spacecraft is:

[0198]

[0199] in, B p =-B d , B e =Bd .

[0200] Step 1.4:

[0201] Building a discrete control model for spacecraft with uncertainty

[0202]

[0203] in, is the uncertainty term of the spacecraft control system and satisfies the following inequality:

[0204]

[0205] Wherein, Φ is a known positive definite matrix; in this example, Φ=0.01I6, where I6 represents a 6×6 identity matrix;

[0206] In the non-zero-sum game framework, the control cost function of the pursuing spacecraft is set as:

[0207]

[0208] Among them, the matrix Q p ,R p is an adjustable known positive definite constant matrix; in this example, Q p =I6,R p =I3, where I3 represents a 3×3 identity matrix;

[0209] The control cost function of the escaping spacecraft is set as:

[0210]

[0211] Among them, the matrix Q e ,R e is an adjustable known positive definite constant matrix; in this example, Q e =0.1I6,R p =0.2I3;

[0212] Controller p,k ,u e,k The design goal is to minimize the control cost function and Where K p is the control gain of the pursuing aircraft, K e is the control gain of the escaping aircraft;

[0213] Among them, step 2 is specifically as follows:

[0214] Under incomplete information, the pursuing spacecraft cannot know the control input of the escaping spacecraft, so a control gain adaptive estimator is designed;

[0215] First, assume that the escaping spacecraft adopts the optimal control strategy, that is, Among them, K e * is the optimal control strategy of the escaping spacecraft, and satisfies the following equation:

[0216]

[0217] Among them, P e is a positive definite matrix and satisfies the following equation:

[0218]

[0219] Among them, β1 and β3 are preset positive constants and satisfy λ max {P e} represents the matrix P e The maximum eigenvalue of; in this example, β1 = 2, β3 = 3;

[0220] The state equation can be written as:

[0221]

[0222] The estimated pursuit state equation of the spacecraft can be written as:

[0223]

[0224] Therefore, the following equation can be obtained:

[0225]

[0226] Multiply both sides by (B e T B e ) -1 B e T , we can get

[0227]

[0228] in,

[0229]

[0230] Control gain of the escaping spacecraft The adaptive estimator of is designed as:

[0231]

[0232] Where Γ is a positive definite matrix, and κ is a positive constant; in this example, Γ = 2I6, κ = 0.5;

[0233] From the above adaptive estimator, we can see that there is a time constant T>0, Gain Estimation Error satisfy:

[0234]

[0235] in,

[0236] Based on the estimated control gain The system state space model can be written as:

[0237]

[0238] in,

[0239] Because the estimation error and relative state error The mutual coupling further increases the difficulty of designing the optimal control strategy for the pursuing spacecraft. To solve this problem, first, assume that the value of the control gain estimator after working for a period of time T is The pursuing spacecraft uses this estimate to design its own control strategy. The state space equation of the game system is:

[0240]

[0241] in,

[0242] Among them, step 3 is specifically: based on the above-mentioned adaptive control gain estimator, the following improved Riccati equation is established:

[0243]

[0244] and

[0245]

[0246] Among them, ρ1=σ1+γ1+1, ρ2=σ2+γ2+1, Here, σ1, σ2, σ3, γ1, γ2 are all positive constants; in this example, σ1 = 0.01, σ2 = 2, σ3 = 0.1, γ1 = 0.1, γ2 = 3;

[0247] Specifically, step 4 is as follows: Based on the above Riccati equation, the following value iteration algorithm is designed:

[0248] Step 4.1: First choose an initial value And initialize the calculation error threshold ò>0; in this example, ò=0.0001;

[0249] Step 4.2: For iteration number j = 1, 2, 3, ..., iterate the matrix Calculate according to the following equation:

[0250]

[0251] Step 4.3: Calculate the control strategy norm error for two consecutive times If e i,k >ò, then go to step 4.2, otherwise, the calculation ends and the optimal value is output

[0252] Step 4.4: Calculate the optimal control strategy u p,k :

[0253]

[0254] Figure 2 and Figure 3 The simulation results of this example are described respectively. Figure 2 Describes the position error curve between the pursuing spacecraft and the escaping spacecraft. Figure 2 It can be concluded that by using the spacecraft control method of the present application, the spacecraft is successfully transferred to the desired orbital position after a period of time. Figure 3 The velocity error curve between the vehicle and the desired trajectory is described. Through analysis, it is found that the relative velocity error eventually converges to zero.

[0255] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game, comprising the following steps: Step 1: Based on dynamics, establish a non-zero-sum game control model of spacecraft with uncertainty; Step 2: Design a control gain adaptive estimator for the target space vehicle under incomplete information; Step 3: Based on the adaptive estimator, the improved Riccati equation for non-zero-sum game control of spacecraft is established; Step 4: Based on the improved Riccati equation, design a value iteration algorithm for the space vehicle control strategy.

2. According to claim 1, a robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game, characterized in that: Step 1 is specifically divided into the following steps: Step 1.1: Establish a non-zero-sum game control model for spacecraft: in, is the vector of the spacecraft's position and velocity; A is the state matrix; B is the coefficient matrix of the control input; u is the control input of the spacecraft. The specific forms of A and B are as follows: in, a0 is the reference orbit radius, μ is the gravitational constant; Step 1.2: Using the Euler discretization method, a discrete control model of the spacecraft is established: or k+1 =A d or k +B d you k Among them, A d =e Aτ , τ is the sampling period, η k is the value of the spacecraft state at the kth moment, u k Enter the value of the spacecraft at time k; Step 1.3: Establish discrete control models for spacecraft of the pursuer and the escaper or p,k+1 =A d or p,k +B d you p,k or e,k+1 =A d or e,k +B d you e,k Among them, u p,k and u e,k are the control inputs of the pursuer and the escaper at the kth moment, η p,k and η p,k are the states of the pursuer and the escaper at the kth moment respectively; Therefore, the pursuit-escape game control model between two spacecraft is: in, B p =-B d , B e =B d ; Step 1.4: Building a discrete control model for spacecraft with uncertainty in, is the uncertainty term of the spacecraft control system and satisfies the following inequality: Among them, Φ is a known positive definite matrix; In the non-zero-sum game framework, the control cost function of the pursuing spacecraft is set as: Among them, the matrix Q p ,R p is an adjustable known positive definite constant matrix; The control cost function of the escaping aircraft is set as: Among them, the matrix Q e ,R e is an adjustable known positive definite constant matrix; Controller p,k ,u e,k The design goal is to minimize the control cost function and Where K p is the control gain of the pursuing aircraft, K e is the control gain of the escaping aircraft.

3. According to claim 2, a robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game, characterized in that: Step 2 is as follows: Under incomplete information, the pursuing spacecraft cannot know the control input of the escaping spacecraft, so a control gain adaptive estimator is designed; First, assume that the escaping spacecraft adopts the optimal control strategy, that is, Among them, K e * is the optimal control strategy of the escaping spacecraft, and satisfies the following equation: Among them, P e is a positive definite matrix and satisfies the following equation: Among them, β1 and β3 are preset positive constants and satisfy λ max {P e } represents the matrix P e The maximum eigenvalue of The state equation can be written as: The pursuit state equation estimated by the pursuer can be written as: Therefore, the following equation can be obtained: Multiply both sides by (B e T B e ) -1 B e T , we can get in, Control gain of the escaping spacecraft The adaptive estimator of is designed as: Among them, Γ is a positive definite matrix, κ is a positive constant; From the above adaptive estimator, we can see that there is a time constant T>0, Gain Estimation Error satisfy: in, Based on the estimated control gain The system state space model can be written as: in, 4. According to claim 2, a robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game, characterized in that: Step 2 is as follows: Under incomplete information, the pursuing spacecraft cannot know the control input of the escaping spacecraft, so a control gain adaptive estimator is designed; First, assume that the escaping spacecraft adopts the optimal control strategy, that is, The state equation can be written as: The pursuit state equation estimated by the pursuer can be written as: Therefore, the following equation can be obtained: Multiply both sides by (B e T B e ) -1 B e T , we can get in, Control gain of the escaping spacecraft The adaptive estimator of is designed as: Among them, Γ is a positive definite matrix, κ is a positive constant; From the above adaptive estimator, we can see that there is a time constant T>0, Gain Estimation Error satisfy: in, Based on the estimated control gain The system state space model can be written as: First, assume that the value of the control gain estimator after working for a period of time T is The pursuing spacecraft uses this estimate to design its own control strategy. The state space equation of the game system is: in, 5. The robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game according to claim 3 or 4, characterized in that: Step 3 is as follows: Based on the above adaptive control gain estimator, the following improved Riccati equation is established: and Among them, ρ1=σ1+γ1+1, ρ2=σ2+γ2+1, Here, σ1, σ2, σ3, γ1, γ2 are all positive constants.

6. The robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game according to claim 5 is characterized in that: Step 4 is as follows: Based on the above Riccati equation, the following value iteration algorithm is designed: Step 4.1: First choose an initial value And meet And initialize the calculation error threshold Step 4.2: For iteration number j = 1, 2, 3, ..., iterate the matrix Calculate according to the following equation: Step 4.3: Calculate the control strategy norm error for two consecutive times if Go to step 4.2, otherwise, the calculation ends and the optimal value is output Step 4.4: Calculate the optimal control strategy u p,k :

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