Unmanned aerial vehicle pursuit and evasion game control method and system based on conservation manifold dimension reduction

Abstract

The application provides a UAV pursuit and evasion game control method and system based on a conservative manifold dimension reduction, wherein the method comprises the following steps: constructing a Lagrangian of a game system based on flight state parameters of a pursuing UAV and an evading UAV participating in the game; performing symmetry analysis on the Lagrangian to obtain a conserved quantity corresponding to the internal symmetry of the game system; eliminating redundant state parameters based on the conserved quantity to map a high-dimensional state space to a low-dimensional conservative manifold, and reconstructing a reduced game equation on the low-dimensional conservative manifold; solving the reduced game equation on the low-dimensional conservative manifold with the conserved quantity as a constraint condition to generate a game control strategy, and controlling the pursuing UAV to perform a pursuit and evasion maneuver action against the evading UAV according to the game control strategy. The method not only reduces the solving complexity, breaks through the calculation bottleneck, and meets the real-time confrontation demand, but also makes the generated strategy naturally satisfy the physical conservation law, greatly improves the executability and safety of the strategy in a real environment.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and in particular to a method and system for controlling a drone in a game of pursuit and escape based on conserved manifold dimensionality reduction. Background Technology

[0002] In the field of high-dimensional dynamic game theory, such as multi-drone air combat, the mainstream techniques include differential game theory, multi-agent reinforcement learning, and evolutionary game algorithms. However, with the increase in the number of game participants and the explosion of state space dimensions, existing technologies face severe challenges.

[0003] Traditional differential game theory requires solving Hamilton-Jacobi-Isaacs (HJI) partial differential equations, whose computational complexity increases exponentially with the number of state variables. In real-time adversarial scenarios, existing numerical methods struggle to converge within milliseconds, resulting in policy lag and failing to meet real-time adversarial requirements. Furthermore, policies generated by existing data-driven methods often violate fundamental physical laws, exhibiting energy non-conservation and momentum mutations. In real-world physical systems, these issues can easily lead to oscillations or loss of control, severely limiting the effectiveness and security of drone pursuit game control. Summary of the Invention

[0004] This invention provides a UAV pursuit and escape game control method and system based on conserved manifold dimensionality reduction, which solves the problems in the prior art where the high computational complexity of high-dimensional partial differential equations leads to the lag of real-time adversarial strategies, and the data-driven method generates strategies that violate physical laws and are prone to causing system oscillation and loss of control.

[0005] This invention provides a game-theoretic control method for UAV pursuit and escape based on conserved manifold dimensionality reduction, comprising: Obtain the flight state parameters of the pursuing drone and the escaping drone participating in the game system, and construct the Lagrange quantity of the game system based on the flight state parameters; Symmetry analysis of the Lagrange quantity yields the conserved quantities corresponding to the inherent symmetry of the game system. Based on the conserved quantities, redundant state parameters in the game system are eliminated to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and the dimension-reduced game equations are reconstructed on the low-dimensional conserved manifold. On the low-dimensional conserved manifold, the reduced-dimensional game equation is solved with the conserved quantities as constraints to generate a game control strategy. Based on the game control strategy, the pursuing drone is controlled to perform pursuit and escape maneuvers against the escaping drone.

[0006] According to the present invention, a game-theoretic control method for UAV pursuit and escape based on conserved manifold dimensionality reduction is provided, wherein the flight state parameters include mass parameters, position vectors, and velocity vectors; The construction of the Lagrange quantities of the game system based on the flight state parameters includes: Based on the mass parameter, the position vector, and the velocity vector, construct the Lagrange quantity of the game system; The Lagrange quantity includes a kinetic energy term, a potential energy term, and a utility functional term; the potential energy term is determined based on the relative distance between the pursuing drone and the escaping drone.

[0007] According to the present invention, a game-theoretic control method for UAV pursuit based on conserved manifold dimensionality reduction is provided, wherein the symmetry analysis of the Lagrange multiplier to obtain the conserved quantities corresponding to the intrinsic symmetry of the game system includes: Continuous transformation group analysis is performed on the Lagrange to obtain the infinitesimal transformation test conditions; If the variation of the Lagrange quantity under the infinitesimal transformation test condition satisfies the preset total derivative condition, then the game system is determined to have a target symmetry corresponding to the infinitesimal transformation test condition, and the symmetry generator corresponding to the target symmetry is determined; the target symmetry includes at least one of spatial translation symmetry, spatial rotation symmetry, and time translation symmetry. Based on Noether's theorem, partial derivatives of the symmetry generator and the Lagrange quantity are obtained to obtain conserved quantities including total momentum, total angular momentum, and total energy.

[0008] According to the present invention, a UAV pursuit and escape game control method based on conserved manifold dimensionality reduction is provided, wherein redundant state parameters in the game system are eliminated based on the conserved quantities to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and the dimensionality-reduced game equations are reconstructed on the low-dimensional conserved manifold, comprising: Using the total momentum conservation and the total angular momentum conservation as dynamic constraints, the motion of the system center of mass of the pursuing drone and the escaping drone in the game system is decoupled to obtain the relative motion state parameters. Based on the relative motion state parameters, a low-dimensional conserved manifold is constructed in the relative motion plane defined by the total angular momentum conservation, and a reduced-dimensional game equation based on the relative motion state parameters is constructed on the low-dimensional conserved manifold.

[0009] According to the present invention, a game-theoretic control method for UAV pursuit based on dimensionality reduction of a conserved manifold is provided, wherein the step of solving the dimensionality-reduced game equation on the low-dimensional conserved manifold with the conserved quantities as constraints to generate a game control strategy includes: In the unconstrained policy space, an update operation is performed along the negative gradient direction of the reduced-dimensional game equation to obtain a temporary policy; Using the total momentum conservation and the total angular momentum conservation as constraints, a quadratic programming optimization problem is constructed; The quadratic programming optimization problem is solved using the Lagrange multiplier method. Based on the solution, the temporary strategy is projected onto the low-dimensional conserved manifold to obtain the game control strategy.

[0010] According to the present invention, a game-theoretic control method for UAV pursuit and escape based on conserved manifold dimensionality reduction is provided, wherein the method controls the pursuing UAV to perform pursuit and escape maneuvers against the escaping UAV based on the game-theoretic control strategy, and further includes: The actual flight status parameters at the current time point are acquired in real time, and the real-time conserved quantities are determined based on the actual flight status parameters. Determine the conservation residual between the real-time conserved quantity and the baseline conserved quantity in the initial state of the game system; If the conserved residual is greater than the residual threshold, then the game system is determined to have symmetry breaking, and the breaking characteristics are determined. Add the environmental disturbance potential energy term corresponding to the broken feature to the Lagrange quantity, and remove the parameters that have lost their conservation properties from the conserved quantity to obtain the reconstructed Lagrange quantity; Based on the reconstructed Lagrange quantity, the dimension of the low-dimensional conserved manifold is dynamically updated, and a new game control strategy is generated on the updated low-dimensional conserved manifold.

[0011] This invention also provides a drone pursuit and escape game control system based on conserved manifold dimensionality reduction, comprising: The acquisition unit is used to acquire the flight state parameters of the pursuing drone and the escaping drone participating in the game in the game system, and to construct the Lagrange quantity of the game system based on the flight state parameters. The analysis unit is used to perform symmetry analysis on the Lagrange quantity to obtain the conserved quantity corresponding to the inherent symmetry of the game system. The reconstruction unit is used to eliminate redundant state parameters in the game system based on the conserved quantity, so as to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstruct the dimension-reduced game equation on the low-dimensional conserved manifold. The control unit is configured to solve the reduced-dimensional game equation on the low-dimensional conserved manifold with the conserved quantities as constraints, generate a game control strategy, and control the pursuing drone to perform pursuit and escape maneuvers against the escaping drone based on the game control strategy.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction as described above.

[0013] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction as described above.

[0014] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction as described above.

[0015] The UAV pursuit and escape game control method and system based on conserved manifold dimensionality reduction provided by this invention significantly reduces the solution complexity by mapping the high-dimensional game problem to a low-dimensional conserved manifold for solution, breaking through the computational bottleneck and meeting the requirements of real-time adversarial scenarios. At the same time, by using conserved quantities as constraints, the generated strategy naturally satisfies the physical conservation laws, eliminates non-physical artifacts, and improves the physical interpretability of the strategy and its execution security and robustness in real-world environments. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction provided by the present invention. Figure 2 This is a schematic diagram of the correspondence between symmetry and conserved quantities based on Noether's theorem provided by the present invention; Figure 3 This is a comparison diagram of the convergence trajectories of the strategies under the conservation manifold constraints provided by this invention; Figure 4 This is a schematic diagram of the UAV pursuit and escape game control system based on conserved manifold dimensionality reduction provided by the present invention; Figure 5 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] Currently, in high-dimensional dynamic game adversarial situations, such as multi-drone air combat, large-scale robot soccer, and financial market regulatory games, the mainstream technical means include differential game theory solutions, multi-agent reinforcement learning, and evolutionary game algorithms.

[0020] However, with the increasing number of game participants and the explosion of state space dimensions, existing technologies face severe challenges in practical applications. On the one hand, traditional differential game theory requires solving high-dimensional Hamiltonian-Jacobi-Isaks (HJI) partial differential equations, the computational complexity of which increases exponentially with the number of state variables. In real-time adversarial scenarios, existing numerical methods often fail to converge within milliseconds, easily leading to policy lag. On the other hand, existing data-driven methods, such as deep reinforcement learning, typically treat the game system as a black box, ignoring the system's inherent physical symmetries. This results in generated policies that frequently violate fundamental physical laws, such as energy non-conservation and momentum mutations, which can easily cause oscillations or loss of control when applied to real physical systems.

[0021] To address this, the present invention provides a UAV pursuit and escape game control method based on dimensionality reduction of conserved manifolds. It aims to start from first principles, utilize the inherent symmetry of the game system to uncover the corresponding physical conservation laws, and map the high-dimensional game problem onto a low-dimensional conserved manifold for dimensionality reduction and solution. This significantly reduces the solution complexity of the model, overcoming the computational bottleneck caused by the curse of dimensionality. Simultaneously, it uses conserved quantities as constraints to force the strategy evolution trajectory to satisfy physical laws, thereby ensuring the executability and security of the generated game control strategy in the real physical world.

[0022] Figure 1 This is a flowchart illustrating the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction provided by the present invention. The executing entity of this method can be the control system on the pursuing UAV or control terminal equipment such as vehicle-mounted / ground command centers, etc. Figure 1 As shown, the method includes: Step 110: Obtain the flight state parameters of the pursuing drone and the escaping drone participating in the game in the game system, and construct the Lagrange quantity of the game system based on the flight state parameters. Step 120: Perform symmetry analysis on the Lagrange quantity to obtain the conserved quantities corresponding to the inherent symmetry of the game system; Step 130: Eliminate redundant state parameters in the game system based on the conserved quantities to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstruct the dimension-reduced game equation on the low-dimensional conserved manifold. Step 140: On the low-dimensional conserved manifold, solve the reduced-dimensional game equation with conserved quantities as constraints to generate a game control strategy. Based on the game control strategy, control the pursuing drone to perform pursuit and escape maneuvers against the escaping drone.

[0023] Specifically, in actual combat scenarios, it is first necessary to acquire the state data of each party in a dynamic system involving multiple participants and existing adversarial and competitive relationships, i.e., a game system. In this specific embodiment of the invention, this could involve acquiring the flight state parameters of a pursuit drone tasked with proactive pursuit and interception, and an evasion drone tasked with evasion and breaching defenses. These flight state parameters describe the drone's motion state and physical properties in space, such as position, velocity, acceleration, attitude angle, angular velocity, and mass.

[0024] Next, based on the acquired flight state parameters, the Lagrangian of the game system (a core scalar function in classical mechanics describing the dynamic characteristics of a system) can be constructed. In a game system, the Lagrangian typically consists of the system's kinetic energy, potential energy, and utility functionals reflecting the goals or costs of the two players. By constructing the Lagrangian, the equilibrium problem of a multi-player game can be transformed into a controlled variational problem.

[0025] Once the Lagrange is constructed, its symmetry can be analyzed to obtain the conserved quantities corresponding to the inherent symmetry of the game system (i.e., the inherent symmetry of the game system, which is the physical symmetry law inherent in the system itself). That is, we study and test whether the Lagrange maintains its basic physical laws under continuous transformation groups, such as spatial translation, spatial rotation, and time translation. Figure 2 This is a schematic diagram of the correspondence between symmetry and conserved quantities based on Noether's theorem provided by this invention, as shown below. Figure 2 As shown, according to Noether's Theorem, every continuous symmetry inherent in a game system necessarily corresponds to a physical quantity that remains unchanged during the system's evolution, i.e., a conserved quantity.

[0026] Once the conserved quantity is obtained, it can be used to directly eliminate redundant state parameters in the game system that are no longer independent due to the constraint of the conserved quantity. This operation can compress and map the high-dimensional state space of the game system, which consists of all independent state variables, such as a 12-dimensional space containing 2 drones × 3-dimensional position × 3-dimensional velocity, to a low-dimensional conserved manifold limited by the conserved quantity, such as reducing the dimension to radial and tangential motion in a 2-dimensional relative plane, with only 4 effective state variables.

[0027] After this, the reduced-dimensional game equations of the game system can be re-established on the low-dimensional conserved manifold with significantly reduced dimensionality, that is, the reconstructed Hamilton-Jacobi-Isaks HJI equations. At this time, the value function is defined only in this low-dimensional subspace, and the amount of computation can be greatly reduced.

[0028] Finally, since the problem has been reduced to a low-dimensional conserved manifold, the Nash equilibrium can be solved within this low-dimensional manifold space. That is, the conserved quantities are used as hard constraints to solve the reduced-dimensional game equations. The optimal solution obtained under these constraints is the optimal maneuver control input sequence that satisfies the physical laws, i.e., the game control strategy. Ultimately, based on this game control strategy, control commands can be sent to the actuators of the pursuing drone to execute corresponding pursuit and escape maneuvers, such as acceleration, turning, climbing, and diving, thereby completing the countermeasures against the escaping drone.

[0029] The UAV pursuit and escape game control method based on conserved manifold dimensionality reduction provided by this invention significantly reduces the solution complexity by mapping the high-dimensional game problem to a low-dimensional conserved manifold for solution, breaking through the computational bottleneck and meeting the requirements of real-time adversarial scenarios. At the same time, by using conserved quantities as constraints, the generated strategy naturally satisfies the physical conservation laws, eliminating non-physical artifacts and improving the physical interpretability of the strategy as well as its execution security and robustness in real-world environments.

[0030] Based on the above embodiments, the flight state parameters include mass parameters, position vectors, and velocity vectors; in step 110, constructing the Lagrange quantities of the game system based on the flight state parameters includes: Construct the Lagrangian of the game system based on mass parameters, position vectors, and velocity vectors; The Lagrange quantity includes a kinetic energy term, a potential energy term, and a utility functional term; the potential energy term is determined based on the relative distance between the pursuing drone and the escaping drone.

[0031] Specifically, in order to accurately establish a basic model that reflects the physical laws and decision-making gains of both sides in the game, in this embodiment of the invention, the flight state parameters may include a mass parameter describing the inertial properties of the UAV, a position vector describing the absolute or relative coordinates of the UAV in space, and a velocity vector describing the speed and direction of the UAV's movement.

[0032] Once the complete set of kinematic physical quantities is determined, the Lagrangian of the game system can be constructed accordingly. Unlike the purely mathematical game model in traditional schemes that only focuses on payoffs, the Lagrangian constructed in this embodiment of the invention is a generalized energy function that integrates physical mechanisms and game theory features, specifically including kinetic energy, potential energy, and utility functional terms.

[0033] Here, the Lagrange quantity This can be expressed by the following formula: in, To pursue the drone and evading drones Quality parameters, and These are the velocity vectors of the pursuing drone and the escaping drone, respectively. and These are the position vectors for pursuing the drone and escaping the drone, respectively.

[0034] In the formula, the first term ( The first term is the kinetic energy term, used to characterize the total physical kinetic energy of the game system at the current speed, i.e., the sum of the kinetic energies of the pursuing drone and the escaping drone; the second term ( , The correlation coefficient is the potential energy term, which is determined based on the relative distance between the pursuing and escaping drones. This term is used to simulate the physical field of interaction between the two sides in space. For example, in a pursuit / escape scenario, the closer the distance, the lower the potential energy, thus naturally creating an attractive force that encourages approach or a repulsive force that drives evasion in the physical model; the third term (… , and The payment matrices are for chasing drones and escaping drones, respectively. and Then it is and The corresponding weights are utility functional terms used to introduce the specific task objectives and payoff functions of both sides in the game, which include the payoff matrix and weight allocation.

[0035] Based on the above Lagrange quantities, the Euler-Lagrange equations can be constructed using the principle of least action: ,in , , These are the velocity vector, position vector, and Lagrange quantity, respectively. To control the input (the actual strategy), the multi-party game equilibrium problem is transformed into a controlled variational problem.

[0036] In this embodiment of the invention, a Lagrangian encompassing kinetic energy, potential energy, and utility functionals is constructed using fundamental physical parameters such as mass, position, and velocity. In particular, the potential energy term is determined by utilizing relative distance, accurately unifying the real physical kinematic characteristics and game payoffs of both sides within the same energy functional framework. This realistically simulates the interaction of UAVs in physical space, thus laying a rigorous and accurate physical and mechanical model foundation for subsequent exploration of symmetry using first principles and transformation of game equilibrium problems into controlled variational problems. This avoids the problem of generation strategies violating physical laws from the outset.

[0037] Based on the above embodiments, step 120 includes: By performing continuous transformation group analysis on the Lagrange, the test conditions for infinitesimal transformations are obtained; If the variation of the Lagrange quantity under the infinitesimal transformation test condition satisfies the preset total derivative condition, then it is determined that the game system has a target symmetry corresponding to the infinitesimal transformation test condition, and the symmetry generator corresponding to the target symmetry is determined; the target symmetry includes at least one of spatial translational symmetry, spatial rotational symmetry and time translational symmetry; Based on Noether's theorem, partial derivatives of the symmetry generators and Lagrange quantities are obtained to obtain the conserved quantities including the total momentum, total angular momentum, and total energy.

[0038] Specifically, the process of performing symmetry analysis on the Lagrange to obtain the conserved quantities corresponding to the inherent symmetry of the game system can include: First, a continuous transformation group analysis can be performed on the Lagrange to obtain the infinitesimal transformation test conditions. Here, continuous transformation group analysis refers to Lie group analysis, that is, defining a transformation group that includes continuous operations such as time translation, spatial translation, spatial rotation, and internal gauge transformations. Based on this transformation group, the infinitesimal transformation test conditions are determined. For example, performing an infinitesimal transformation on the flight state parameters, such as... , and These are the flight state parameters before and after the transformation. For infinitesimal parameters, For the corresponding symmetry generator.

[0039] Next, verify the Lagrange diurnal quantity. Variation under infinitesimal transformation test conditions Whether the preset total derivative condition is met, i.e., verification Does the condition (that is, differing by a total derivative term) hold true (where...)? (These are boundary terms). If the equation holds, then the game system is determined to be invariant under this transformation, i.e., it possesses the corresponding objective symmetry. Simultaneously, the factors that make the equation hold are recorded. It is a symmetric generator.

[0040] In a game theory system, the system exists in a uniform space with no wind and no gravity gradient. The identified target symmetry can include at least one of spatial translational symmetry, spatial rotational symmetry, and time translational symmetry. For example, for any vector... Transformation At that time, since potential energy depends only on the relative distance Therefore, the Lagrange By keeping the symmetry constant, we can identify spatial translational symmetry and its corresponding symmetry generators; similarly, we can identify the symmetry generators corresponding to spatial rotational symmetry and temporal translational symmetry.

[0041] Then, based on Noether's theorem, partial derivatives can be calculated for the aforementioned symmetry generators and Lagrange quantities to obtain the conserved quantities including total momentum, total angular momentum, and total energy. Specifically, according to Noether's theorem, for each symmetry generator, the corresponding conserved quantities can be obtained by solving the partial derivatives. For example, the three core conserved quantities can be precisely derived: (1) The total momentum conservation quantity derived from spatial translation symmetry , The vector of total momentum constant; (2) The total angular momentum conservation quantity is derived from the rotational symmetry of space. , The vector of total angular momentum constant; (3) The total energy conservation quantity derived from time translation symmetry ,in, This represents the total energy value. For the overall function, that is ; The total potential energy, i.e. .

[0042] These three factors together constitute the conserved quantities of the game system, providing a physical constraint basis for subsequent dimensionality reduction and reconstruction.

[0043] In this embodiment of the invention, by introducing continuous transformation group analysis and Noether's theorem, the target symmetry such as spatial translation, spatial rotation, and time translation of the Lagrange quantity is identified using infinitesimal transformation tests. Based on this, the conserved quantities such as total momentum, total angular momentum, and total energy are solved by partial derivatives. This realizes an automated mapping mechanism from a pure mathematical game model to a rigorous physical mechanics model. It can automatically and accurately discover the inherent physical conservation laws of the game system without relying on human prior experience. This not only makes the generated game strategy naturally subject to the hard constraints of real physical laws, but also greatly improves the rationality and feasibility of UAV control strategies in the real physical world. It also provides theoretical support for the reliable dimensionality reduction of high-dimensional game state space to low-dimensional manifold.

[0044] Based on the above embodiments, step 130 includes: Using the conservation of total momentum and total angular momentum as dynamic constraints, the motion of the system's center of mass in the game system is decoupled from that of the pursuing drone and the escaping drone, and the relative motion state parameters are obtained. Based on the relative motion state parameters, a low-dimensional conserved manifold is constructed in the relative motion plane defined by the total angular momentum conservation, and a dimension-reduced game equation based on the relative motion state parameters is constructed on the low-dimensional conserved manifold.

[0045] Specifically, the process of eliminating redundant state parameters in the game system based on conserved quantities to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstructing the dimension-reduced game equations on the low-dimensional conserved manifold, can specifically include: After deriving the conserved quantities, in order to overcome the computational bottleneck of solving high-dimensional partial differential equations, in this embodiment of the invention, the conservation of total momentum and total angular momentum can be used as dynamic constraints to decouple the center-of-mass motion. That is, since the absolute motion coordinates of the UAV in the air contain a lot of redundant information for the nature of the pursuit and escape confrontation, the conservation of total momentum and total angular momentum can be directly used as strict dynamic constraints. For example, if the state space of the game system is 12-dimensional, the total momentum conservation equation can be used... It can precisely decouple and separate the shared system centroid motion of both sides in the game. In other words, because the centroid is in a constant state of motion, it no longer affects the relative pursuit and escape posture of both sides. By decoupling, redundant variables related to absolute motion can be eliminated, thereby extracting the relative motion state parameters that truly determine the outcome of the game.

[0046] After decoupling the center of mass motion, the equation of conservation of total angular momentum is then applied. According to the principles of physics, the conservation of total angular momentum means that the relative motion trajectories of two drones will be strictly restricted to a fixed two-dimensional plane, that is, the relative motion plane defined by the conservation of total angular momentum. Therefore, the originally complex three-dimensional space chasing problem can be mapped and restricted to radial and tangential motion within this relative motion plane.

[0047] After the two constraint eliminations described above, the original 12-dimensional high-dimensional space was successfully compressed, leaving only 4 valid state variables. The reduced-dimensional space formed by these 4 valid state variables is the low-dimensional conserved manifold. Subsequently, in this low-dimensional subspace The intrinsically defined value function is used to reconstruct the dimension-reduced Hamilton-Jacobi-Isaks (HJI) partial differential equation, i.e., the dimension-reduced game equation.

[0048] In this embodiment of the invention, by using the conservation of total momentum and total angular momentum as dynamic constraints, the motion of the center of mass of the two-machine system is decoupled, and the relative motion is restricted to a two-dimensional plane defined by angular momentum. This compresses and maps the massive high-dimensional state space onto a low-dimensional conserved manifold with very few effective variables to reconstruct the game equations, completely eliminating redundant state parameters. This significantly reduces the computational cost of the reconstructed dimensionality-reduced game equations, solving the problems of the curse of dimensionality and exponential computational bottleneck faced by traditional high-dimensional differential game solving. This lays the foundation for generating convergent game strategies in real time within milliseconds.

[0049] Based on the above embodiments, in step 140, the reduced-dimensional game equation is solved on the low-dimensional conserved manifold using conserved quantities as constraints to generate a game control strategy, including: In the unconstrained policy space, update operations are performed along the negative gradient direction of the reduced-dimensional game equation to obtain a temporary policy; With the conservation of total momentum and total angular momentum as constraints, a quadratic programming optimization problem is constructed; Solving quadratic programming optimization problems based on the Lagrange multiplier method; Based on the solution results, the temporary strategy is projected onto a low-dimensional conserved manifold to obtain the game control strategy.

[0050] Specifically, the process of solving the reduced-dimensional game equation on a low-dimensional conserved manifold with conserved quantities as constraints to generate a game control strategy can include: After dimensionality reduction, the final Nash equilibrium strategy needs to be determined. However, since traditional gradient algorithms are prone to getting stuck in local Nash equilibria or limit cycle oscillations in non-convex game landscapes, this invention proposes a conservation-guided prediction-projection iterative solution mechanism.

[0051] In detail, the process begins with prediction, which involves updating the policy along the negative gradient direction of the reduced-dimensional game equation in the unconstrained policy space to obtain a temporary policy. Here, the unconstrained policy space refers to the traditional policy search domain that has not been subject to any physical constraints. Within this space, the gradient of the reduced-dimensional game equation (such as the Hamiltonian H corresponding to the HJI equation) is calculated. And update the policy of the previous round along the negative gradient direction, such as... ,in and The first Wheel and Wheel strategy, Using a step size, a temporary strategy with exploratory properties can be obtained. Since the prediction process only pursues mathematical extrema, this temporary strategy often violates the physical mechanism of the game system, such as causing momentum mutations.

[0052] To correct this physical discrepancy, projection is required, that is, constructing a quadratic programming optimization problem with the conservation of total momentum and total angular momentum as constraints. Specifically, this involves using the conservation of total momentum and total angular momentum to maintain physical consistency as hard constraints, and minimizing the distance difference between the actual strategy and the temporary strategy as the optimization objective, thus constructing a standard quadratic programming optimization problem. The mathematical model of this problem can be expressed as: Solving... , and These are the actual strategy and the temporary strategy, respectively.

[0053] Subsequently, the quadratic programming optimization problem is solved using the Lagrange multiplier method, and the temporary strategy is projected onto a low-dimensional conserved manifold based on the solution to obtain the game control strategy. That is, the Lagrange multiplier method is introduced to analytically solve the aforementioned quadratic programming problem. Figure 3 This is a comparison diagram of the convergence trajectories of the strategy under the conservation manifold constraint provided by this invention, as shown in the figure. Figure 3 As shown, the trajectory of traditional gradient methods often diverges or oscillates freely in invalid regions, while in this embodiment of the invention, the orthogonal projection operator ( This forces the temporary strategy, which originally deviated from the laws of physics, back onto a lower-dimensional conserved manifold. On the curved surface. The strategy for output after projection. This is the game control strategy for the current iteration round. This process iterates cyclically, and when both the strategy change and the residual of the conserved quantity are less than a set threshold, the final Nash equilibrium strategy is output, ensuring that the updated velocity or control law strictly satisfies the conservation of momentum and angular momentum.

[0054] In this embodiment of the invention, based on unconstrained gradient update prediction, orthogonal projection using quadratic programming and the Lagrange multiplier method with momentum and angular momentum conservation constraints is introduced. This tightly restricts the strategy search space to a physically valid low-dimensional conserved manifold. On the one hand, the conserved manifold restricts the exploration of invalid regions, and the conserved quantities, as natural Lyapunov functions, theoretically guarantee the global asymptotic stability of the algorithm in non-convex game scenarios, effectively avoiding getting trapped in local optima or limit cycle oscillations. On the other hand, the projection iteration mechanism ensures that the algorithm converges extremely quickly (experiments show that it converges 5 times faster than the traditional PRD (Pseudo-Random Distribution) algorithm), and the game control strategy generated in each iteration strictly adheres to physical conservation laws, providing extremely high physical interpretability and robustness for the pursuit-escape game decision-making.

[0055] Based on the above embodiments, in step 140, based on a game-theoretic control strategy, the pursuing drone is controlled to perform pursuit and escape maneuvers against the evading drone, and then the process further includes: The actual flight status parameters at the current time point are obtained in real time, and the real-time conserved quantities are determined based on the actual flight status parameters; Determine the conservation residual between the real-time conserved quantity and the baseline conserved quantity in the initial state of the game system; If the conserved residual is greater than the residual threshold, then the game system is determined to have symmetry broken, and the breaking characteristics are determined. Add the environmental perturbation potential energy term corresponding to the broken feature to the Lagrange quantity, and remove the parameters that have lost their conservation properties from the conserved quantities to obtain the reconstructed Lagrange quantity; Based on the reconstructed Lagrange quantity, the dimension of the low-dimensional conserved manifold is dynamically updated, and a new game control strategy is generated on the updated low-dimensional conserved manifold.

[0056] Specifically, during the actual execution of combat missions by UAVs, the pursuit and escape environment is often complex and dynamically changing, such as sudden gusts of wind, airflow disturbances, and load changes. Therefore, after issuing instructions to the execution mechanism and controlling the pursuit UAV to perform pursuit and escape maneuvers against the escaping UAV, adaptive environmental monitoring can also be carried out.

[0057] In detail, the actual flight state parameters at the current time point can be obtained in real time, and real-time conserved quantities can be determined accordingly. That is, due to the possibility of small or sudden disturbances in the environment, it is necessary to continuously collect the UAV's motion state data at the current time point, i.e., the actual flight state parameters. Then, these real-time data are substituted into the previously derived conservation equations to calculate the current physical values, i.e., real-time conserved quantities, such as the real-time total momentum conservation quantity.

[0058] Next, the conservation residuals between the real-time conserved quantities and the baseline conserved quantities in the initial state of the game system need to be calculated. Here, the baseline conserved quantities refer to the constant vectors calculated from the initial state under ideal, undisturbed conditions at the start of the game and considered constant. By calculating the degree of deviation between the real-time values ​​and the baseline values, the conservation residuals are obtained, serving as a quantitative indicator of how much the current state of the game system deviates from the ideal physical conservation model.

[0059] If the conserved residuals exceed a pre-set residual threshold, the game system is determined to have experienced symmetry breaking, and the breaking characteristics are identified. Specifically, when the conserved residuals exceed the residual threshold, indicating a breaking, it means that the external environment has applied additional forces or energy, disrupting the original physical symmetry of the game system. Therefore, symmetry breaking is determined. By analyzing the direction and magnitude of the changes in the conserved residuals, breaking characteristics can be extracted. For example, it can be identified that a unidirectional strong wind disturbance has caused the loss of spatial translational symmetry.

[0060] Upon sensing a sudden environmental change, a model reconstruction mechanism is triggered. This involves explicitly modeling external disturbances (such as sudden external forces) into the original Lagrangian. For example, a wind resistance potential energy term or a dissipation term (i.e., an environmental disturbance potential energy term) caused by strong winds can be added to the Lagrangian. Subsequently, conserved quantities are recalculated, and physical quantities that no longer remain constant due to symmetry breaking (i.e., parameters that have lost their conservation properties, such as momentum that is no longer conserved after wind resistance) are removed. This process corrects and establishes a new Lagrangian, which is known as the reconstructed Lagrangian.

[0061] Finally, the dimension of the low-dimensional conserved manifold can be dynamically updated based on the reconstructed Lagrangian, and a new game control strategy can be generated on the updated low-dimensional conserved manifold. That is, since the conserved quantities have changed, the original dimensionality reduction constraints also change accordingly, so the dimension of the low-dimensional conserved manifold needs to be adjusted. The projection gradient algorithm can then be run on the updated manifold space to obtain a game control strategy that counteracts sudden environmental changes, i.e., a new game control strategy.

[0062] In this embodiment of the invention, by establishing an environmental perception and monitoring mechanism with the residual of the conserved quantity as the core, and combining the residual threshold to determine symmetry breaking, a perturbation term is introduced into the Lagrange quantity to dynamically update the dimension of the conserved manifold and the game strategy, which endows the game system with strong environmental adaptability and anti-interference robustness. When the adversarial environment changes abruptly (such as encountering wind field interference or load changes), it can keenly perceive the deviation of physical laws and immediately reconstruct the underlying physical model without manual intervention or time-consuming retraining. This ensures that the UAV swarm can still maintain high efficiency and high reliability of distributed game decision-making in a complex and ever-changing real adversarial environment with unknown perturbations.

[0063] It should be noted that, in addition to its application in drone pursuit games, the method provided by this invention can also be flexibly extended and applied to complex adversarial scenarios such as high-frequency financial market maker games. Specifically, in high-frequency quantitative trading and market maker games in financial markets, the state space of the financial game system has extremely high dimensionality and changes very rapidly. For this scenario, the method provided by this invention, after constructing the basic model of the game system, performs symmetry analysis on it, thereby identifying that under the closed market assumption, the financial game system possesses internal normative symmetry.

[0064] Based on the aforementioned internal normative symmetry, and according to Noether's theorem, the corresponding conserved quantity, namely the conservation of total funds, can be derived. In the subsequent model dimensionality reduction and Nash equilibrium strategy solution process, this conserved fund quantity can be used as a hard constraint, explicitly embedded into the optimality conditions of the game, to strictly constrain the generation trajectory of order flow.

[0065] By solving this problem using a dimensionality reduction and constraint method based on the conservation of capital manifold, we can prevent the generation of false arbitrage strategies that cause the total capital in the market to increase or decrease out of thin air, from the underlying logic and mechanism. This strict constraint at the physical mechanism level completely eliminates the unrealistic artifacts that are easily generated in financial deduction by traditional black box models, thereby ensuring that the capital curve of the generated trading strategy can converge smoothly in long-term backtesting and in real trading environments, and greatly improving the global stability and live robustness of high-frequency quantitative trading strategies.

[0066] The UAV pursuit and escape game control system based on conserved manifold dimensionality reduction provided by the present invention is described below. The UAV pursuit and escape game control system based on conserved manifold dimensionality reduction described below can be referred to in correspondence with the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction described above.

[0067] Figure 4 This is a schematic diagram of the UAV pursuit and escape game control system based on conserved manifold dimensionality reduction provided by the present invention, as shown below. Figure 4 As shown, the system includes: The acquisition unit 410 is used to acquire the flight state parameters of the pursuing drone and the escaping drone participating in the game in the game system, and to construct the Lagrange quantity of the game system based on the flight state parameters. Analysis unit 420 is used to perform symmetry analysis on the Lagrange quantity to obtain the conserved quantity corresponding to the inherent symmetry of the game system; The reconstruction unit 430 is used to eliminate redundant state parameters in the game system based on the conserved quantity, so as to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstruct the dimension-reduced game equation on the low-dimensional conserved manifold. The control unit 440 is used to solve the reduced-dimensional game equation on the low-dimensional conserved manifold with the conserved quantity as a constraint, generate a game control strategy, and control the pursuing drone to perform pursuit and escape maneuvers against the escaping drone based on the game control strategy.

[0068] The UAV pursuit and escape game control system provided by this invention significantly reduces the solution complexity by mapping the high-dimensional game problem to a low-dimensional conserved manifold for solution, breaking through the computational bottleneck and meeting the requirements of real-time adversarial scenarios. At the same time, by using conserved quantities as constraints, the generated strategy naturally satisfies the physical conservation laws, eliminating non-physical artifacts and improving the physical interpretability of the strategy as well as its execution security and robustness in real-world environments.

[0069] Based on the above embodiments, the flight state parameters include mass parameters, position vector, and velocity vector; the acquisition unit 410 is used for: Based on the mass parameter, the position vector, and the velocity vector, construct the Lagrange quantity of the game system; The Lagrange quantity includes a kinetic energy term, a potential energy term, and a utility functional term; the potential energy term is determined based on the relative distance between the pursuing drone and the escaping drone.

[0070] Based on the above embodiments, the analysis unit 420 is used for: Continuous transformation group analysis is performed on the Lagrange to obtain the infinitesimal transformation test conditions; If the variation of the Lagrange quantity under the infinitesimal transformation test condition satisfies the preset total derivative condition, then the game system is determined to have a target symmetry corresponding to the infinitesimal transformation test condition, and the symmetry generator corresponding to the target symmetry is determined; the target symmetry includes at least one of spatial translation symmetry, spatial rotation symmetry, and time translation symmetry. Based on Noether's theorem, partial derivatives of the symmetry generator and the Lagrange quantity are obtained to obtain conserved quantities including total momentum, total angular momentum, and total energy.

[0071] Based on the above embodiments, the reconstruction unit 430 is used for: Using the total momentum conservation and the total angular momentum conservation as dynamic constraints, the motion of the system center of mass of the pursuing drone and the escaping drone in the game system is decoupled to obtain the relative motion state parameters. Based on the relative motion state parameters, a low-dimensional conserved manifold is constructed in the relative motion plane defined by the total angular momentum conservation, and a reduced-dimensional game equation based on the relative motion state parameters is constructed on the low-dimensional conserved manifold.

[0072] Based on the above embodiments, the control unit 440 is used for: In the unconstrained policy space, an update operation is performed along the negative gradient direction of the reduced-dimensional game equation to obtain a temporary policy; Using the total momentum conservation and the total angular momentum conservation as constraints, a quadratic programming optimization problem is constructed; The quadratic programming optimization problem is solved using the Lagrange multiplier method. Based on the solution, the temporary strategy is projected onto the low-dimensional conserved manifold to obtain the game control strategy.

[0073] Based on the above embodiments, the system further includes an update unit, used for: The actual flight status parameters at the current time point are acquired in real time, and the real-time conserved quantities are determined based on the actual flight status parameters. Determine the conservation residual between the real-time conserved quantity and the baseline conserved quantity in the initial state of the game system; If the conserved residual is greater than the residual threshold, then the game system is determined to have symmetry breaking, and the breaking characteristics are determined. Add the environmental disturbance potential energy term corresponding to the broken feature to the Lagrange quantity, and remove the parameters that have lost their conservation properties from the conserved quantity to obtain the reconstructed Lagrange quantity; Based on the reconstructed Lagrange quantity, the dimension of the low-dimensional conserved manifold is dynamically updated, and a new game control strategy is generated on the updated low-dimensional conserved manifold.

[0074] Figure 5 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 5As shown, the electronic device may include: a processor 510, a communications interface 520, a memory 530, and a communications bus 540, wherein the processor 510, the communications interface 520, and the memory 530 communicate with each other through the communications bus 540. The processor 510 can call logic instructions in the memory 530 to execute a drone pursuit-escape game control method based on conserved manifold dimensionality reduction. This method includes: acquiring flight state parameters of the pursuing drone and the escaping drone participating in the game system, and constructing the Lagrange quantity of the game system based on the flight state parameters; performing symmetry analysis on the Lagrange quantity to obtain the conserved quantity corresponding to the inherent symmetry of the game system; eliminating redundant state parameters in the game system based on the conserved quantity to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstructing the dimensionality-reduced game equation on the low-dimensional conserved manifold; solving the dimensionality-reduced game equation on the low-dimensional conserved manifold with the conserved quantity as a constraint to generate a game control strategy; and controlling the pursuing drone to perform pursuit-escape maneuvers against the escaping drone based on the game control strategy.

[0075] Furthermore, the logical instructions in the aforementioned memory 530 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0076] On the other hand, the present invention also provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, which, when executed by a computer, enable the computer to execute the UAV pursuit-escape game control method based on conserved manifold dimensionality reduction provided by the above methods. This method comprises: acquiring flight state parameters of the pursuing UAV and the escaping UAV participating in the game system, and constructing the Lagrange quantity of the game system based on the flight state parameters; performing symmetry analysis on the Lagrange quantity to obtain the conserved quantity corresponding to the inherent symmetry of the game system; eliminating redundant state parameters in the game system based on the conserved quantity to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstructing the dimensionality-reduced game equation on the low-dimensional conserved manifold; solving the dimensionality-reduced game equation on the low-dimensional conserved manifold with the conserved quantity as a constraint to generate a game control strategy; and controlling the pursuing UAV to perform pursuit-escape maneuvers against the escaping UAV based on the game control strategy.

[0077] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the above-described method for UAV pursuit and escape game control based on conserved manifold dimensionality reduction. The method includes: acquiring flight state parameters of the pursuing UAV and the escaping UAV participating in the game system, and constructing the Lagrange quantity of the game system based on the flight state parameters; performing symmetry analysis on the Lagrange quantity to obtain the conserved quantity corresponding to the inherent symmetry of the game system; eliminating redundant state parameters in the game system based on the conserved quantity to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstructing the dimensionality-reduced game equation on the low-dimensional conserved manifold; solving the dimensionality-reduced game equation on the low-dimensional conserved manifold with the conserved quantity as a constraint to generate a game control strategy; and controlling the pursuing UAV to perform pursuit and escape maneuvers against the escaping UAV based on the game control strategy.

[0078] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0079] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A game-theoretic control method for UAV pursuit and escape based on conserved manifold dimensionality reduction, characterized in that, include: Obtain the flight state parameters of the pursuing drone and the escaping drone participating in the game system, and construct the Lagrange quantity of the game system based on the flight state parameters; Symmetry analysis of the Lagrange quantity yields the conserved quantities corresponding to the inherent symmetry of the game system. Based on the conserved quantities, redundant state parameters in the game system are eliminated to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and the dimension-reduced game equations are reconstructed on the low-dimensional conserved manifold. On the low-dimensional conserved manifold, the reduced-dimensional game equation is solved with the conserved quantities as constraints to generate a game control strategy. Based on the game control strategy, the pursuing drone is controlled to perform pursuit and escape maneuvers against the escaping drone.

2. The UAV pursuit and escape game control method based on conserved manifold dimensionality reduction according to claim 1, characterized in that, The flight state parameters include mass parameters, position vector, and velocity vector; The construction of the Lagrange quantities of the game system based on the flight state parameters includes: Based on the mass parameter, the position vector, and the velocity vector, construct the Lagrange quantity of the game system; The Lagrange quantity includes a kinetic energy term, a potential energy term, and a utility functional term; the potential energy term is determined based on the relative distance between the pursuing drone and the escaping drone.

3. The UAV pursuit and escape game control method based on conserved manifold dimensionality reduction according to claim 1, characterized in that, The symmetry analysis of the Lagrange multiplier yields the conserved quantities corresponding to the intrinsic symmetry of the game system, including: Continuous transformation group analysis is performed on the Lagrange to obtain the infinitesimal transformation test conditions; If the variation of the Lagrange quantity under the infinitesimal transformation test condition satisfies the preset total derivative condition, then the game system is determined to have a target symmetry corresponding to the infinitesimal transformation test condition, and the symmetry generator corresponding to the target symmetry is determined; the target symmetry includes at least one of spatial translation symmetry, spatial rotation symmetry, and time translation symmetry. Based on Noether's theorem, partial derivatives of the symmetry generator and the Lagrange quantity are obtained to obtain conserved quantities including total momentum, total angular momentum, and total energy.

4. The UAV pursuit and escape game control method based on conserved manifold dimensionality reduction according to claim 3, characterized in that, The process of eliminating redundant state parameters in the game system based on the conserved quantities to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstructing the dimension-reduced game equations on the low-dimensional conserved manifold, includes: Using the total momentum conservation and the total angular momentum conservation as dynamic constraints, the motion of the system center of mass of the pursuing drone and the escaping drone in the game system is decoupled to obtain the relative motion state parameters. Based on the relative motion state parameters, a low-dimensional conserved manifold is constructed in the relative motion plane defined by the total angular momentum conservation, and a reduced-dimensional game equation based on the relative motion state parameters is constructed on the low-dimensional conserved manifold.

5. The UAV pursuit and escape game control method based on conserved manifold dimensionality reduction according to claim 4, characterized in that, The process of solving the reduced-dimensional game equation on the low-dimensional conserved manifold, using the conserved quantities as constraints, to generate a game control strategy includes: In the unconstrained policy space, an update operation is performed along the negative gradient direction of the reduced-dimensional game equation to obtain a temporary policy; Using the total momentum conservation and the total angular momentum conservation as constraints, a quadratic programming optimization problem is constructed; The quadratic programming optimization problem is solved using the Lagrange multiplier method. Based on the solution, the temporary strategy is projected onto the low-dimensional conserved manifold to obtain the game control strategy.

6. The UAV pursuit and escape game control method based on conserved manifold dimensionality reduction according to any one of claims 1 to 5, characterized in that, The step of controlling the pursuing drone to perform pursuit and escape maneuvers against the escaping drone based on the game-theoretic control strategy further includes: The actual flight status parameters at the current time point are acquired in real time, and the real-time conserved quantities are determined based on the actual flight status parameters. Determine the conservation residual between the real-time conserved quantity and the baseline conserved quantity in the initial state of the game system; If the conserved residual is greater than the residual threshold, then the game system is determined to have symmetry breaking, and the breaking characteristics are determined. Add the environmental disturbance potential energy term corresponding to the broken feature to the Lagrange quantity, and remove the parameters that have lost their conservation properties from the conserved quantity to obtain the reconstructed Lagrange quantity; Based on the reconstructed Lagrange quantity, the dimension of the low-dimensional conserved manifold is dynamically updated, and a new game control strategy is generated on the updated low-dimensional conserved manifold.

7. A game-theoretic control system for unmanned aerial vehicle (UAV) pursuit and escape based on conserved manifold dimensionality reduction, characterized in that, include: The acquisition unit is used to acquire the flight state parameters of the pursuing drone and the escaping drone participating in the game in the game system, and to construct the Lagrange quantity of the game system based on the flight state parameters. The analysis unit is used to perform symmetry analysis on the Lagrange quantity to obtain the conserved quantity corresponding to the inherent symmetry of the game system. The reconstruction unit is used to eliminate redundant state parameters in the game system based on the conserved quantity, so as to map the high-dimensional state space of the game system to a low-dimensional conserved manifold, and reconstruct the dimension-reduced game equation on the low-dimensional conserved manifold. The control unit is configured to solve the reduced-dimensional game equation on the low-dimensional conserved manifold with the conserved quantities as constraints, generate a game control strategy, and control the pursuing drone to perform pursuit and escape maneuvers against the escaping drone based on the game control strategy.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the UAV pursuit and escape game control method based on conserved manifold dimensionality reduction as described in any one of claims 1 to 6.

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