Victory method and system for escorting non-cooperative dynamic targets

Abstract

This application discloses a winning method and system for protecting a non-cooperative dynamic objective, relating to the field of attack-defense game theory. The method includes: establishing a dynamic model of a cluster system with a non-cooperative dynamic objective; considering a one-to-one attack-defense subgame, constructing an escape region and an extended escape region based on the dynamic model and the defense winning condition, and designing an on-site defense strategy; designing an optimization problem based on the escape region and the optimal trajectories of both attackers and defenders, and determining the uniqueness of the optimal solution to the optimization problem; performing win-loss analysis on the subgame based on the properties of the optimal solution to the optimization problem and different initial game states, and designing an optimal solution defense strategy; achieving a defensive victory by adopting either the on-site defense strategy or the optimal solution defense strategy based on the initial game state; considering a multi-participant attack-defense game, using the defense winning result of the one-to-one attack-defense subgame and an order matching algorithm to solve for the maximum matching in many-to-many attack-defense scenarios. This application effectively solves the attack-defense game problem under non-cooperative dynamic objectives.

Description

Technical Field

[0001] This application relates to the field of offensive and defensive game theory technology, and in particular to a winning method and system for protecting non-cooperative dynamic targets. Background Technology

[0002] In 1965, the world's first monograph on differential games, *Differential Games*, was published. As a powerful mathematical tool, differential games can be used to analyze the strategic behavior of participants operating in a continuous state and action space. As a type of differential game, offensive-defensive differential games have significant theoretical value in scenarios where cooperation and confrontation coexist, such as protecting high-value resources and malicious interception. The earliest research on offensive-defensive games can be traced back to around 1999. In recent years, numerous offensive-defensive game scenarios, solution methods, and system descriptions have emerged, driving the theoretical development of offensive-defensive games. These games consider an adversarial scenario where a group of attackers aims to enter an area protected by multiple defenders. Compared to traditional chase-and-escape games, offensive-defensive differential games, due to their dual adversarial nature, lead to multiple possible outcomes, making them more complex and challenging.

[0003] Attack-defense game theory for static targets (target regions) has been extensively explored, resulting in many excellent works, such as attack-defense games involving multiple participants, crazy drivers, environments with obstacles, uncertain observations, and non-convex target sets. Building upon static targets, an increasing number of scholars, both domestic and international, have begun to focus on attack-defense game theory for dynamic targets, namely, given the motion characteristics of the target, how to analyze the criteria for victory and defeat in attack-defense games and design cooperative winning strategies. Among these, the study of attack-defense game theory for cooperative dynamic targets has a long history. Cooperative dynamic target attack-defense game theory, also known as three-body game theory, mainly considers the attack-defense confrontation between the defender, the attacker, and the target. The attacker wants to attack the target while avoiding being intercepted by the defender, while the defender and the target can be seen as a combination, jointly adopting strategies to intercept the target before the attacker attacks, thus ensuring the target's safety. This type of game theory was proposed in 1976, and many results have emerged since then, focusing on single-integrator models. However, research on non-cooperative dynamic targets is scarce. Offensive and defensive games with non-cooperative dynamic objectives refer to situations where the objective moves along a given trajectory without actively cooperating with the defender, who must then protect the objective through their own strategies. This type of game has important applications, such as when a dynamic objective needs to complete tasks like transportation or patrolling but lacks the resources and capabilities to actively cooperate with the defender. Offensive and defensive games with non-cooperative objectives are widely used in scenarios such as personnel and equipment escort, cargo transfer, and naval escort, and represent one of the most pressing challenges in the field of offensive and defensive games.

[0004] The current state of research on attack-defense games with dynamic objectives primarily focuses on cooperative dynamic objectives, with limited literature addressing non-cooperative dynamic objectives. Furthermore, non-cooperative dynamic objective attack-defense games face common challenges and limitations inherent in the genre, such as reliance on approximate analytical solutions, heavy computational burdens, a limited number of participants, and a lack of winning criteria. Therefore, it is necessary to study multi-participant attack-defense games with non-cooperative dynamic objectives, analyzing whether defenders can successfully protect the objective and under what conditions successful protection is guaranteed, and further designing computationally simple and effective defensive strategies. Summary of the Invention

[0005] The purpose of this application is to provide a winning method and system for protecting non-cooperative dynamic targets, which effectively solves the offensive and defensive game problem under non-cooperative dynamic targets.

[0006] To achieve the above objectives, this application provides the following solution.

[0007] Firstly, this application provides a winning method for protecting a non-cooperative dynamic target. The winning method includes: establishing a dynamic model of a cluster system containing a non-cooperative dynamic target; decomposing the game problem of the cluster system into multiple sub-game problems involving one defender and one attacker; defining the defense winning condition and the defender's capture method; the cluster system includes multiple defenders, multiple attackers, and one non-cooperative dynamic target; the defender's capture method is point capture; considering a one-to-one attack-defense sub-game, constructing an escape region based on the dynamic model and the defense winning condition; the escape region is a set of locations that the attacker can safely reach under any strategy adopted by the defender; constructing an extended escape region based on the geometric characteristics of the escape region; and further... The dynamic model and the extended escape zone are used to design on-site defense strategies. Based on the dynamic model and the defense winning conditions, the game's terminal and corresponding cost function are constructed, and the properties of the optimal strategies and optimal trajectories for both the defender and the attacker are determined. Based on the escape zone and the optimal trajectories of both sides, an optimization problem is designed, and the uniqueness of the optimal solution to the optimization problem is determined. Based on the properties of the optimal solution to the optimization problem and different initial game states, win-loss analysis is performed on the subgames, and the optimal solution defense strategy is designed. Based on different initial game states, either the on-site defense strategy or the optimal solution defense strategy is adopted to achieve a defensive victory. Considering multi-participant attack-defense games, the defense winning results of one-to-one attack-defense subgames and the sequence matching algorithm are used to solve for the maximum matching of many-to-many attack-defense.

[0008] In a second aspect, this application also provides a computer system comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the winning method for protecting non-cooperative dynamic targets as described in the first aspect.

[0009] Based on the specific embodiments provided in this application, the following technical effects are disclosed.

[0010] First, this application fully considers the application scenario of protecting non-cooperative dynamic targets, effectively establishing a dynamic model of a cluster system with one non-cooperative dynamic target, and conducting subsequent analysis based on this model. Second, this application decomposes the game problem of the cluster system into multiple sub-game problems involving one defender and one attacker. By defining the defense winning condition and the defender's capture method, constructing escape areas and extended escape areas, and applying the dynamic model, an effective on-site defense strategy is designed. Then, based on the escape areas and the optimal trajectories of both attackers and defenders, this application designs an optimization problem. By analyzing the uniqueness of the optimal solution to this problem, and then using the properties of the optimal solution of the optimization problem and different initial game states, the win-loss analysis of the sub-games is performed, and a defense strategy based on the optimal solution of the optimization problem is designed. Finally, this application considers multi-participant attack-defense games, using the defense winning result of one-to-one attack-defense sub-games and the order matching algorithm to obtain the maximum matching of many-to-many attack-defense, effectively solving the attack-defense game problem under non-cooperative dynamic targets. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of a winning method for protecting non-cooperative dynamic targets in an embodiment of this application.

[0013] Figure 2 This is a scenario diagram of a multi-participant attack and defense game with a non-cooperative moving objective in this application embodiment.

[0014] Figure 3 This is a schematic diagram of the escape area in an embodiment of this application; Figure 3 (a) Schematic diagram of the escape area and safe distance; Figure 3 (b) Schematic diagram of the expanded escape area and on-site defense strategy.

[0015] Figure 4This is a schematic diagram of the strategy in the first case in the embodiments of this application; Figure 4 (a) A diagram illustrating the on-field defensive strategy employed by the defenders; Figure 4 (b) A diagram showing the defender remaining stationary.

[0016] Figure 5 This is a schematic diagram of the strategy in the second case in the embodiments of this application; Figure 5 (a) Strategies for the defender A schematic diagram; Figure 5 (b) is a schematic diagram of the defender and attacker moving toward the optimal solution to the optimization problem.

[0017] Figure 6 This is a schematic diagram of the strategy in the third case in the embodiments of this application; Figure 6 (a) is a diagram illustrating how the target safely reaches the destination before the attacker is captured by the defender; Figure 6 (b) is a schematic diagram of a multi-player offensive and defensive game with a non-cooperative dynamic objective; Figure 6 (c) is a schematic diagram of the terminal state of a multi-participant attack and defense game.

[0018] Figure 7 This is a schematic diagram of the internal structure of the computer system in an embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] In recent years, significant progress has been made in offensive and defensive game theory with cooperative dynamic objectives. Among these advancements, some scholars have studied the variational inequality descriptions and numerical solutions of win / loss criteria and winning strategies under dynamic constraints. Others have explored specific cooperative or capture strategies for the fast defender scenario, deriving analytical representations of game boundaries. Still others have investigated optimal strategies under finite perception constraints and multiple defenders, and further studied linear quadratic equilibrium strategies for defenders in multiple modes. Research on offensive and defensive game theory with non-cooperative dynamic objectives is relatively limited. One scholar considered a scenario where an airborne asset with fixed control input is escorted by a wingman, obtaining the optimal flight distance for both sides by solving high-order polynomials, thus deriving the optimal feedback strategy. Some scholars have analyzed and numerically solved the HJI equations for double-barrier scenarios with time-varying dynamics, objectives, and constraints. Others have analyzed offensive and defensive games under constant flow fields, analytically constructing game boundaries and designing winning strategies for both sides. However, to date, no work has been conducted on the scenario of a non-cooperative dynamic target moving on a line segment, and valuable research results are still lacking in the analysis of the victory criteria and the solution methods for winning strategies in this scenario.

[0021] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Common symbol definitions: Let and Represent real numbers and positive real numbers respectively. express n A two-dimensional real vector column (i.e., a two-dimensional real vector space). This represents the Euclidean norm. All vectors in this application are column vectors. Representing vectors Transpose, using express The unit disk in the middle, i.e. .

[0023] In one exemplary embodiment, a winning method for protecting non-cooperative dynamic targets is provided, such as... Figure 1 As shown, the winning strategy for this non-cooperative dynamic objective is as follows.

[0024] Step S1: Establish a dynamic model of a cluster system with a non-cooperative dynamic objective, and decompose the game problem of the cluster system into multiple sub-game problems involving a defender and an attacker, defining the winning condition for the defender and the method of the defender to capture.

[0025] In this embodiment, the (attack-defense game) cluster system includes multiple defenders, multiple attackers, and a non-cooperative dynamic target. The defenders are captured using point-to-point capture. Consider one... In planar attack and defense differential games, there are One defender, One attacker and one non-cooperative dynamic target The set of defenders is represented as The attacker set is represented as Assume the defender and attacker are homogeneous point masses, moving in a simple model, while The attacker and defender move along a line segment. The dynamics models of the attacker and defender are represented as follows.

[0026] .

[0027] .

[0028] In the formula, for The first derivative, For the first i One defender exist t Location at any given moment ; for The first derivative, For the first j attackers exist t Location at any given moment ; and They are respectively and exist t The control input at any given time belongs to the set. ; and They are respectively and Maximum speed, , ; and They are respectively and exist The position at that moment; and They are respectively and The initial position.

[0029] There is a starting point The destination is line segments Defined as , Indicates location, This is the proportionality constant. Because... It is non-cooperative; it moves with a fixed control input. On the field, they will not actively cooperate with the defender. The dynamic model is expressed as follows.

[0030] .

[0031] In the formula, for The first derivative, for exist t Location at any given moment ; for speed, ; for exist The position at that moment; for The initial position; for The control input is from point to unit vector, .therefore, The motion is represented as follows.

[0032] .

[0033] In the formula, for from Exercise The time required .

[0034] All dependencies , , All variables are time-related; for convenience, unless otherwise specified, they will be omitted in the following text. t Omitted.

[0035] Furthermore, considering the scenario where the defender is faster than the attacker, and the attacker is faster than the target, and The speed ratio between them is defined as ,Will and The speed ratio between them is defined as Considering point capture (i.e., the capture radius of the defender capturing the attacker is 0), when Pursuit And the distance between them is 0, that is The arrest was carried out in a timely manner. Similarly, hour Successful attack .

[0036] In offensive and defensive games where there are non-cooperative dynamic objectives, Hope from arrive The security campaign is on the online segment, and attackers are attempting to... Attack before reaching the finish line And avoid being caught by the defender; at the same time, the defender is attacked by the attacker. and Try to capture the attacker before reaching the finish line, or delay the attacker's attack. ,until Reach the finish line.

[0037] This game employs a state feedback information structure, where both the defender and the attacker can obtain the real-time positions and maximum speeds of all participants, and... The game's movement patterns are clear, but defenders and attackers cannot obtain control input from their opponents. Due to the complex intra-team cooperation and inter-team competition among participants, it is difficult to directly analyze the entire game. Therefore, the game is decomposed into multiple subgames, each containing one defender and one attacker. , and ,make This represents the state (i.e., position) of a subgame. express No arrests , No attack , Did not arrive The set of states of the subgame is specifically represented as follows.

[0038] .

[0039] Furthermore, in a subgame between a defender and an attacker, the defense's victory is defined as follows: if There exists a defensive strategy that makes it possible for the opponent to win regardless of when When a strategy is adopted, if one of the following conditions is met, then it is called... right For one A defensive victory was achieved. (1) In attack , arrive Before, Successful capture This situation is called a capture-defense victory; (2) In attack Before, Arrived successfully This situation is called a delayed defense winning.

[0040] Step S2: Consider a one-to-one attack and defense subgame, and construct the escape zone based on the dynamics model and the defense winning condition.

[0041] In this embodiment, the escape zone is the set of locations that the attacker can safely reach, regardless of the defender's strategy. Given , satisfy The escape zone is defined as being in Regardless of What strategy to adopt? All can be reached without being A collection of locations where the capture took place.

[0042] .

[0043] In the formula, For and , The escape area; It is a potential function.

[0044] Defined as: .

[0045] The closure of the escape region is defined as: In fact, the boundary of the escape region is an Apollonius circle, therefore It is bounded and strictly convex.

[0046] In the given , In this case, the center of the escape area and radius It can be obtained through the following calculation.

[0047] .

[0048] Therefore, the closure of the escape region can be equivalently represented as .

[0049] Step S3: Construct an extended escape zone based on the geometric characteristics of the escape zone, and design an on-site defense strategy based on the dynamic model and the extended escape zone.

[0050] In this embodiment, inspired by the work of M. Dorothy et al., the Apollonius circle is extended into a larger concentric circle. For a small constant... A larger closure for escaping is introduced.

[0051] .

[0052] In the formula, To expand the closure of the escape region.

[0053] Known yes The dominant domain, that is to say able to be no later than arrive any point, and It can be earlier than arrive At any point. The work of M. Dorothy et al. shows that even and They do not move toward the same point on the Apollonius circle. It is still possible to capture within an arbitrarily close neighborhood of the initial Apollonius circle. ,regardless What strategy should be adopted? Based on this, the following defensive strategy is introduced, namely the on-site defensive strategy, which will be used as the defender's winning strategy under certain conditions.

[0054] from t At any time, if Adopt on-site defensive strategy ,for , On-site defensive strategy function at any time satisfy: So regardless What strategy to adopt? It can be guaranteed that: (1) for (2) Within a finite time, exist Arrested.

[0055] Step S4: Based on the dynamic model and the defense winning condition, construct the game's terminal and the corresponding cost function, and determine the properties of the optimal strategy and optimal trajectory for the defender and the attacker.

[0056] In this embodiment, when exist Go to exercise, and The subgames between them will have different terminal outcomes, and the next step is to... and The optimal strategy and optimal trajectory are analyzed. Let... and They represent and The initial and final moments of the subgame.

[0057] Assumption Arrive safely Although the attack was unsuccessful. , We will still try to minimize the number of terminals and The distance, and We want to maximize this distance, and the cost function can be defined as follows.

[0058] .

[0059] Conversely, if able to be Arrest arrive Previous successful attack ,So We hope to minimize interactions with terminals. The distance, and We want to maximize this distance, and the cost function can be defined as follows.

[0060] .

[0061] According to optimal control theory, a subgame can be transformed into an optimal control problem where the terminal state is constrained and the terminal state is free at the last moment. Based on the above cost function, analysis of different terminal states can reveal... and The optimal trajectory has the following properties. For a given state... ,if against Guard So: if in arrive , attack Before, Arrest So in Down and The optimal trajectory is a straight line, and their optimal control input is constant and is controlled by... Uniquely certain; if in attack Before, arrive So in Down The optimal trajectory is a straight line, and its optimal control input is constant and is controlled by... Uniquely certain; if in Arrest , arrive Before, Successful attack So in Down and The optimal trajectory is a straight line, and their optimal control input is constant and is controlled by... The only certainty.

[0062] Step S5: Based on the escape area and the optimal trajectories of both the attacker and defender, design an optimization problem and determine the uniqueness of the optimal solution to the optimization problem.

[0063] In this embodiment, based on the properties of the optimal strategy and the optimal trajectory, it can be known that regardless of how the game terminates... They will prioritize attacking along straight lines. Known It is an escape zone, therefore Will choose Find a point on the [plane] and move towards it in a straight line. Next, we introduce a safety distance, defined as when [the distance is...]. Along from Exercise During the process, and The minimum distance between them is expressed as The safe distance can be obtained by solving the following optimization problem: for a given state... ,make and They represent optimization problems respectively. The optimal solution and optimal value.

[0064] .

[0065] in, Minimize means to minimize the function; The objective function in the optimization problem is defined by "subject to".

[0066] Although the constraints in the optimization problem are convex, the optimization problem itself is also non-convex because the objective function is non-convex. The following examples illustrate the non-convexity of the objective function: Let... , , , , Consider two feasible points , ,Pick ,at this time satisfy: .

[0067] This clearly does not conform to the definition of a convex function.

[0068] The uniqueness of the optimal solution, that is, for a given state ,if The optimal value satisfies Then the optimal solution It is unique. Based on the expressions for the objective function and constraints above, it can be seen that... Described The strategy is to select a point. Moving in a straight line toward him, so that passing through After time and The distance is the smallest. Therefore, when when, The optimal solution corresponds to The optimal strategy. When the optimal strategy is adopted... The optimal control input is uniquely determined, therefore, considering the strong convexity of the feasible set, it can be explained that... The uniqueness of.

[0069] Step S6: Based on the properties of the optimal solution to the optimization problem and different initial states of the game, perform win / loss analysis on the subgame and design the optimal solution defense strategy.

[0070] In this embodiment, although Even though it is non-convex, it can still guarantee that the optimal solution can be found through optimization with multiple initial values, due to the uniqueness of its optimal solution. At this point, the preparatory work for the defensive winning conditions and strategies for one-to-one subgame problems is complete. The following section presents the winning conditions and strategies for the defender protecting the target in a subgame.

[0071] from t Moment, for a state ,consider against Guard from Exercise , then: if So regardless What strategy can be adopted to guarantee a victory through delayed defense in this situation? On-site defensive strategies can be adopted for capture. ;if , And safe distance ,So Strategies can be adopted Come to protect Exercise ,regardless What strategy to adopt; if So regardless What strategy to adopt? On-site defensive strategies can be adopted to protect the team. Exercise .

[0072] Step S7: Based on different initial game states, adopt on-site defensive strategies or optimal solution defensive strategies to achieve a defensive victory.

[0073] Step S8: Consider a multi-participant attack and defense game, and use the defensive winning result and order matching algorithm of a one-to-one attack and defense subgame to solve for the maximum matching of many-to-many attack and defense.

[0074] In this embodiment, considering a multi-participant attack and defense game, the sequential matching algorithm proposed by Yan et al. can be used to solve the maximum matching between defenders and attackers, and the excess defenders are preferentially assigned to the nearest attackers. Combined with the above defense strategy, the algorithm can guarantee a lower bound on the number of attackers to be captured.

[0075] To verify the effectiveness of the aforementioned winning method for protecting non-cooperative dynamic targets, this embodiment also provides... Figure 2 The diagram shows a multi-player attack and defense game scenario with a non-cooperative dynamic objective. In this scenario, defenders (red) protect an objective (green) against attackers (blue) who want to attack the objective. The objective moves from the starting point to the ending point along a line segment (brown).

[0076] exist Figure 3 In (a), the yellow escape area yes Able to reach without being The area for the arrest is marked by a gray dashed line indicating a safe distance. It means when Along from Exercise During the process, and The minimum distance between; Figure 3 In (b), the pink area It refers to a constant. , and The closure of the escape region is extended between them, and the yellow dashed circles represent the different closures. and The boundary of the escape zone formed at that location. If Keep a constant input, then On-site defensive strategies can be adopted. Internal arrest .

[0077] exist Figure 4 In (a), the first case: If this is established, then a delayed defense is guaranteed to win. Adopting on-site defensive strategies, in Arrest ,regardless What strategies should be adopted, among which ; Figure 4 (b) indicates that in this initial state, Able to arrive safely ,even though Remain still.

[0078] exist Figure 5 In (a), the second case: , and . Take strategy Can Arrest, thereby ensuring Safety. In Figure 5 In (b), and At the same time, it moves towards the optimal solution to the optimization problem. exist upper The capture. At this point, the optimal trajectory for both is a straight line.

[0079] exist Figure 6 In (a), the third case: You can select , making , The purpose of adopting an on-site defensive strategy is to... Arrest ,exist quilt Before the arrest, Priority has arrived safely. ;exist Figure 6 (b) is a multi-player attack and defense game involving 8 defenders and 6 attackers, where the gray dashed lines represent attack and defense pairs; Figure 6 (c) represents the terminal state of a multi-player attack and defense game, in which all attackers have been captured and are marked with a yellow star.

[0080] In summary, the winning method for protecting non-cooperative dynamic targets proposed in this application is applicable to multi-player attack-defense games where the non-cooperative dynamic target moves along a line segment. For a subgame between a defender and an attacker, the optimal control inputs of the participants are proven to be constant, uniquely determined by the initial state given a cost function, and their optimal trajectories are straight lines. The safe distance is defined as the minimum distance between the attacker and the non-cooperative dynamic target, which can be obtained by solving a non-convex optimization problem with a unique optimal solution. The three winning conditions proposed in this application cover three initial states, and the corresponding defense strategies enable the defender to safely protect the non-cooperative dynamic target. In multi-player games, a sequential matching algorithm can be used to solve for the maximum matching between the attacker and defender, thus guaranteeing a lower bound on the number of attackers to be captured.

[0081] In another exemplary embodiment, a computer system is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 7 As shown, the computer system includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores dynamic models. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When executed by the processor, the computer program implements a winning method for protecting non-cooperative dynamic targets.

[0082] Those skilled in the art will understand that Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer system to which the present application is applied. A specific computer system may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0083] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0084] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0085] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0086] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0087] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method of winning against a non-cooperative dynamic target, characterized in that, The winning methods for protecting non-cooperative dynamic targets include: A dynamic model of a cluster system with a non-cooperative dynamic objective is established, and the game problem of the cluster system is decomposed into multiple sub-game problems involving one defender and one attacker. The winning condition for the defender and the method of capturing the defender are defined. The cluster system includes multiple defenders, multiple attackers and a non-cooperative dynamic objective. The method of capturing the defender is point capture. Considering a one-to-one attack and defense subgame, an escape region is constructed based on the dynamic model and the defense winning condition; the escape region is the set of locations that the attacker can safely reach under any strategy adopted by the defender. An extended escape region is constructed based on the geometric characteristics of the escape region, and an on-site defense strategy is designed based on the dynamic model and the extended escape region. Based on the dynamic model and the defense winning condition, the game's terminal and corresponding cost function are constructed, and the properties of the optimal strategies and optimal trajectories for the defender and attacker are determined. Based on the escape area and the optimal trajectories of both the attacker and defender, an optimization problem is designed, and the uniqueness of the optimal solution to the optimization problem is determined. Based on the properties of the optimal solution to the optimization problem and different initial states of the game, win-loss analysis is performed on the subgame, and a defense strategy for the optimal solution is designed. Depending on the different initial states of the game, the on-site defense strategy or the optimal solution defense strategy is adopted to achieve a defensive victory. Considering a multi-participant attack-defense game, we use the defensive winning result of a one-to-one attack-defense subgame and the order matching algorithm to find the maximum matching of many-to-many attack-defense.

2. The method of claim 1, wherein: The dynamic model is expressed as follows: ； ； ； In the formula, for The first derivative, For the first i One defender exist t The position at that moment; for The first derivative, For the first j attackers exist t The position at that moment; and They are respectively and exist t Time-based control input; and They are respectively and Maximum speed; and They are respectively and exist The position at that moment; and They are respectively and The initial position; and They are the set of defenders and the set of attackers, respectively. for The first derivative, Non-cooperative dynamic goals exist t The position at that moment; for speed; for Control input; for exist The position at that moment; for The initial position.

3. The method of claim 1, wherein: The non-cooperative dynamic target operates on a line segment with fixed control inputs and does not actively cooperate with the defender; The line segment is represented as: ； wherein denotes a line segment; denotes a position; is a two-dimensional real vector space; and are the start and end points of respectively; is a scale factor; The motion of the non-cooperative dynamic target is represented as follows: ； In the formula, Non-cooperative dynamic goals exist t The position at that moment; for speed; for Control input; for from Exercise The time required.

4. The method of claim 1, wherein: In the aforementioned subgame problem, if There exists a defensive strategy that makes it possible for the opponent to win regardless of when If a strategy is adopted that is met under any of the following conditions, then it is called... right For one A defensive victory was achieved. In attack , reach before, successfully capture , this situation is called capture defense win; In attacks before, successful arrival This is called a delayed defensive win; in, For the first i One defender; For the first j One attacker; For non-cooperative dynamic objectives; For line segments The end point.

5. The method of claim 1, wherein: The escape region is represented as: ； In the formula, For the first i One defender and the j attackers , The escape area; Indicates location; It is a two-dimensional real vector space; It is a potential function; The closure of the escape region is represented as: ； wherein is the closure of and are the center and radius of the evasion region, respectively is the Euclidean norm​ The closure of the extended escape region is represented as: ； wherein is the closure of the evasion region; is a constant.

6. The method of claim 1, wherein: The on-site defense strategy is expressed as follows: ； ； In the formula, For the first i One defender exist On-site defensive strategies at all times ; for The on-site defensive strategy function at any given moment; It is the Euclidean norm; for and the j attackers The speed ratio between them; and They are respectively t Constantly avoid the center and radius of the area; and They are respectively Constantly avoid the center and radius of the area; It is a constant; and They are respectively and exist The location at any given moment.

7. The method of claim 1, wherein: The properties of the optimal strategies and optimal trajectories for both defenders and attackers include: To one If For Escort Then: If in arrive , attack Before, Arrest ,So and The optimal trajectory is a straight line, and the optimal control input is constant and is... Uniquely certain; If in attack Before, arrive ,So The optimal trajectory is a straight line, and the optimal control input is constant and is... Uniquely certain; If in Arrest , arrive Before, Successful attack ,So and The optimal trajectory is a straight line, and the optimal control input is constant and is... Uniquely certain; in, The state of the game for pieces. For the first i One defender Location, For the first j attackers Location, Non-cooperative dynamic goals Location; For line segments The end point.

8. The method of claim 1, wherein: The optimization problem is expressed as: ； ； In the formula, minimize means minimizing the function; Indicates location; It is a two-dimensional real vector space; The objective function in the optimization problem; subject to represents the constraints; It is a potential function; Non-cooperative dynamic goals exist t The position at that moment; for speed; for Control input; For the first j attackers Location; for The maximum speed.

9. The method of claim 1, wherein: Based on the properties of the optimal solution to the optimization problem and different initial game states, win / loss analysis is performed on the subgame, and optimal solution defense strategies are designed, specifically including: From t time to time, one , consider for escorting from move to , then: if So regardless Whatever strategy is adopted, a delayed defense is guaranteed to win. In this situation, On-site defensive strategy for arrest ; if , and So regardless What strategy to adopt? All can adopt strategies Come to protect Exercise ; If , then no matter what strategy is taken, on-site defense strategy can be taken to escort ; in, For the first i One defender; For the first j One attacker; For non-cooperative dynamic objectives; The state of a piece game; express No arrests , No attack , Did not arrive The set of states of a subgame; and They are line segments The starting point and the ending point; for and The speed ratio between them; for and The speed ratio between them; Indicates when Along from Exercise During the process, and The minimum distance between them; To optimize the optimal solution to the problem; To avoid the closure of the region; for Strategies; for Location; for Location; for Location; It is the Euclidean norm.

10. A computer system comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the winning method for protecting a non-cooperative dynamic target as claimed in any one of claims 1-9.

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