A bounded rationality game control method for spacecraft cluster pursuit-evasion under incomplete information

Abstract

The application discloses a kind of finite-rationality game control methods for spacecraft cluster pursuit and evasion under incomplete information, by designing multiple pursuit spacecraft cluster information interaction topology and state tracking error model, relax the complete rationality assumption and build k-level finite-rationality game framework;Design adaptive escapee 1-level strategy estimator, realize the online estimation of unknown control gain;Based on Hamilton function, develop inverse reinforcement learning algorithm, identify the weight matrix of escape spacecraft target function;Adaptive dynamic programming technology is used to solve coupled Hamilton-Jacobi equation, obtain the approximate optimal strategy of each level of finite-rationality game;Estimation error is converted into hierarchical belief probability using Softmax probability mapping, construct multi-model tracking strategy, realize real-time identification of escape spacecraft cognitive level and adaptive switching of tracking strategy;The application can estimate the intention of escape spacecraft online under the condition of incomplete information and identify its rational level, effectively improve the cooperative hunting ability and adaptive control performance of tracking spacecraft cluster.

Description

Technical Field

[0001] This invention relates to the field of multi-spacecraft control technology, specifically to a bounded rational game control method for spacecraft swarm pursuit and escape under incomplete information. Background Technology

[0002] Existing research on spacecraft swarm pursuit-escape game theory largely focuses on solving Nash equilibrium under the assumption of perfect rationality. This assumes that all participants are fully aware of the game structure, the opponent's strategy space, and the payoff function, and can perform infinite-level strategy reasoning. However, in real-world space combat missions, due to limited communication, sensor accuracy constraints, and computational resources, spacecraft often only possess bounded rationality, failing to meet the ideal requirement of perfect rationality. Furthermore, existing control strategies typically assume that the pursuer has complete knowledge of the escaper's objective function weight matrix. However, under conditions of incomplete information, the escaper's true intentions (such as the state weights and control weights in performance indicators) are unknown to the pursuer, making control strategies designed based on the perfect information assumption ineffective in practical applications.

[0003] Meanwhile, while existing bounded rationality game theory methods can partially alleviate the limitations of the perfect rationality assumption, they still fall short in addressing the problem of identifying adversary intentions under incomplete information. Specifically, the objective function weight matrix of an escaping spacecraft is difficult to obtain through direct measurement, and traditional system identification methods are unsuitable for dynamically coupled systems with game-theoretic characteristics. Furthermore, existing solutions for control strategies based on differential game theory typically rely on coupled Hamiltonian-Jacobi equations (HJ equations). These partial differential equations are computationally intensive and suffer from the curse of dimensionality, making them difficult to implement online in real-world spacecraft onboard computing environments. More importantly, existing methods for online identification of the adversary's cognitive level (rational level) often assume prior knowledge of the adversary's strategy. Summary of the Invention

[0004] Purpose of the Invention: The purpose of this invention is to provide a bounded rationality game control method for spacecraft swarm pursuit under incomplete information. This method enables online estimation and hierarchical identification of the objective function weights of the tracking spacecraft swarm for the escaping spacecraft, and generates a multi-model adaptive tracking strategy based on bounded rationality game theory. This ensures that the swarm system can still complete the collaborative pursuit mission under conditions of information asymmetry. It also solves the problems of unknown opponent intentions and limited rationality levels in existing spacecraft swarm pursuit games under incomplete information.

[0005] Technical solution: The present invention provides a bounded rationality game control method for spacecraft swarm pursuit and escape under incomplete information, comprising the following steps:

[0006] (1) Design a multi-tracking mode for spacecraft clusters, construct an information interaction topology diagram of the spacecraft cluster, and establish a state tracking error model in the spacecraft cluster;

[0007] (2) Under the assumption of perfect rationality, the cooperative target tracking problem is modeled as a non-zero-sum differential game between the pursuer and the escaper. The game performance index containing the relative distance coordination term and the input constraint penalty term is designed. The assumption of perfect rationality is relaxed, and a level 0 tracking spacecraft model, a level 0 escape spacecraft model and a level 1 escape spacecraft model are built respectively.

[0008] (3) Design an adaptive escaper level 1 policy estimator to estimate the level 1 control gain of the unknown escape spacecraft based on the state error;

[0009] (4) Using the policy estimation results, an inverse reinforcement learning algorithm is developed based on the Hamiltonian function to identify the intention of the escaping spacecraft and obtain the estimated weight matrix of the objective function of the escaping spacecraft;

[0010] (5) Based on the estimated weight matrix, establish the estimated k-level model of the tracking spacecraft cluster and the escape spacecraft, design a multi-spacecraft finite rationality game solution method, and use adaptive dynamic programming technology to solve the coupled Hamilton-Jacobi equation;

[0011] (6) After identifying the target weight of the opponent, the tracking spacecraft switches to a higher rationality level. Based on the estimated k-level model, the estimated state index set containing all rationality levels of the escaped spacecraft is pre-calculated. By measuring the error between the actual state of the escaped spacecraft and the estimated state at each level online, the error vector is transformed into the level belief probability using Softmax probability mapping. A multi-model tracking strategy is constructed to realize the real-time identification of the cognitive level of the escaped spacecraft and the adaptive switching of the tracking strategy.

[0012] Furthermore, step (1) includes the following steps:

[0013] (1.1) Graph theory is used to describe the information interaction relationship of each spacecraft in the spacecraft cluster, and to construct the information interaction topology graph within the tracking spacecraft cluster and between the tracking spacecraft and the escape spacecraft;

[0014] (1.2) In the local vertical-local horizontal coordinate system, the relative motion of each spacecraft with respect to the virtual spacecraft is described by the Clohessy-Wiltshire equation;

[0015] (1.3) Based on the relative state deviation between each spacecraft, define the tracking error of each tracking spacecraft and the escape error of each escaping spacecraft, and establish the corresponding error dynamics equations.

[0016] Furthermore, step (2) includes the following steps:

[0017] (2.1) The game objectives of each tracking spacecraft and escape spacecraft are described by a linear quadratic performance index; wherein, the performance index includes a penalty term for state tracking error and a penalty term for control energy consumption;

[0018] (2.2) Under the assumption of perfect rationality, a multi-chasing-one non-zero sum differential game model is established, and the control strategies of each spacecraft constitute a Nash equilibrium;

[0019] (2.3) After relaxing the assumption of perfect rationality, the bounded rationality interaction behavior constructed by k-level game theory includes: the 0-level escape spacecraft ignores the existence of the tracking spacecraft, the 0-level tracking spacecraft solves the optimal control problem based on the assumption that the escape spacecraft has no adversarial consciousness, and the 1-level escape spacecraft formulates the optimal escape plan for the 0-level tracking strategy.

[0020] Furthermore, step (3) includes the following steps:

[0021] (3.1) Design an adaptive state observer based on the escape error dynamics, and use the deviation between the observer state and the actual state to drive the online update of the control gain;

[0022] (3.2) Design and estimate the first-level escape strategy and construct the state estimation error dynamics;

[0023] (3.3) Design an adaptive update law to estimate the unknown control gain matrix, and use the interval excitation characteristics of historical data signals to ensure the convergence of weights;

[0024] (3.4) By constructing a calculation expression based on the dynamics of the escape spacecraft itself, an adaptive law reconstruction containing unmeasurable signal terms is achieved, thereby making the strategy estimation error asymptotically stable.

[0025] Furthermore, in step (3.3), a historical data integral term is introduced into the adaptive update law. An information matrix is ​​constructed by integrating the state data within a preset time window. A triggering mechanism based on interval excitation conditions is designed to activate the historical data correction term when the state data first meets the interval excitation conditions. A mapping function is constructed to record the historical moment when the minimum eigenvalue of the information matrix reaches its maximum value. The historical data at that moment is used to correct the adaptive update law. By constructing a computable expression based on the dynamics of the escape spacecraft, the unmeasurable term containing the product of unknown control gain and historical data is transformed into an explicit expression that only depends on measurable state quantities, thus realizing the complete computability of the adaptive update law.

[0026] Furthermore, step (4) includes the following steps:

[0027] (4.1) Establish the Hamiltonian function and the corresponding Hamilton-Jacobi equation for a first-stage escape spacecraft;

[0028] (4.2) A single-layer neural network is used to approximate the value function, the state quadratic cost term, and the control cost term respectively, and the corresponding basis function vectors are designed;

[0029] (4.3) Construct an approximate inverse Bellman error and a computable control residual. Combine the control residual and the inverse Bellman error into a unified matrix equation through a parameterization method. Design an adaptive update law for the weight vector and use a concurrent learning method to enhance the learning process using historical data.

[0030] (4.4) Construct a dynamic historical queue management strategy, and gradually increase the feature values ​​of the information matrix by selectively replacing data points to ensure the rapid convergence and high asymptotic accuracy of inverse reinforcement learning weight estimation;

[0031] (4.5) Calculate the estimated weight matrix of the objective function of the escape spacecraft based on convergent weight estimation.

[0032] Further, step (4.4) of constructing the dynamic historical queue management strategy is as follows: obtain the current state data and strategy estimate as candidate data points; determine whether the historical queue storage space is full; if not full, calculate the minimum eigenvalue of the batch error matrix corresponding to the historical queue after adding candidate data points, and when the minimum eigenvalue is greater than the historical record threshold, store the candidate data points in the historical queue and update the threshold; if full, compare the current state estimate error with the historical record error, and when the current error is smaller and the minimum eigenvalue is greater than the threshold, replace the earliest stored data point in the historical queue with the candidate data point; perform batch least squares update of the inverse reinforcement learning weight vector according to the updated historical queue.

[0033] Furthermore, step (5) is as follows:

[0034] (5.1) Based on the estimated weight matrix, establish an estimated k-level model for the tracking spacecraft cluster and the escaping spacecraft;

[0035] (5.2) Design a recursive solution method for the finite rationality game of multiple spacecraft. The specific process is as follows: For the k-level tracking spacecraft, solve the optimal tracking problem based on the k-1 level escape strategy; for the k+1 level escape spacecraft, solve the optimal escape problem based on the k-level tracking strategy; define the Hamiltonian function and the corresponding Hamilton-Jacobi equation for each level of spacecraft, and derive the optimal strategy for each level through the extreme value conditions;

[0036] (5.3) Adaptive dynamic programming technique is used to solve the coupled Hamilton-Jacobi equation, and an evaluation neural network is constructed to approximate the objective functions of each party;

[0037] (5.4) Design the adaptive update rate of the weights of the neural network to realize the online approximation of the pursuit strategy and escape strategy at each level, and ensure that the tracking error and the escape error are consistent and eventually bounded.

[0038] Furthermore, step (6) includes the following steps:

[0039] (6.1) After the tracking spacecraft switches to a higher rationality level, the estimated state index set containing all possible rationality levels of the escaped spacecraft is pre-calculated based on the estimated k-level model;

[0040] (6.2) Within a preset time interval, calculate the cumulative error difference between the actual escape error and the estimated escape error at each level, and construct an error vector;

[0041] (6.3) The error vector is mapped to a hierarchical belief probability distribution using the Softmax function, and the temperature parameter controls the smoothness of the probability distribution;

[0042] (6.4) Construct a multi-model escape strategy by weighting the escape strategies at each level according to the belief probability, and design a multi-model tracking strategy to enable the tracking spacecraft cluster to optimize the hybrid model of all possible low-level strategies of the opponent, so as to realize the real-time identification of the cognitive level of the escape spacecraft and the adaptive switching of the tracking strategy.

[0043] Furthermore, the rationality level of the tracking spacecraft is a set of even-numbered levels, including levels 0, 2, 4 up to the maximum rationality level; the rationality level of the escaping spacecraft is a set of odd-numbered levels, including levels 1, 3 up to the maximum rationality level minus one; the tracking spacecraft determines the current rationality level of the escaping spacecraft in real time through the Softmax probability distribution, and simultaneously adapts to different levels of escape strategies based on a multi-model strategy, completing the collaborative pursuit mission under conditions of information asymmetry.

[0044] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: By constructing a bounded rationality game framework, this invention overcomes the limitations of the perfect rationality assumption and effectively describes the interactive behavior of spacecraft swarms under incomplete information; through an adaptive policy estimator and inverse reinforcement learning algorithm, it achieves online estimation of the objective function weights of escaping spacecraft, solving the problem of unknown adversary intentions; based on adaptive dynamic programming technology to solve the coupled HJ equations, it avoids the computational difficulties of directly solving complex partial differential equations; through Softmax probability mapping and multi-model tracking strategies, it achieves real-time identification and policy switching of the rationality level of escaping spacecraft, enabling not only the adaptive capability of tracking spacecraft swarms in asymmetric information environments but also collaborative pursuit. Attached Figure Description

[0045] Figure 1 This is a flowchart of the present invention;

[0046] Figure 2 This is an LVLH coordinate system diagram of the present invention;

[0047] Figure 3 This is a graph showing the change in escape error estimation error under the bounded rationality multi-chase-one-escape game method of the present invention;

[0048] Figure 4 This is a graph showing the variation of the first-stage control gain error of an escape spacecraft under the bounded rational multi-pursuit-one-escape game method of the present invention.

[0049] Figure 5 This is a graph showing the weight changes in inverse reinforcement learning under the bounded rationality multi-chase-one-escape game method of this invention.

[0050] Figure 6 This is a graph showing the Softmax probability variation under the bounded rationality multi-chase-one-escape game method of this invention;

[0051] Figure 7 This is a trajectory diagram of a spacecraft swarm chasing and escaping under the bounded rational multi-chase-one-escape game method of the present invention;

[0052] Figure 8 This is a graph showing the variation of spacecraft cluster tracking error under the bounded rational multi-chase-one-escape game method of the present invention. Detailed Implementation

[0054] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0055] like Figure 1 As shown, a bounded rationality game-theoretic control method for spacecraft swarm pursuit and escape under incomplete information includes the following steps:

[0056] Step 1: Design a multi-tracking-one mode for spacecraft clusters, construct an information interaction topology diagram of the spacecraft cluster, and establish a state tracking error model within the spacecraft cluster. Construct a system with... A cluster consisting of a tracking spacecraft and an escape spacecraft.

[0057] Graph theory is used to describe the information interaction between each spacecraft in the cluster, thus obtaining the information interaction topology graph of the entire multi-tracking-one spacecraft cluster; wherein, the information interaction topology graph within the tracking spacecraft cluster is defined as: Vertex set Represents tracking spacecraft nodes, edge sets This indicates tracking information exchange between spacecraft; from nodes To the node The edge is defined as: , This indicates that tracking spacecraft i can receive information from tracking spacecraft j; if Then the weight ;otherwise, The in-degree matrix is ​​defined as a diagonal matrix. ,in ; The neighborhood set is defined as: In addition, by adding nodes Represent the escaped spacecraft and construct an extended directed graph. This represents the information interaction topology graph within a multi-track spacecraft cluster, with a vertex set. This indicates information exchange between multiple spacecraft; from the node To the node The edge is defined as: , This indicates that the escaping spacecraft can access information about the tracking spacecraft i; if Then the weight ;otherwise, Similarly, from the node To the node The edge is defined as: ;like ,but ;otherwise, The entry degree of an escaped spacecraft is defined as... The neighbor set is defined as .

[0058] To describe the pursuit-escape game process, a Local-Vertical Local-Horizontal (LVLH) coordinate system is established for the multi-spacecraft system. Its origin O is located at the center of mass of the virtual spacecraft, and its directions are defined by unit vectors OX, OY, and OZ, as follows: Figure 1 As shown.

[0059] In the LVLH coordinate system, the first Tracking spacecraft ( and escape spacecraft The state of the virtual spacecraft is represented as a six-dimensional vector. , Spacecraft The relative motion in this coordinate system is described by the Clohessy-Wiltshire (CW) equations:

[0060]

[0061] in, spacecraft Relative acceleration in the OX, OY, and OZ directions. The angular velocity of a virtual spacecraft orbiting the Earth; , and These are the control forces acting on spacecraft s from the X, Y, and Z directions, respectively. Let be the mass of the spacecraft . Define the control input vector. Then the dynamic equation in the CW equation can be written as:

[0062] Where: matrix and The system matrix is ​​specifically represented as follows:

[0063] .

[0064] In a pursuit-escape game, the goal of a swarm of tracking spacecraft is to track the escaping spacecraft while simultaneously moving closer together to achieve coordinated tracking. Therefore, considering coordination, , The tracking error is defined as:

[0065]

[0066] use It can be easily derived The dynamic is as follows:

[0067]

[0068] In the formula: .

[0069] On the other hand, the escape spacecraft distances itself from the attack of the swarm of tracking spacecraft. Therefore, the escape spacecraft... The escape error is:

[0070]

[0071] escape spacecraft The dynamic is as follows:

[0072]

[0073] In the formula: .

[0074] Step 2: Under the assumption of perfect rationality, model the cooperative target tracking problem as a non-zero-sum differential game between the pursuer and the escaper, and design a game performance index that includes a relative distance coordination term and an input constraint penalty term. Relaxing the assumption of perfect rationality, build a level 0 tracking spacecraft model, a level 0 escape spacecraft model, and a level 1 escape spacecraft model respectively.

[0075] Based on optimal control theory, a linear quadratic performance index can be used to describe the target of each pursuer. Therefore, each tracking spacecraft... , The performance index function is:

[0076]

[0077] In the formula: It is a symmetric positive definite matrix. Weight constants. Used to adjust the intensity of the penalty. To track the control energy consumption weight matrix of a spacecraft, Input weighting coefficients to track spacecraft velocity; 3 A 3-dimensional identity matrix.

[0078] On the other hand, escape spacecraft It strives to maximize its distance from neighboring tracking spacecraft. (Escape spacecraft) The performance index function is:

[0079]

[0080] In the formula: Weighting constant Used to adjust the intensity of penalties; It is a symmetric positive definite matrix. For the control energy consumption weight matrix of the escape spacecraft, Input weighting coefficients for the escape spacecraft velocity.

[0081] Note that a spacecraft's performance metrics depend not only on its own behavior but also on the behavior of its neighbors. Indicates except The set of strategies for tracking all external spacecraft. Indicates except The set of strategies for all spacecraft outside the region. Therefore, their dependence on neighbor strategies can be explicitly represented, i.e., for tracking spacecraft, there is... For escape spacecraft .

[0082] An infinitely rational spacecraft is one that is aware of the existence of the game and understands the structure of the decision-making mechanism. Therefore, a perfectly rational multi-pursuit game is:

[0083]

[0084]

[0085] In the formula: and These are tracking spacecraft , and escape spacecraft The game value.

[0086] Control strategy and A Nash equilibrium is formed, satisfying the following inequality

[0087]

[0088]

[0089] The agreement applies to all spacecraft in the game.

[0090] In Nash equilibrium, each spacecraft uses its own optimal policy in relation to the optimal policies of its neighbors. The perfectly rational process by which players evaluate their rewards based on all combinations of competing policies is not a good model for human decision-making. Therefore, this invention breaks through the assumption of perfect rationality and employs k-level game theory to construct the interaction behavior of multiple tracking spacecraft and one escape spacecraft with bounded rationality.

[0091] A level 0 escape spacecraft will ignore the existence of the tracking spacecraft, that is... The strategy for tracking spacecraft at level 0 is based on the assumption that "the escaping spacecraft has no adversarial awareness," and the following optimal control problem is solved:

[0092]

[0093] The corresponding constraints are: In the formula: .

[0094] The optimal control input for tracking the spacecraft at level 0 is:

[0095]

[0096] In the formula: the value function is taken as a quadratic form of the state. nuclear matrix Satisfies the following Riccati equation: In the formula: .

[0097] Subsequently, when the tracking spacecraft determines that the escaping spacecraft is unable to perform evasive maneuvers, the Level 1 escaping spacecraft formulates an optimal escape plan for this situation. Therefore, this level solves the following optimal control problem from the perspective of the escaping spacecraft:

[0098]

[0099] The corresponding constraints are:

[0100]

[0101] The corresponding strategy for the escape spacecraft at level 1 can be designed as follows:

[0102]

[0103] At the start of a practical bounded rationality adversarial mission, the incomplete information tracking spacecraft swarm adopts a Level 0 strategy, while the complete information escape spacecraft adopts a Level 1 strategy. By constructing Level 0 tracking spacecraft models, Level 0 escape spacecraft models, and Level 1 escape spacecraft models, a foundation can be provided for the control gain estimation in step 2 and the inverse reinforcement learning in step 3.

[0104] Step 3: Design an adaptive escaper level 1 policy estimator based on state error. Estimate the first-level control gain of the unknown escape spacecraft.

[0105] Design an adaptive observer for the first-order dynamic error of the escapee. The convergence of the weights of the adaptive policy estimator depends on the excitation characteristics of the historical data signal.

[0106] The dynamic error in this task scenario is:

[0107]

[0108] To estimate the gain matrix Based on this dynamic error, an observer is designed:

[0109]

[0110] In the formula: yes The estimate, It makes A stable gain matrix is ​​one that is a symmetric positive definite matrix. Satisfying the equation , where given and .

[0111] Estimated escape spacecraft level 1 strategy It is given by the following formula:

[0112]

[0113] In the formula: yes The estimate.

[0114] Next, we define the state estimation error. The dynamics are obtained by subtracting the observer dynamics from the dynamics error in this task scenario:

[0115]

[0116] In the formula: This is the policy estimation error. Subsequently, for... The following adaptive update law is proposed:

[0117]

[0118] Where: constant Learning gain The specific adjustments should be made during simulation based on experimental conditions. Using historical data, it is defined as:

[0119]

[0120]

[0121] In the formula: It is the integration interval. yes The time when the interval incentive condition is first met. The mapping function is defined as follows:

[0122]

[0123]

[0124] To ensure the convergence of weight estimation errors, the data signals in the historical queue must satisfy the interval excitation condition: a fixed time window starting at any given time. Within the time window, the minimum eigenvalue of the outer product integral matrix of the data signal is greater than zero, meaning that the data signal maintains sufficient amplitude and frequency of change to ensure that the amount of information required for weight estimation is sufficient.

[0125] Term in the Renewal Law (28) Includes unmeasurable signals To ensure its feasibility, it must be expressed using measurable signals. The challenge lies in... Includes unknown gain matrix and historical data matrix The product. The product is constructed by utilizing the dynamics of the escaped spacecraft itself. The computable expression is derived by separating the unknowns from the dynamic equations of the escaped spacecraft. This is achieved, and thus we obtain:

[0126]

[0127] because It is in full order. Reversible, therefore,

[0128]

[0129] Next, multiply both sides of the above equation by... and from arrive Integrating, we get:

[0130]

[0131] use This computable expression, the adaptive update law, is restated as follows:

[0132]

[0133] Under the dynamic error in this task scenario, if the first-order policy gain matrix... Using an adaptive update law can guarantee the estimation error. and Gradual stabilization.

[0134] Under the action of this adaptive update law, the state estimation bias and policy gain estimation bias can be asymptotically stabilized, ensuring the effectiveness of the inverse reinforcement learning introduced in step three.

[0135] Step 4: Using the policy estimation from Step 2, develop an IRL algorithm based on the Hamiltonian function to identify the escape spacecraft's intent and obtain the estimated weight matrix of the escape spacecraft's objective function.

[0136] The Hamiltonian function for a level 1 escape spacecraft is:

[0137]

[0138] Value function Satisfy the following HJ equation:

[0139]

[0140] To facilitate matrix estimation and Value function and secondary cost items and Approximation using a single-layer neural network:

[0141]

[0142]

[0143]

[0144] Where: vector and This represents the ideal weight. Specifically, By symmetric matrix Elemental composition:

[0145] The corresponding basis functions and It is a known characteristic that is continuously differentiable and has a locally continuous Lipschitz gradient. Basis function vectors Defined as:

[0146] The approximation error is caused by and This is represented by the choice of basis functions such that the original functions and their respective derivatives lie in a compact set. It is uniformly bounded. Therefore, for any given positive constant, it is bounded. ,exist , making , , and .

[0147] Unknown ideal weight , and Estimated separately by online , and Approximation. Furthermore, the value function... The satisfied HJ equations are unrealizable in practice because they rely on a Level 1 strategy trained on an unknown escape spacecraft in a swarm of pursuing spacecraft. To construct a computable error metric, the unknown signal is replaced by its corresponding estimate, i.e., the estimation strategy of the escaping spacecraft. .

[0148] Substituting this estimate into the HJ equation yields the approximate inverse Bellman error (IBE).

[0149]

[0150] In the formula:

[0151] The difference between the ideal HJ solution and the IBE results in an approximation error, which is bounded. To ensure that the estimated weights satisfy the optimality condition, the optimality condition needs to be incorporated in addition to the approximate IBE.

[0152] The optimality condition derived from the HJ equation is The ideal term Replace with its online estimate This yields a calculable control residual. And an approximation error :

[0153]

[0154]

[0155] In the formula:

[0156] In order to optimize the residual with IBE Combine, item Using weight vectors Parameterization is performed by constructing a state dependency matrix. To achieve this parameterization, .matrix It is given by the following formula:

[0157]

[0158] In the formula: It is A row vector of dimension, whose dimensional row vector is the first row vector of dimension. One element is 1, and all other elements are 0.

[0159] Will Substitution The final parameterized control residuals are obtained:

[0160]

[0161] Due to control residuals and approximate IBE All about weight It is linear, and these two expressions are combined into a single matrix equation to facilitate the estimation process.

[0162] The optimal trajectory remains invariant under positive scaling of the objective function, meaning that the IRL can only determine the weight parameters to a scaling factor. Therefore, to obtain a unique solution without loss of generality, a weight is determined by anchoring it to a predefined constant. The last element corresponds to , is fixed to achieve this normalization.

[0163] In order to incorporate specific weights ,from and Extracting contents The terms yield a combined equation:

[0164]

[0165] Where: weight Combinatorial basis function matrix and predefined vectors They are defined as follows:

[0166]

[0167]

[0168] In the formula: .

[0169] Based on the error expression Weight vector The update law design is In the formula: The update law requires the matrix to be updated. The requirement of satisfying continuous incentives for convergence is difficult to meet. To relax this condition, a concurrent learning method is employed, which utilizes historical data to enhance the learning process. Specifically, a historical queue is maintained. Each data point Use this queue The data in will The equation in the equation is expanded into a batch error equation:

[0170]

[0171] In the formula: They are:

[0172]

[0173] First, the HJ equation is reconstructed as follows: The structure of the medium batch error is then considered, followed by the function approximation error. The following expression for the batch error equation is obtained:

[0174]

[0175] In the formula: Term This is the weight estimation error; the ideal weight vector is defined as follows: Residual term Not dependent on Due to approximation error composition.

[0176] Since the dynamic error in this scenario is linear, the term It is Lipschitz continuous. Furthermore, due to the basis functions... Its gradient is locally Lipschitz continuous, and since the approximation error is bounded, the residual term... It is also bounded. Specifically, its norm is:

[0177]

[0178] After establishing the batch error equation, the weight vector is given below. The adaptive update law.

[0179] Weight vector Updated using the following adaptive law:

[0180]

[0181] Where: 0.025 It is an adaptive gain, a preset fixed constant that is adjusted during simulation based on experimental conditions. (Matrix) It is a time-varying least squares gain, updated according to the following formula:

[0182]

[0183] Where: 0.00005 It is the forgetting factor, which is a preset fixed constant that is adjusted according to the experimental conditions during simulation.

[0184] According to the adaptive law Weighting error The update rate is:

[0185]

[0186] The convergence speed of weight estimation depends critically on the matrix composed of historical data. The minimum eigenvalue. To accelerate convergence and improve the final estimation accuracy, a dynamic historical queue management strategy is implemented through a historical queue update method based on observation data. This method selectively replaces data points to gradually increase the matrix. The eigenvalues ​​of the data are used to improve data quality. Initially, to address the potential rank deficiency problem, the primary data admission condition was to maximize... This continues until a full-rank matrix is ​​formed. Subsequently, when the policy estimator's estimation error converges in step 2, the admission criterion is modified to prioritize new data associated with smaller estimation errors. These two phased approaches reduce residual terms. The magnitude of the value ensures fast convergence and high asymptotic accuracy of the weight estimation.

[0187] Based on the output of the adaptive policy estimator, a historical queue update step is performed, which includes:

[0188] S1: Obtain the current escape error, the estimated level 0 strategy of the tracking spacecraft, and the estimated level 1 strategy of the escaping spacecraft as candidate data points;

[0189] S2: Determine whether the storage space of the historical queue is full;

[0190] S3: If not full, calculate the minimum eigenvalue of the batch error matrix corresponding to the historical queue after adding the candidate data point. When the minimum eigenvalue is greater than the historical record threshold, store the candidate data point in the historical queue and update the threshold.

[0191] S4: If the current state is full, compare the current state estimation error with the historical record error. When the current error is smaller and the minimum feature value is greater than the threshold, replace the earliest stored data point in the historical queue with the candidate data point.

[0192] S5: Based on the updated historical queue, perform batch least squares update of the inverse reinforcement learning weight vector.

[0193] To ensure the accuracy of the inverse reinforcement learning algorithm's estimation of the escaped spacecraft's intention weights... For convergence, the data in the historical queue must satisfy the information sufficiency condition. Specifically, in the sampling time sequence... The batch error matrix is ​​part of the historical data set. The minimum feature value must be greater than a preset threshold. This condition ensures that the historical data has sufficient persistent excitation, allowing the weight estimation error to converge to a bounded neighborhood and preventing weight estimation divergence due to insufficient data information. In practical engineering implementation, the minimum feature value is gradually increased through the dynamic historical queue management strategy until the preset threshold is met.

[0194] Based on the data in the historical queue that meets the information sufficiency condition, the weight vector of the escape spacecraft's objective function is trained online using the batch least squares weight update law. Since the minimum eigenvalue of the historical data matrix is ​​greater than a preset threshold, the weight estimation error... Ultimately, the convergence converges to a finite neighborhood. This convergence property ensures that the Level 0 tracking spacecraft can stably estimate the objective function weight matrix of the escape spacecraft even when the intention of the Level 1 escape spacecraft is unknown. The estimated weight matrix can be calculated using specific basis functions. and This leads to the generation of effective, higher-level bounded rationality pursuit strategies.

[0195] Step 5: Based on the estimated weight matrix, establish an estimated k-level model for the tracking spacecraft cluster and the escaping spacecraft, design a multi-spacecraft finite rationality game solution method, and use adaptive dynamic programming technology to solve the coupled HJ equations.

[0196] Level 1: Solve the following optimal control problem from the perspective of an escaping spacecraft:

[0197]

[0198] The corresponding constraints are:

[0199]

[0200] The corresponding strategy for the escape spacecraft at level 1 can be designed as follows:

[0201]

[0202] The following HJ equation is satisfied:

[0203]

[0204] In the In a round-robin strategy game, each tracking spacecraft The optimal strategy needs to be determined by solving the following minimization problem:

[0205]

[0206] In the formula: The corresponding constraints are:

[0207]

[0208] It can be defined as:

[0209]

[0210] The corresponding Hamiltonian function is defined as follows:

[0211]

[0212]

[0213] Value function Satisfy the following HJ equation:

[0214]

[0215] By using extreme conditions The strategy for tracking the spacecraft at level k is as follows:

[0216]

[0217] escape spacecraft The hierarchical strategy input for tracking spacecraft is Solve the following optimal control problem in the hierarchical case:

[0218]

[0219] The corresponding constraints are:

[0220]

[0221] The corresponding Hamiltonian function is defined as follows:

[0222]

[0223]

[0224] Value function Satisfy the following HJ equation:

[0225]

[0226] By using extreme conditions escape spacecraft The corresponding strategies for each level can be obtained as follows:

[0227]

[0228] Since the above HJ equations are all coupled partial differential equations, we will use adaptive dynamic programming to solve this set of equations.

[0229] For each Class Tracking Spacecraft ,as well as Level escape spacecraft Construct separate evaluation neural networks to approximate the objective functions of each party:

[0230]

[0231]

[0232] In the formula: and It is used to evaluate the unknown weights of a neural network. and It is the number of neurons in the hidden layer of the neural network. and It is an activation function. and It is the approximation error. By constructing the gradient rate of change of the objective function, we can obtain...

[0233]

[0234]

[0235] In the formula: , , , .

[0236] To ensure the stable convergence of the learning process of the evaluation neural network, the following constraints are imposed on the approximation error and ideal weights of the neural network: the approximation error of the evaluation neural network to the objective function and , and its derivative and Both are bounded, meaning they satisfy: , In the formula: The known positive constants; the ideal weights of the evaluation neural network. and Bounded, meaning satisfying: In the formula: and It is a known positive constant.

[0237] Due to ideal neural network weights and The following estimates the weights of the neural network, and then reconstructs each... Class Tracking Spacecraft The objective function is:

[0238]

[0239]

[0240] In the formula: and These are the estimated neural network weights.

[0241] An approximation can be obtained. Pursuit strategy and The strategy is

[0242]

[0243]

[0244] Construct an approximate Hamiltonian function as follows:

[0245]

[0246]

[0247] In the formula: and This represents the approximation error of the Hamiltonian function.

[0248] To estimate neural network weights and The adaptive weight update rate of the neural network is given below. The weight update rate of the neural network is:

[0249]

[0250]

[0251] In the formula: and It is the learning rate of the neural network.

[0252] So, how do we evaluate the weight error of a neural network? and Consistent is ultimately bounded, and for shelf Class Tracking Spacecraft In a confrontational scenario, and Consistency is ultimately bounded.

[0253] Step 6: After identifying the target weight of the adversary, the tracking spacecraft switches to stage 2, based on the estimated... The model pre-calculates an estimated state index set containing all rational levels of the escaped spacecraft. By measuring the error between the actual state of the escaped spacecraft and the estimated state at each level online, the error vector is transformed into hierarchical belief probabilities using Softmax probability mapping. A multi-model tracking strategy is then constructed to achieve real-time identification of the cognitive levels of the escaped spacecraft and switching of tracking strategies.

[0254] The tracking spacecraft has a maximum level of rationality of , , it will be Hierarchical escape drones based on The level model pre-computes a model containing all A set of indexes for rational levels.

[0255] Specifically The tracking spacecraft will now track the error. and escape error Substitute The level model calculates and And based on the Level 0 strategy currently used to track spacecraft. Pre-calculate all corresponding values ​​within a certain time interval. Estimated escape error under hierarchical escape strategy .

[0256] In time interval Within, the true escape error at the current moment ,and Estimated escape error for hierarchical escape spacecraft The error between them is defined as:

[0257]

[0258] Each error element Stacked into the following vector:

[0259]

[0260] The following softmax function will convert the error vector This is mapped to a reinforcement signal that rewards elements in the vector that are closer to the true level, i.e., reinforces the smallest element, thereby obtaining the time period. Internal escape spacecraft adopts Hierarchical strategy probability for:

[0261]

[0262] In the formula: For the softmax temperature parameter, 0 This is a pre-set positive constant, which is adjusted according to the experimental conditions during simulation. This parameter controls the concentration of the Softmax output, i.e. The smaller, the smallest hierarchy probability The larger.

[0263] Next, the tracking spacecraft will develop a multi-model tracking strategy, optimizing a hybrid model of all possible low-level strategies of the adversary, so that the tracking spacecraft cluster can more robustly cope with adversaries with different levels of cognition.

[0264] Calculate the escape spacecraft's usage Hierarchical strategy probability Subsequently, the tracking spacecraft determined that the adversary's multi-model escape strategy was:

[0265]

[0266] Each tracking spacecraft The multi-model tracking strategy needs to be formulated by solving the following minimization problem:

[0267]

[0268] The corresponding constraints are: .

[0269] The corresponding Hamiltonian function is defined as follows:

[0270]

[0271] Value function Satisfy the following HJ equation:

[0272]

[0273] By using extreme conditions Tracking spacecraft The multi-model tracking strategy yields:

[0274]

[0275] The adaptive dynamic programming technique in step 5 can yield an approximate multi-model pursuit strategy as follows:

[0276]

[0277] So, for shelf Class Tracking Spacecraft In a confrontational scenario, and Consistency is ultimately bounded.

[0278] The present invention can calculate and obtain a bounded rational game controller for all tracking spacecraft in the cluster under incomplete information, thereby realizing the bounded rational tracking control of all tracking spacecraft on escaped spacecraft with complete information under incomplete information.

[0279] This implementation uses a cluster consisting of three tracking spacecraft with incomplete information and a maximum rationality level of 4, and one escape spacecraft with complete information and a maximum rationality level of 3, to verify the effectiveness of the proposed bounded rationality game control method. , Cluster point set The diagram formed It is fully connected.

[0280] First, the physical parameters and initial states of the tracking and escaping spacecraft are set. A simulation experiment of a bounded rationality spacecraft pursuit / escape mission is then conducted based on the following physical parameters: kg; 300kg; assuming the virtual spacecraft's orbital radius is 42241 km and its orbital period is 24 h, then it can be calculated that... rad / s.

[0281] The initial states of the three tracking spacecraft and one escape spacecraft are set as follows:

[0282]

[0283]

[0284]

[0285]

[0286] Then, set the weight matrix in the performance metrics, for the first... A tracking spacecraft, The weight matrix is ​​designed as follows:

[0287]

[0288]

[0289] Based on the parameters set above, the simulation experiment will begin.

[0290] To demonstrate the correlation between the changes in simulation results and incomplete information and bounded rationality game strategies, the simulation process is divided into two stages based on the convergence time of the estimated escape spacecraft objective function weight matrix: the first stage is the simulation of a multi-spacecraft cluster chasing after intent recognition; the second stage is the simulation of a multi-spacecraft cluster chasing after intent recognition.

[0291] The first phase of the simulation experiment is as follows: Before intent recognition, since the tracking spacecraft does not know the objective function weight matrix of the escape spacecraft, the incomplete information tracking spacecraft cluster adopts a level 0 strategy and the complete information escape spacecraft adopts a level 1 strategy at the start of the actual bounded rationality adversarial mission.

[0292] To ensure Satisfying the Hurwitz condition, assuming The initial estimate of the first-level control gain matrix of the tracking spacecraft for the escaping spacecraft is set as follows: And select the relevant parameters as follows: .

[0293] To ensure that the interval excitation condition is met, it is necessary to perform [the necessary actions] within a finite time interval. Apply an excitation signal, i.e.

[0294]

[0295] In the formula, ,

[0296] Under the influence of interval excitation, the tracking spacecraft can utilize escape error. Online estimation of the first-level control gain matrix of the escape spacecraft, and the escape error estimation error as follows: Figure 3As shown, the performance of the adaptive policy estimator is as follows: Figure 4 As shown in the figure, the state estimation error can be seen from the graph. It converged to 0 at 45 seconds. The estimation error also converged to zero.

[0297] The implementation parameters of the inverse reinforcement learning algorithm are: , , , And historical queue The maximum length is set to 50. Initial weight vector. The initial gain matrix is The basis functions are chosen as a quadratic combination of escape errors, i.e.

[0298] ,

[0299]

[0300]

[0301]

[0302] Inverse reinforcement learning algorithm Activation occurs at a specific time because the state estimation error has converged by this point, making the data used by the inverse reinforcement learning algorithm more accurate. For example... Figure 5 As shown, the estimated weights and The convergence towards the preset value is accompanied by a steady-state error. This is as expected, since the performance of inverse reinforcement learning is ultimately limited by bounded error. The inverse reinforcement learning weights converge at 65s, based on the basis function. and and inverse reinforcement learning weights The settings allow for the calculation of:

[0303]

[0304]

[0305] Simulation results show that, through the designed policy estimation and inverse reinforcement learning algorithm, the tracking spacecraft can achieve a bounded estimate of the objective function weights of the escaping spacecraft.

[0306] The second phase of the simulation experiment involves training the system using adaptive dynamic programming techniques after intent recognition. The system employs a multi-level estimation model to pre-calculate an estimated state index set containing all rational levels of the escaped spacecraft. By measuring the error between the actual state of the escaped spacecraft and the estimated state at each level online, the error vector is transformed into hierarchical belief probabilities using Softmax probability mapping. This enables the construction of a multi-model tracking strategy for subsequent tracking tasks.

[0307] exist At 65s, according to and Each tracking spacecraft is trained using adaptive dynamic programming techniques. Level 2 estimation model. At this point, the tracking spacecraft cluster switches to a Level 2 tracking strategy, and the escaping spacecraft switches to a Level 3 escape strategy.

[0308] Figure 6 Demonstrates interaction with opponents After collecting sufficient data, the Softmax temperature parameter When, Softmax probability The distribution of these states is as follows. It can be observed that the tracking spacecraft believes the escaping spacecraft has the following probabilistic belief states: 17.90% for Level 1 and 82.10% for Level 3. Therefore, the tracking spacecraft can utilize a multi-model strategy to simultaneously adapt to the escaping spacecraft's strategy level and take corresponding countermeasures.

[0309] The basis function vectors are selected as follows:

[0310]

[0311]

[0312]

[0313]

[0314]

[0315] .

[0316] Figure 7 The simulation demonstrates the positional changes of the tracking spacecraft cluster and the escaped spacecraft during the simulation process. The simulation results in the figure show that each spacecraft in the tracking spacecraft cluster can capture the escaped spacecraft. Figure 8 The simulation results show the changes in tracking error during the pursuit and escape of a cluster of spacecraft. The simulation results in the figure show that the tracking error continuously decreases and eventually approaches 0, demonstrating the effectiveness of the control.

[0317] In summary, the method described in this invention can not only identify the objective function weight matrix of a boundedly rational escape spacecraft with complete information in the case of incomplete information in a boundedly rational tracking spacecraft cluster, but also ensure that the tracking spacecraft cluster completes the pursuit mission.

[0318] The above description provides a detailed account of the method described in this invention, but it is obvious that the specific implementation of this invention is not limited thereto. For those skilled in the art, various obvious modifications made to this invention without departing from the spirit and scope of the claims are within the protection scope of this invention.

Claims

1. A bounded rationality game control method for spacecraft swarm pursuit and escape under incomplete information, characterized in that, Includes the following steps: (1) Design a multi-tracking mode for spacecraft clusters, construct an information interaction topology diagram of the spacecraft cluster, and establish a state tracking error model in the spacecraft cluster; (2) Under the assumption of perfect rationality, the cooperative target tracking problem is modeled as a non-zero-sum differential game between the pursuer and the escaper. The game performance index containing the relative distance coordination term and the input constraint penalty term is designed. The assumption of perfect rationality is relaxed, and a level 0 tracking spacecraft model, a level 0 escape spacecraft model and a level 1 escape spacecraft model are built respectively. (3) Design an adaptive escaper level 1 policy estimator to estimate the level 1 control gain of the unknown escape spacecraft based on the state error; (4) Using the policy estimation results, an inverse reinforcement learning algorithm is developed based on the Hamiltonian function to identify the intention of the escaping spacecraft and obtain the estimated weight matrix of the objective function of the escaping spacecraft; (5) Based on the estimated weight matrix, establish the estimated k-level model of the tracking spacecraft cluster and the escape spacecraft, design a multi-spacecraft finite rationality game solution method, and use adaptive dynamic programming technology to solve the coupled Hamilton-Jacobi equation; (6) After identifying the target weight of the opponent, the tracking spacecraft switches to a higher rationality level. Based on the estimated k-level model, the estimated state index set containing all rationality levels of the escaped spacecraft is pre-calculated. By measuring the error between the actual state of the escaped spacecraft and the estimated state at each level online, the error vector is transformed into the level belief probability using Softmax probability mapping. A multi-model tracking strategy is constructed to realize the real-time identification of the cognitive level of the escaped spacecraft and the adaptive switching of the tracking strategy.

2. The bounded rationality game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 1, characterized in that, Step (1) includes the following steps: (1.1) Graph theory is used to describe the information interaction relationship of each spacecraft in the spacecraft cluster, and to construct the information interaction topology graph within the tracking spacecraft cluster and between the tracking spacecraft and the escape spacecraft; (1.2) In the local vertical-local horizontal coordinate system, the relative motion of each spacecraft with respect to the virtual spacecraft is described by the Clohessy-Wiltshire equation; (1.3) Based on the relative state deviation between each spacecraft, define the tracking error of each tracking spacecraft and the escape error of each escaping spacecraft, and establish the corresponding error dynamics equations.

3. The bounded rational game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 1, characterized in that, Step (2) includes the following steps: (2.1) The game objectives of each tracking spacecraft and escape spacecraft are described by a linear quadratic performance index; wherein, the performance index includes a penalty term for state tracking error and a penalty term for control energy consumption; (2.2) Under the assumption of perfect rationality, a multi-chasing-one non-zero sum differential game model is established, and the control strategies of each spacecraft constitute a Nash equilibrium; (2.3) After relaxing the assumption of perfect rationality, the bounded rationality interaction behavior constructed by k-level game theory includes: the 0-level escape spacecraft ignores the existence of the tracking spacecraft, the 0-level tracking spacecraft solves the optimal control problem based on the assumption that the escape spacecraft has no adversarial consciousness, and the 1-level escape spacecraft formulates the optimal escape plan for the 0-level tracking strategy.

4. The bounded rationality game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 1, characterized in that, Step (3) includes the following steps: (3.1) Design an adaptive state observer based on the escape error dynamics, and use the deviation between the observer state and the actual state to drive the online update of the control gain; (3.2) Design and estimate the first-level escape strategy and construct the state estimation error dynamics; (3.3) Design an adaptive update law to estimate the unknown control gain matrix, and use the interval excitation characteristics of historical data signals to ensure the convergence of weights; (3.4) By constructing a calculation expression based on the dynamics of the escape spacecraft itself, an adaptive law reconstruction containing unmeasurable signal terms is achieved, thereby making the strategy estimation error asymptotically stable.

5. The bounded rationality game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 4, characterized in that, In step (3.3), a historical data integral term is introduced into the adaptive update law, and an information matrix is ​​constructed by integrating the state data within a preset time window; a triggering mechanism based on interval excitation conditions is designed, and the historical data correction term is activated when the state data first meets the interval excitation conditions. Construct a mapping function to record the historical moment when the minimum eigenvalue of the information matrix reaches its maximum value, and use the historical data at that moment to correct the adaptive update law; By constructing a computable expression based on the dynamics of escaped spacecraft, the unmeasurable terms containing the product of unknown control gain and historical data are transformed into explicit expressions that depend only on measurable state variables, thus achieving the complete computability of the adaptive update law.

6. The bounded rational game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 1, characterized in that, Step (4) includes the following steps: (4.1) Establish the Hamiltonian function and the corresponding Hamilton-Jacobi equation for a first-stage escape spacecraft; (4.2) A single-layer neural network is used to approximate the value function, the state quadratic cost term, and the control cost term respectively, and the corresponding basis function vectors are designed; (4.3) Construct an approximate inverse Bellman error and a computable control residual. Combine the control residual and the inverse Bellman error into a unified matrix equation through a parameterization method. Design an adaptive update law for the weight vector and use a concurrent learning method to enhance the learning process using historical data. (4.4) Construct a dynamic historical queue management strategy, and gradually increase the feature values ​​of the information matrix by selectively replacing data points to ensure the rapid convergence and high asymptotic accuracy of inverse reinforcement learning weight estimation; (4.5) Calculate the estimated weight matrix of the objective function of the escape spacecraft based on convergent weight estimation.

7. The bounded rational game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 1, characterized in that, Step (4.4) to construct the dynamic historical queue management strategy is as follows: Obtain the current state data and strategy estimate as candidate data points; determine whether the historical queue storage space is full; if not full, calculate the minimum eigenvalue of the batch error matrix corresponding to the historical queue after adding candidate data points. When the minimum eigenvalue is greater than the historical record threshold, store the candidate data points in the historical queue and update the threshold; if full, compare the current state estimate error with the historical record error. When the current error is smaller and the minimum eigenvalue is greater than the threshold, replace the earliest stored data point in the historical queue with the candidate data point; perform batch least squares update of the inverse reinforcement learning weight vector according to the updated historical queue.

8. The bounded rationality game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 1, characterized in that, Step (5) is as follows: (5.1) Based on the estimated weight matrix, establish an estimated k-level model for the tracking spacecraft cluster and the escaping spacecraft; (5.2) Design a recursive solution method for the finite rationality game of multiple spacecraft. The specific process is as follows: For the k-level tracking spacecraft, solve the optimal tracking problem based on the k-1 level escape strategy; for the k+1 level escape spacecraft, solve the optimal escape problem based on the k-level tracking strategy; define the Hamiltonian function and the corresponding Hamilton-Jacobi equation for each level of spacecraft, and derive the optimal strategy for each level through the extreme value conditions; (5.3) Adaptive dynamic programming technique is used to solve the coupled Hamilton-Jacobi equation, and an evaluation neural network is constructed to approximate the objective functions of each party; (5.4) Design the adaptive update rate of the weights of the neural network to realize the online approximation of the pursuit strategy and escape strategy at each level, and ensure that the tracking error and the escape error are consistent and eventually bounded.

9. The bounded rationality game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 1, characterized in that, Step (6) includes the following steps: (6.1) After the tracking spacecraft switches to a higher rationality level, the estimated state index set containing all possible rationality levels of the escaped spacecraft is pre-calculated based on the estimated k-level model; (6.2) Within a preset time interval, calculate the cumulative error difference between the actual escape error and the estimated escape error at each level, and construct an error vector; (6.3) The error vector is mapped to a hierarchical belief probability distribution using the Softmax function, and the temperature parameter controls the smoothness of the probability distribution; (6.4) Construct a multi-model escape strategy by weighting the escape strategies at each level according to the belief probability, and design a multi-model tracking strategy to enable the tracking spacecraft cluster to optimize the hybrid model of all possible low-level strategies of the opponent, so as to realize the real-time identification of the cognitive level of the escape spacecraft and the adaptive switching of the tracking strategy.

10. A bounded rational game control method for spacecraft swarm pursuit and escape under incomplete information as described in claim 9, characterized in that, The rationality level of the tracking spacecraft is a set of even-numbered levels, including levels 0, 2, 4 up to the maximum rationality level; the rationality level of the escaping spacecraft is a set of odd-numbered levels, including levels 1, 3 up to the maximum rationality level minus one; the tracking spacecraft determines the current rationality level of the escaping spacecraft in real time through the Softmax probability distribution, and simultaneously adapts to different levels of escape strategies based on a multi-model strategy, completing the collaborative pursuit mission under conditions of information asymmetry.

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