A Robust Control Method for Spacecraft Pursuit and Escape Game Theory Based on Incomplete Information in Non-Zero-Sum Game Theory

Abstract

This invention discloses a robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game, mainly comprising the following steps: Step 1: Establishing a non-zero-sum game control model for spacecraft containing uncertainties based on dynamics; Step 2: Designing an adaptive estimator for the control gain of the target spacecraft under incomplete information; Step 3: Establishing an improved Riccati equation for the non-zero-sum game control of spacecraft based on the adaptive estimator; Step 4: Designing a value iteration algorithm for the spacecraft control strategy based on the improved Riccati equation. This control method overcomes the adverse effects of uncertainty in the pursuit and escape game system and solves the problem of unknown cost function and control strategy of the target spacecraft, ensuring the effectiveness and control accuracy of the spacecraft pursuit strategy.

Description

Technical Field

[0001] This invention belongs to the field of intelligent control technology for spacecraft, and particularly relates to a robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game. Background Art

[0002] Spacecraft, as the primary carriers of the future space environment, are of great significance to national space security and development. The pursuit and escape game involving spacecraft has always been a key issue in space warfare and is widely used in space operations, such as space target reconnaissance and non-cooperative target detection.

[0003] When designing spacecraft control strategies, the spacecraft is susceptible to uncertainties such as various external environmental perturbations, which can severely reduce the control accuracy. Therefore, it is necessary to incorporate the impact of these uncertainties into the control performance indicators. However, the unknown nature of these uncertainties increases the design complexity of spacecraft controllers.

[0004] Various control methods have been proposed for the adversarial control problem of spacecraft pursuit and escape, such as discrete-time fault-tolerant zero-sum games and event-triggered nonlinear zero-sum games. However, in real-world adversarial environments, it is difficult for both sides to obtain each other's cost functions and the target spacecraft's control strategy. In this situation, zero-sum games are unsuitable for modeling pursuit and escape games under incomplete information, while non-zero-sum game theory does not require the cost functions of the two sides to be completely opposite, making it more suitable for pursuit and escape game scenarios with incomplete information for spacecraft. Therefore, designing a non-zero-sum game pursuit and escape control method under incomplete information remains a challenge for spacecraft pursuit and escape control. Summary of the Invention

[0005] To address the spacecraft pursuit and escape game control problem under conditions of partially unknown information, this paper proposes a robust control method for spacecraft pursuit and escape game under incomplete information based on non-zero-sum game theory, overcoming the shortcomings of existing technologies and making full use of non-zero-sum game theory.

[0006] To address the aforementioned technical problems, this invention proposes a robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game, comprising the following steps:

[0007] Step 1: Based on dynamics, establish a non-zero-sum game control model for spacecraft that includes uncertainties;

[0008] Step 2: Design an adaptive estimator for the control gain of the target spacecraft under incomplete information;

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

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

[0011] Step 1 specifically consists of the following steps:

[0012] Step 1.1:

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

[0014]

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

[0016]

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

[0018] Step 1.2:

[0019] Using the Euler discretization method, a discrete control model for a 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 Let u be the value of the spacecraft's state at time k. k Input the value for the spacecraft at time k.

[0022] Step 1.3:

[0023] Establish discrete control models for the spacecraft of both the pursuing and escaping forces.

[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 η represents the control inputs at time k for the pursuing and escaping sides, respectively. p,k and η p,k These represent the states of the pursuing and escaping sides at time k, respectively.

[0027] Therefore, the game control model for the pursuit and escape between the two spacecraft is as follows:

[0028]

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

[0030] Step 1.4:

[0031] Establish a discrete control model for a spacecraft that incorporates uncertainties.

[0032]

[0033] in, Let be the uncertainty term in the spacecraft control system, and satisfy the following inequality:

[0034]

[0035] Where Φ is a known positive definite matrix.

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

[0037]

[0038] Where, matrix Q p ,R p It is an adjustable known positive definite constant matrix.

[0039] The control cost function for the escape-space spacecraft is set as follows:

[0040]

[0041] Where, matrix Q e ,R e It is an adjustable known positive definite constant matrix.

[0042] controller u p,k ue,k The design objective is to minimize the control cost function. and Where K p For the control gain of the pursuing aircraft, K e For the control gain of the escaping aircraft;

[0043] Step 2 specifically involves:

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

[0045] First, assume that the escaping spacecraft adopts an optimal control strategy, i.e. Among them, K e * The optimal control strategy for the escape-space spacecraft satisfies the following equation:

[0046]

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

[0048]

[0049] Where β1 and β3 are preset positive constants, and satisfy the following conditions: λ max {P e} represents matrix P e The largest eigenvalue;

[0050] The state equation can be written as:

[0051]

[0052] The 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 You can get

[0057]

[0058] in,

[0059]

[0060] Control gain of escape spacecraft The adaptive estimator is designed as follows:

[0061]

[0062] Where Γ is a positive definite matrix and κ is a positive constant.

[0063] As can be seen from the above adaptive estimator, there exists a time constant T > 0 for... Gain estimation error satisfy:

[0064]

[0065] in,

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

[0067]

[0068] in,

[0069] Because of 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 address this issue, firstly, we assume that the value of the control gain estimator after operating 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] Specifically, step 3 involves establishing the following improved Riccati equation based on the aforementioned adaptive control gain estimator:

[0073]

[0074] and

[0075]

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

[0077] Specifically, step 4 involves designing the following value iteration algorithm based on the Riccati equation described above:

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

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

[0080]

[0081] Step 4.3: Calculate the norm error of the control strategy between two consecutive calculations. If e i,k If the result is greater than or equal to 0, proceed 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 this invention are that it overcomes the adverse effects of uncertainty in the pursuit-escape game system and solves the problem of unknown target spacecraft cost function and control strategy, thus ensuring the effectiveness and control accuracy of the spacecraft pursuit strategy. Attached Figure Description

[0085] Figure 1 This is an overall flowchart of the method of the present invention;

[0086] Figure 2 A graph showing the positional error between the pursuing spacecraft and the escaping spacecraft.

[0087] Figure 3 This is the velocity error curve between the spacecraft and the desired trajectory. Detailed Implementation

[0088] This invention proposes a robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game. The specific implementation of this invention is further illustrated below with reference to the accompanying drawings.

[0089] It should be noted that the embodiments described in this invention are merely some, not all, of the embodiments of this invention. Other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are all within the scope of protection of this invention.

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

[0091] Step 1: Based on dynamics, establish a non-zero-sum game control model for spacecraft that includes uncertainties;

[0092] Step 2: Design an adaptive estimator for the control gain of the target spacecraft under incomplete information;

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

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

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

[0096] Step 1 specifically consists of the following steps:

[0097] Step 1.1:

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

[0099]

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

[0101]

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

[0103] Step 1.2:

[0104] Using the Euler discretization method, a discrete control model for a 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 Let u be the value of the spacecraft's state at time k. k Input the value for the spacecraft at time k.

[0107] Step 1.3:

[0108] Establish discrete control models for the spacecraft of both the pursuing and escaping forces.

[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 η represents the control inputs at time k for the pursuing and escaping sides, respectively. p,k and η p,k These represent the states of the pursuing and escaping sides at time k, respectively.

[0112] Therefore, the game control model for the pursuit and escape between the two spacecraft is as follows:

[0113]

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

[0115] Step 1.4:

[0116] Establish a discrete control model for a spacecraft that incorporates uncertainties.

[0117]

[0118] in, Let be the uncertainty term in the spacecraft control system, and satisfy the following inequality:

[0119]

[0120] Where Φ is a known positive definite matrix.

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

[0122]

[0123] Where, matrix Q p ,R p It is an adjustable known positive definite constant matrix.

[0124] The control cost function for the escape-space spacecraft is set as follows:

[0125]

[0126] Where, matrix Q e ,R e It is an adjustable known positive definite constant matrix.

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

[0128] Step 2 specifically involves:

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

[0130] First, assume that the escaping spacecraft adopts an optimal control strategy, i.e. Among them, K e * The optimal control strategy for the escape-space spacecraft satisfies the following equation:

[0131]

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

[0133]

[0134] Where β1 and β3 are preset positive constants, and satisfy the following conditions: λ max {P e} represents matrix P e The largest eigenvalue;

[0135] The state equation can be written as:

[0136]

[0137] The 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 You can get

[0142]

[0143] in,

[0144]

[0145] Control gain of escape spacecraft The adaptive estimator is designed as follows:

[0146]

[0147] Where Γ is a positive definite matrix and κ is a positive constant.

[0148] As can be seen from the above adaptive estimator, there exists a time constant T > 0 for... Gain estimation error satisfy:

[0149]

[0150] in,

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

[0152]

[0153] in,

[0154] Because of 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 address this issue, firstly, we assume that the value of the control gain estimator after operating 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] Specifically, step 3 involves establishing the following improved Riccati equation based on the aforementioned adaptive control gain estimator:

[0158]

[0159] and

[0160]

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

[0162] Specifically, step 4 involves designing the following value iteration algorithm based on the Riccati equation described above:

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

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

[0165]

[0166] Step 4.3: Calculate the norm error of the control strategy between two consecutive calculations. If e i,k If the result is greater than or equal to 0, proceed 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 spacecraft.

[0170] To address this issue, a specific implementation plan 2 is proposed below, which mainly improves the state-space equation of the game system in step 2. Specific Implementation Example 2:

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

[0173] Step 1: Based on dynamics, establish a non-zero-sum game control model for spacecraft that includes uncertainties;

[0174] Step 2: Design an adaptive estimator for the control gain of the target spacecraft under incomplete information;

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

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

[0177] Step 1 specifically consists of the following steps:

[0178] Step 1.1:

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

[0180]

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

[0182]

[0183] in, a0 is the reference orbital radius, and 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 for a 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 Let u be the value of the spacecraft's state at time k. k Input the value for the spacecraft at time k. In this example, τ = 0.1;

[0192] Step 1.3:

[0193] Establish discrete control models for the spacecraft of both the pursuing and escaping forces.

[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 η represents the control inputs at time k for the pursuing and escaping sides, respectively. p,k and η p,k These represent the states of the pursuing and escaping sides at time k, respectively.

[0197] Therefore, the game control model for the pursuit and escape between the two spacecraft is as follows:

[0198]

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

[0200] Step 1.4:

[0201] Establish a discrete control model for a spacecraft that incorporates uncertainties.

[0202]

[0203] in, Let be the uncertainty term in the spacecraft control system, and satisfy the following inequality:

[0204]

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

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

[0207]

[0208] Where, matrix Q p ,R p A known positive definite constant matrix that can be adjusted; in this example, Q p =I6,R p =I3, where I3 represents a 3×3 identity matrix;

[0209] The control cost function for the escape-space spacecraft is set as follows:

[0210]

[0211] Where, matrix Q e ,R e A known positive definite constant matrix that can be adjusted; in this example, Q e =0.1I6,R p =0.2I3;

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

[0213] Step 2 specifically involves:

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

[0215] First, assume that the escaping spacecraft adopts an optimal control strategy, i.e. Among them, K e * The optimal control strategy for the escape-space spacecraft satisfies the following equation:

[0216]

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

[0218]

[0219] Where β1 and β3 are preset positive constants, and satisfy the following conditions: λ max {P e} represents matrix P e The largest eigenvalue; in this example, β1 = 2, β3 = 3;

[0220] The state equation can be written as:

[0221]

[0222] The state equation for the pursuit estimated by 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 You can get

[0227]

[0228] in,

[0229]

[0230] Control gain of escape spacecraft The adaptive estimator is designed as follows:

[0231]

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

[0233] As can be seen from the above adaptive estimator, there exists a time constant T > 0 for... Gain estimation error satisfy:

[0234]

[0235] in,

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

[0237]

[0238] in,

[0239] Because of 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 address this issue, firstly, we assume that the value of the control gain estimator after operating 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] Specifically, step 3 involves establishing the following improved Riccati equation based on the aforementioned adaptive control gain estimator:

[0243]

[0244] and

[0245]

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

[0247] Specifically, step 4 involves designing the following value iteration algorithm based on the Riccati equation described above:

[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 numbers j = 1, 2, 3..., the iteration matrix... Calculate according to the following equation:

[0250]

[0251] Step 4.3: Calculate the norm error of the control strategy between two consecutive calculations. If e i,k If the result is greater than or equal to 0, proceed 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 for this example are described separately, where Figure 2 The position error curves of the pursuing spacecraft and the escaping spacecraft are described. Figure 2 It can be concluded that, by using the spacecraft control method of this application, the spacecraft successfully transferred to the desired orbital position after a period of time. Figure 3 The velocity error curves of the spacecraft and the desired trajectory are described. Through analysis, it is found that the relative velocity errors eventually converge to zero.

[0255] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are 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 within the protection scope of the present invention.

Claims

1. A robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game, comprising the following steps: Step 1: Based on dynamics, establish a non-zero-sum game control model for spacecraft that includes uncertainties; Step 2: Design an adaptive estimator for the control gain of the target spacecraft under incomplete information; Step 3: Based on the adaptive estimator, establish the improved Riccati equation for the non-zero-sum game control of the spacecraft; Step 4: Based on the improved Riccati equation, design a value iteration algorithm for the spacecraft control strategy; Among them, the characteristic is that, Step 1 consists of the following steps: Step 1.1: Establish a non-zero-sum game control model for spacecraft: in, Let A be a vector relating the spacecraft's position and velocity; let B be the state matrix; let B be the coefficient matrix of the control input; and let u be the control input of the spacecraft. The specific forms of A and B are as follows: in, a0 is the reference orbital radius, and μ is the gravitational constant; Step 1.2: Using the Euler discretization method, a discrete control model for a 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 Let u be the value of the spacecraft's state at time k. k Input the value for the spacecraft at time k; Step 1.3: Establish discrete control models for the spacecraft of both the pursuing and escaping forces. 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 η represents the control inputs at time k for the pursuing and escaping sides, respectively. p,k and η p,k These represent the states of the pursuing and escaping sides at time k, respectively. Therefore, the game control model for the pursuit and escape between the two spacecraft is as follows: in, B p =-B d B e =B d ; Step 1.4: Establish a discrete control model for a spacecraft that incorporates uncertainties. in, Let be the uncertainty term in the spacecraft control system, and satisfy the following inequality: Where Φ is a known and determined positive definite matrix; In a non-zero-sum game framework, the control cost function of the pursuing spacecraft is set as follows: Where, matrix Q p ,R p It is an adjustable known positive definite constant matrix; The control cost function of the escape vehicle is set as follows: Where, matrix Q e ,R e It is an adjustable known positive definite constant matrix; controller u p,k u e,k The design objective is to minimize the control cost function. and Where K p For the control gain of the pursuing aircraft, K e The control gain for the escaping aircraft.

2. The robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game, as described in claim 1, is characterized in that... Step 2 is as follows: Under incomplete information, the pursuing spacecraft cannot know the control input of the escaping spacecraft, so an adaptive control gain estimator is designed. First, assume that the escaping spacecraft adopts an optimal control strategy, i.e. Among them, K e * The optimal control strategy for the escape-space spacecraft satisfies the following equation: Among them, P e It is a positive definite matrix and satisfies the following equation: Where β1 and β3 are preset positive constants, and satisfy the following conditions: λ max {P e } represents matrix P e The largest eigenvalue; The state equation can be written as: The 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 You can get in, Control gain of escape spacecraft The adaptive estimator is designed as follows: Where Γ is a positive definite matrix and κ is a positive constant; As can be seen from the above adaptive estimator, there exists a time constant T > 0 for... Gain estimation error satisfy: in, Based on estimated control gain The system state-space model can be written as: in, 3. The robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game, as described in claim 2, is characterized in that... Step 2 is as follows: Under incomplete information, the pursuing spacecraft cannot know the control input of the escaping spacecraft, so an adaptive control gain estimator is designed. First, assume that the escaping spacecraft adopts an optimal control strategy, i.e. The state equation can be written as: The state equation estimated by the pursuer can be written as: Therefore, the following equation can be obtained: Multiply both sides simultaneously It can be obtained in, Control gain of escape spacecraft The adaptive estimator is designed as follows: Where Γ is a positive definite matrix and κ is a positive constant; As can be seen from the above adaptive estimator, there exists a time constant T > 0 for... Gain estimation error satisfy: in, Based on estimated control gain The system state-space model can be written as follows: First, assume that the value of the control gain estimator after operating 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, 4. A robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game, as described in claim 3, is characterized in that... Step 3 specifically involves: 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, and γ2 are all positive constants.

5. A robust control method for spacecraft pursuit and escape game based on incomplete information in a non-zero-sum game, as described in claim 4, is characterized in that... Step 4 specifically involves: Based on the Riccati equation above, the following value iteration algorithm is designed: Step 4.1: First, choose an initial value. And satisfy And initialize the calculation error threshold. Step 4.2: For iteration numbers j = 1, 2, 3..., the iteration matrix... Calculate according to the following equation: Step 4.3: Calculate the norm error of the control strategy between two consecutive calculations. if Then proceed 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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