Unmanned aerial vehicle cross interception method based on cooperative probability game analysis
By constructing a hybrid model of UAV dynamics and solving the optimal control problem using the Nikaido-Isoda function, the complexity of cooperative game and competitive behavior in multi-UAV systems is solved, achieving the stability of generalized Nash equilibrium and the optimality of the cross-interception strategy.
Patent Information
- Application Number
- CN202511225154.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-29
- Publication Date
- 2025-11-18
AI Technical Summary
Existing technologies struggle to effectively handle complex tasks in multi-UAV systems, especially cooperative game theory and competitive behavior in hybrid systems, and fail to fully consider the complex behaviors and randomness components caused by heterogeneous interactions.
A hybrid dynamic model of defensive and offensive drones is constructed, policy constraints are set, and the optimal control problem is solved using the Nikaido-Isoda function and regularization term to find a generalized Nash equilibrium solution to achieve cross-interception.
Cross-interception based on cooperative probabilistic game theory was realized in multi-UAV systems, ensuring the stability of generalized Nash equilibrium and the optimality of the cross-interception strategy, thus solving the problems of mixed behavior and randomness in complex systems.
Smart Images
Figure CN120973066A_ABST
Abstract
Description
Technical Field
[0001] This disclosure relates to the field of UAV attack and defense cooperative game theory technology, and in particular to a UAV cross-interception method based on cooperative probability game analysis. Background Technology
[0002] In recent years, the cross-interception of cooperative game theory and drone security has been a hot topic in many research fields such as game theory, optimal control, and security verification. Quadrotor drones, in particular, are increasingly involved in applications that are difficult for humans to perform, such as search and rescue, reconnaissance, resource exploration, and forest fire prevention. However, with the increasing number of drones, centralized control of these drones is becoming increasingly difficult. Therefore, research on the control of multi-drone systems has gradually shifted towards distributed methods. One of the research goals of distributed drones is that they need to handle various complex tasks, including generalized Nash equilibria, when studying cooperative game theory. Existing research rarely considers multi-drone systems with both cooperative and competitive behaviors. Furthermore, complex systems, such as air traffic and infrastructure, often exhibit complex behaviors caused by heterogeneous interactions, which are inherently hybrid. The uncertainty of interleaved discrete and continuous evolution has also led to the emergence of stochastic system models that simultaneously contain deterministic and stochastic components.
[0003] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.
[0004] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention
[0005] The purpose of this disclosure is to provide a method for cross-interception of drones based on cooperative probabilistic game analysis, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.
[0006] According to embodiments of this disclosure, a method for cross-interception of unmanned aerial vehicles (UAVs) based on cooperative probabilistic game theory analysis is provided, the method comprising: Construct a hybrid dynamics model of defensive drones and a hybrid dynamics model of attack drones, and set policy constraints for defensive drones; The task of intercepting and defending against drones is formulated as an optimal control problem that minimizes the objective function and satisfies policy constraints; The Nikaido-Isoda function is used to solve the optimal control problem in order to find a feasible solution with predictive programming. A regularization term is introduced to smooth the Nikaido-Isoda function, and an improved solution set with a cross-interception strategy is obtained to arrive at the final interception method.
[0007] Furthermore, the steps of constructing a hybrid dynamics model of the defensive drone and a hybrid dynamics model of the attacking drone, and setting policy constraints for the defensive drone, include: Constructing a dynamic hybrid model of defense drones:
[0008] in, To defend against the speed of drone i, To defend against the maximum speed of drones, Control functions for defending against drones, For random items in defense against drones, The initial coordinates for defending against drones; Constructing a hybrid dynamics model of the attack drone:
[0009] in, For the speed of attacking drone j, To attack the drone's maximum speed, For attacking the control functions of drones, For the random items of attacking drones, The initial coordinates for attacking the drone; Set the policy constraints for defending against drones as follows:
[0010] in, The relative coordinates for defending against drones, For the strategy set of all other defensive drones except for defensive drone i, A joint constraint for all defense drones.
[0011] Furthermore, the task of intercepting and defending against drones is formulated as an optimal control problem that minimizes the objective function and satisfies policy constraints: The task of intercepting and defending against drones can be formulated as an optimal control problem that minimizes the objective function:
[0012] in, This is the optimal control function. Let be the objective function. This is the optimal control function.
[0013] Furthermore, the steps of using the Nikaido-Isoda function to solve the optimal control problem to find a feasible solution with predictive programming include: Constructing the Nikaido-Isoda function:
[0014] in, This is a feasible solution for the k-th round. This is a feasible solution for the (k+1)th round. Let k be the objective function. Let the objective function be the objective function for the (k+1)th round. The upper bound of the Nikaido-Isoda function is:
[0015] For a defensive drone i, given that the strategies of other defensive drones are fixed, a local optimization problem is solved to obtain the optimal strategy that minimizes its own objective function. ; Iterate through all defensive drones and calculate the optimal strategy for each drone to obtain the latest strategy set. ; Based on the Nikaido-Isoda function, the global minimum of the optimal control problem is calculated to obtain a feasible solution that satisfies the policy constraints of defending against unmanned aerial vehicles: .
[0016] Furthermore, the steps of introducing a regularization term to smooth the Nikaido-Isoda function and solving for the improved solution set with a cross-interception strategy to obtain the final interception method include: Introducing a regularization term to smooth the Nikaido-Isoda function:
[0017] in, For regularization parameters; The value function of the regularized Nikaido-Isoda function is then:
[0018] Minimize value function To achieve the objective, solve the optimal control problem to obtain an improved solution set. .
[0019] Furthermore, the value function satisfies:
[0020] in, For containing The Nikaido-Isoda function with parameters.
[0021] Furthermore, the improved solution set satisfies ,and .
[0022] According to a second aspect of the present disclosure, a system is provided that includes: The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects: In the embodiments of this disclosure, the UAV cross-interception method based on cooperative probabilistic game analysis described above, on the one hand, establishes a hybrid dynamic model with deterministic and stochastic characteristics, and sets control constraints for the defenders and other defenders respectively; then, the achievement objective is decoupled into two stages. In the first stage, a feasible solution with predictive planning is found using the Nikaido-Isoda function; in the second stage, an improved solution set with cross-interception is further calculated using equality regularization; the optimal solution set is also the generalized Nash equilibrium solution. On the other hand, cooperative probabilistic game analysis is used based on the hybrid dynamic model with deterministic and stochastic characteristics to analyze strategies with UAV security guarantees. This method incorporates optimal control with predictive planning and strategy optimization for cross-interception. Considering the optimality problem of cooperative game, the obtained feasible solution set is the solution of generalized Nash equilibrium, ensuring the stability of generalized Nash equilibrium and the optimality of the cross-interception strategy. Attached Figure Description
[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.
[0024] Figure 1 The diagram illustrates the steps of a drone cross-interception method based on cooperative probabilistic game analysis in an exemplary embodiment of this disclosure. Figure 2 A schematic diagram illustrating a scenario of the drone cross-interception method based on cooperative probabilistic game analysis in an exemplary embodiment of this disclosure; Figure 3 A flowchart illustrating the specific process of the drone cross-interception method based on cooperative probabilistic game analysis in an exemplary embodiment of this disclosure is shown. Figure 4 A simulation diagram of a game is shown in an exemplary embodiment of this disclosure; Figure 5 This illustrates a time-varying diagram of the minimum distance between defenders in an exemplary embodiment of this disclosure; Figure 6 This illustrates a time-varying graph of the minimum distance between each defender and its corresponding attacker in an exemplary embodiment of this disclosure. Detailed Implementation
[0025] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
[0026] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.
[0027] This example implementation provides a method for cross-interception of drones based on cooperative probabilistic game theory analysis. (Reference) Figure 1 As shown, the drone cross-interception method based on cooperative probability game analysis may include: Step S101: Construct a hybrid dynamics model of the defensive drone and a hybrid dynamics model of the attacking drone, and set policy constraints for the defensive drone; Step S102: The task of intercepting and defending against drones is formulated as an optimal control problem that minimizes the objective function and satisfies policy constraints; Step S103: Solve the optimal control problem using the Nikaido-Isoda function to find a feasible solution with predictive programming; Step S104: Introduce a regularization term to smooth the Nikaido-Isoda function, solve for the improved solution set with cross-interception strategy, and obtain the final interception method.
[0028] The above-described UAV cross-interception method based on cooperative probabilistic game theory analysis proposes two approaches. First, a hybrid dynamic model with deterministic and stochastic elements is established, with control constraints set for each defender. The objective is then decoupled into two stages: in the first stage, a feasible solution with predictive programming is found using the Nikaido-Isoda function; in the second stage, an improved solution set with cross-interception is further calculated using equality regularization. The resulting optimal solution set is also a generalized Nash equilibrium solution. Second, cooperative probabilistic game theory is used to analyze strategies that ensure UAV safety based on the hybrid dynamic model. This method incorporates optimal control through predictive programming and strategy optimization for cross-interception. Considering the optimality of cooperative game theory, the obtained feasible solution set is a generalized Nash equilibrium solution, guaranteeing the stability of the generalized Nash equilibrium and the optimality of the cross-interception strategy.
[0029] Below, we will refer to Figures 1 to 6 The steps of the above-described UAV cross-interception method based on cooperative probability game analysis in this example implementation will be described in more detail.
[0030] In steps S101 and S102, a hybrid dynamics model of the defensive drone and a hybrid dynamics model of the attacking drone are constructed, and policy constraints of the defensive drone are set; the interception task of the defensive drone is expressed as an optimal control problem that minimizes the objective function and satisfies the policy constraints.
[0031] Specifically, such as Figure 2 The image shows a scenario illustration of a drone cross-interception method based on cooperative probabilistic game theory analysis. Red represents the attacker, blue the defender, and green the target. Figure 3 The diagram shows a flowchart of the drone cross-interception method based on cooperative probability game analysis.
[0032] The overall objective of this application is to intercept attackers and prevent them from reaching the target area. For each drone in a multi-drone system, the following settings are configured: This refers to the defender (i.e., the defender against drones). The relative coordinates and control inputs. Let... Including the defender The strategies of all other defenders, namely If the defender strategy set Depending on the strategies of other defenders, the strategy set of this application can be represented as follows: ,in Let a non-empty closed set represent the joint constraint of all defenders. It is allowed to be non-convex. Because of the set The properties, therefore It is also a closed set. In summary, the strategy proposed in this application can be described mathematically as an optimal control problem:
[0033] The deterministic part of a stochastic system with control input (a dynamical hybrid model) is represented by the following decoupled system:
[0034]
[0035] in, These represent the states of the defender and the attacker, respectively. These represent the control functions for the defender and the attacker, respectively. Each defender has the same maximum speed. Each attacker has the same maximum speed .
[0036] Assume that the movements of both the defender and the attacker are subject to Brownian motion. Due to the influence of the drone, its dynamics can be represented by the following stochastic differential equation:
[0037]
[0038] The joint state and initial conditions of the UAVs become respectively .
[0039] First, the general form of the strategy constraint in this application is defined as follows:
[0040] in, Depends on the defender The decisions of other defenders are referred to as the joint constraints of this application.
[0041] In step S103, the optimal control problem is solved using the Nikaido-Isoda function to find a feasible solution with predictive programming.
[0042] Specifically, since the goal of this application is to minimize the objective function... This optimization problem can be solved using the Nikaido-Isoda function, specifically:
[0043] in, and These are two feasible solutions to the strategy. yes In the defender The objective function improves upon the existing one, while all other defenders maintain their policies unchanged. Furthermore, its upper bound can be expressed as...
[0044] in, for It is non-negative. Therefore, it is true if and only if and hour, This is a generalized Nash equilibrium solution of the policy. Therefore, finding a solution to the policy is equivalent to calculating the global minimum of the optimization problem:
[0045] Additionally, a policy solution set The generalized Nash equilibrium solution referred to as the strategy in this application is if and only if Satisfying the inequality:
[0046] in, and Defenders The optimal strategy and the general strategy. In addition to the defenders The optimal strategy for all other defenders.
[0047] In step S104, a regularization term is introduced to smooth the Nikaido-Isoda function, and an improved solution set with a cross-interception strategy is obtained to arrive at the final interception method.
[0048] Specifically, the second-stage cross-interception strategy further optimizes step S103 to overcome the non-differentiability issue caused by feasible solutions during optimization. Specifically, this application utilizes an equality regularization method to transition from the first stage to the second stage. To this end, [the following is set...] Define it as a fixed parameter:
[0049] Therefore, for We can derive the value function:
[0050] In addition, the value function satisfies the property .
[0051] Furthermore, It is a generalized Nash equilibrium solution of the strategy proposed in this application if and only if and Specifically, assuming It is a generalized Nash equilibrium solution if and only if Satisfying inequalities You can get and Therefore, we have:
[0052] in, This means
[0053] because .therefore, .
[0054] Conversely, assuming and .So Established. Settings A random number. Definition:
[0055] Among them, set The convexity indicates that for ,have For a specific We can obtain:
[0056] Divide both sides by . and make
[0057]
[0058]
[0059] This applies to all. ,therefore It is a generalized Nash equilibrium solution.
[0060] In one specific embodiment, the verification process of this application is as follows: Figures 4 to 6 As shown, Figure 4 This is a game simulation diagram. Figure 5 for Figure 4 The time-varying diagram of the minimum distance between defenders in the simulation. Figure 6 for Figure 4 The time-varying graph of the minimum distance between each defender and its corresponding attacker in the simulation.
[0061] Two defenders (black) and two maneuvering attackers (red) are engaged in an obstacle avoidance game. The two defenders are playing a cooperative game, assuming they do not communicate with each other. The maneuvering attackers are controlled by a time-optimal control law. Defender D1 is initially assigned to attacker A1, at which point there may be a potential conflict between the two defenders. When using the method of this patent, the defender's nearest attacker switches from stage I to stage II, and the nearest attacker is reassigned. The optimal trajectory of the defender is represented by a solid line, while the dashed line corresponds to the suboptimal trajectory of the attacker after reassignment under the same initial conditions. The baseline method (model predictive control) results in D1→A1 and D2→A2, while the method of this application, with predictive planning and cross-chasing, results in D1→A2 and D2→A1, ensuring collision avoidance between the defenders.
[0062] The beneficial effects of this application are as follows: This application can be applied to multi-UAV attack and defense game models, realizing cooperative probabilistic games with competitive behavior and cross-interception of defender formations.
[0063] (1) Existing methods focus on cooperative game theory in deterministic systems. The method in this application establishes a cooperative probabilistic game theory based on a hybrid deterministic and stochastic dynamic system to analyze strategies with UAV security.
[0064] (2) Existing methods do not consider multi-UAV systems with cooperative and competitive behaviors. The method in this application designs optimal control and cross-interception strategy optimization with predictive programming.
[0065] (3) Considering the optimality problem of cooperative game, the feasible solution set obtained by the method of this application is the solution of generalized Nash equilibrium, which guarantees the stability of generalized Nash equilibrium and the optimality of cross-interception strategy.
[0066] It should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., in the above description indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of this disclosure and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this disclosure.
[0067] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.
[0068] In the embodiments of this disclosure, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this disclosure according to the specific circumstances.
[0069] In embodiments of this disclosure, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.
[0070] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.
[0071] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.
Claims
1. A method for cooperative probability game analysis based UAV cross-interception, characterized in that, The method comprises: constructing a hybrid dynamic model of the defense unmanned aerial vehicle and a hybrid dynamic model of the attack unmanned aerial vehicle, and setting a strategy constraint of the defense unmanned aerial vehicle; expressing an interception task of the defense unmanned aerial vehicle as an optimal control problem of minimizing an objective function, and meeting the strategy constraint; solving the optimal control problem by using a Nikaido-Isoda function to find a feasible solution with a predictive plan; introducing a regularization term to smooth the Nikaido-Isoda function, solving an improved solution set with a cross-interception strategy, and obtaining a final interception method.
2. The method of claim 1, wherein, In the step of constructing a hybrid dynamic model of the defense unmanned aerial vehicle and a hybrid dynamic model of the attack unmanned aerial vehicle, and setting a strategy constraint of the defense unmanned aerial vehicle, the step comprises: constructing a hybrid dynamic model of the defense unmanned aerial vehicle: wherein, Vmax is the maximum speed of the drone i, Vmax is the maximum speed of the drone i, Vmax is the maximum speed of the drone i, Vmax is the maximum speed of the drone i, Vmax is the maximum speed of the drone i, constructing a hybrid dynamic model of the attack unmanned aerial vehicle: wherein, is the velocity of the attacking drone j, is the maximum velocity of the attacking drone, is the control function of the attacking drone, is the random term of the attacking drone, is the initial coordinates of the attacking drone; setting the strategy constraint of the defense unmanned aerial vehicle as: wherein, for the relative coordinates of the defense UAV, for the strategy set of all other defense UAVs except the defense UAV i, for the joint constraints of all defense UAVs.
3. The method of claim 2, wherein, expressing an interception task of the defense unmanned aerial vehicle as an optimal control problem of minimizing an objective function, and meeting the strategy constraint: expressing an interception task of the defense unmanned aerial vehicle as an optimal control problem of minimizing an objective function: wherein, is the optimal control function, is the objective function, is the optimal control function.
4. The method of claim 3, wherein, In the step of solving the optimal control problem by using a Nikaido-Isoda function to find a feasible solution with a predictive plan, the step comprises: constructing a Nikaido-Isoda function: wherein, is a feasible solution for the kth round, is a feasible solution for the (k+1)th round, is an objective function for the kth round, is an objective function for the (k+1)th round; the upper bound of the Nikaido-Isoda function is: For defense UAV i, in the case of other defense UAV strategies being fixed, the local optimization problem is solved to obtain the optimal strategy that minimizes its own objective function ; traversing all defense drones, calculating optimal strategies of all defense drones to obtain the latest strategy set ; based on the Nikaido-Isoda function, calculating a global minimum value of the optimal control problem to obtain a feasible solution meeting the strategy constraint of the defense unmanned aerial vehicle: 。 5. The method of claim 4, wherein, In the step of introducing a regularization term to smooth the Nikaido-Isoda function, solving an improved solution set with a cross-interception strategy, and obtaining a final interception method, the step comprises: introducing a regularization term to smooth the Nikaido-Isoda function: wherein is a regularization term parameter; the value function of the Nikaido-Isoda function after regularization is: to minimize a value function solving an optimal control problem to obtain an improved solution set .
6. The method of claim 5, wherein, the value function meets: wherein containing Nikaido-Isoda function of the parameters.
7. The method of claim 6, wherein, The improved solution set satisfies , and .