Method for intercepting maneuvering target based on linear quadratic differential game proportional guidance

Abstract

The application discloses a method for intercepting a maneuvering target based on linear quadratic differential game proportional guidance, which comprises the following steps: obtaining a meeting state quantity and constructing a locally linearized relative lateral dynamic equation rate based on the two-dimensional relative motion relationship between a pursuit side and a target; describing the locally linearized relative lateral dynamic equation as a finite time domain zero-sum linear quadratic differential game, constructing a lateral deviation and lateral velocity approximate state vector according to the meeting state quantity, and solving an optimal lateral control quantity of the pursuit side; corresponding the optimal lateral control quantity of the pursuit side with a proportional guidance law, calculating an instruction angular velocity of the pursuit side, and realizing online interception of the target. The application can realize real-time adjustment of the heading angular velocity of a fixed-wing unmanned aerial vehicle, and improve the success rate of online interception of a target rotor-wing unmanned aerial vehicle. The application can be widely applied to the technical field of maneuvering target interception.

Description

Technical Field

[0001] This invention relates to the field of maneuvering target interception technology, and in particular to a maneuvering target interception method based on linear quadratic differential game proportional guidance. Background Technology

[0002] Among existing UAV interception and pursuit control methods, proportional guidance is widely used due to its simple structure and convenient engineering implementation. However, traditional proportional guidance usually uses fixed navigation coefficients, which are difficult to adaptively adjust to changes in target maneuvering, closing velocity, line-of-sight angular rate, and relative geometry. When the target exhibits maneuvering behaviors such as returning to base, evasion, or sudden changes in course, fixed-parameter guidance laws are prone to problems such as insufficient response, conservative control, or reduced interception efficiency.

[0003] On the other hand, differential game theory methods can characterize the optimal strategies of both sides from the perspective of the adversarial relationship between the pursuer and the target, but their direct output is usually the optimal lateral control variable or state feedback matrix, which is not easy to directly embed into existing proportional guidance structures in engineering. If a complex optimization controller is used directly, it may also bring problems such as high real-time computation pressure, weak parameter interpretability, and poor compatibility with existing flight control architectures. Summary of the Invention

[0004] To address the aforementioned technical problems, the purpose of this invention is to provide a maneuvering target interception method based on linear quadratic differential game proportional guidance, which can achieve real-time adjustment of the heading angular velocity of fixed-wing UAVs and improve the success rate of online interception of target rotary-wing UAVs.

[0005] The first technical solution adopted in this invention is: a maneuvering target interception method based on linear quadratic differential game proportional guidance, comprising the following steps: Based on the two-dimensional relative motion relationship between the pursuing fixed-wing UAV and the target rotary-wing UAV, the rendezvous state variables are obtained and the relative lateral dynamic equations after local linearization are constructed. The rendezvous state variables include relative distance, closing velocity and line-of-sight angular rate. The relative lateral dynamic equation after local linearization is described as a finite-time zero-sum linear quadratic differential game. Based on the intersection state variables, an approximate state vector of lateral deviation and lateral velocity is constructed, and the optimal lateral control quantity of the pursuer is obtained. By mapping the optimal lateral control quantity of the pursuer to the proportional guidance law and calculating the command angular velocity of the pursuer's fixed-wing UAV, online interception of the target rotary-wing UAV is achieved.

[0006] Furthermore, the step of obtaining the rendezvous state variables and constructing the locally linearized relative lateral dynamic equations based on the two-dimensional relative motion relationship between the pursuing fixed-wing UAV and the target rotary-wing UAV specifically includes: Set the position, velocity, and normal acceleration of the pursuing fixed-wing UAV and the target rotary-wing UAV respectively, and determine the intersection geometry. Based on the intersection geometry, determine the relative distance and line-of-sight angular rate between the pursuing fixed-wing UAV and the target rotary-wing UAV; Based on the inertial coordinate system, and combining the position and velocity information of the pursuing fixed-wing UAV and the target rotary-wing UAV, the kinematic equations of the pursuing and target UAVs are constructed. Based on the kinematic equations of the pursuer and the target, the heading angles of the pursuer and the target are introduced, the relative position vectors of the pursuer and the target are defined, and the closing velocity is obtained. Based on the assumptions of small-angle linearization and short-time scale, the nonlinear pursuit problem is approximated as a relative lateral motion problem. The lateral deviation and lateral velocity are taken as state variables, and the relative lateral dynamic equations after local linearization are constructed.

[0007] Furthermore, the kinematic equations of the pursuing and target parties are specifically expressed as follows: In the above formula, This indicates the speed of the pursuing fixed-wing drone. Indicates the speed of the target rotary-wing drone. Indicates the heading angle of the pursuing party. Indicates the heading angle of the target. This indicates that the pursuing fixed-wing drone was in velocity components in the direction, This indicates that the pursuing fixed-wing drone was in velocity components in the direction, Indicates the target rotary-wing drone in velocity components in the direction, Indicates the target rotary-wing drone in The velocity component in the direction.

[0008] Furthermore, the step of describing the locally linearized relative lateral dynamic equation as a finite-time zero-sum linear quadratic differential game, constructing approximate state vectors of lateral deviation and lateral velocity based on the intersection state variables, and obtaining the optimal lateral control quantity for the pursuing party specifically includes: Based on the relative lateral dynamics equation after local linearization, the guidance confrontation between the pursuer and the target is described as a finite-time zero-sum linear quadratic differential game. Based on finite-time zero-sum linear quadratic differential game, a performance index function is constructed by setting the state weight matrix, the pursuer's control weight, the target's control weight, and the prediction time domain. Based on the performance index function, the pursuing party's control matrix and the target party's control matrix are set to form an equivalent adversarial matrix, and the Riccati differential equation is integrated in reverse to obtain the feedback matrix at the current time. Based on the rendezvous state variables, construct approximate state vectors for lateral deviation and lateral velocity, and combine them with the feedback matrix at the current moment to obtain the optimal lateral control variable for the pursuing party.

[0009] Furthermore, the expression for the performance index function is as follows: In the above formula, Represents a performance metric function. Represents the finite prediction time domain. Represents the state weight matrix. This indicates that the pursuing side controls the weight. Indicates the target party's control weight. Represents the terminal weight matrix. Represents the system state vector. This indicates the control input of the pursuing party. This represents the control input from the target side.

[0010] Furthermore, the specific expression of the Riccati differential equation is as follows: In the above formula, Indicates the target party's control weight. Represents the terminal weight matrix. Represents the state weight matrix. This represents the first derivative of matrix P with respect to time, i.e., the rate of change of the Riccati matrix with respect to time. The Riccati matrix, representing the coefficient matrix corresponding to the optimal value function, is used to characterize the impact of state variables on performance indicators during game optimization. This represents the system state matrix, used to describe the natural evolution of the system state under no control input. This represents the control input matrix of the pursuing party, used to describe how the pursuing party's control input affects changes in the system state. This represents the target control input matrix, which describes how the target control quantity affects changes in the system state.

[0011] Furthermore, the expression for the optimal lateral control quantity of the pursuing party is as follows: In the above formula, This represents the feedback matrix at the current moment. This indicates that the pursuing side controls the weight. Indicates the target party's control weight. Indicates the current time The system state vector, Indicates the current time The optimal control input for the pursuing side. Indicates the current time The optimal control input for the target side. This represents the attacking control input matrix. This represents the target control input matrix.

[0012] Furthermore, the step of mapping the optimal lateral control quantity of the pursuer to the proportional guidance law and calculating the command angular velocity of the pursuer's fixed-wing UAV to achieve online interception of the target rotary-wing UAV specifically includes: The optimal lateral control quantity of the pursuing party is mapped to the proportional guidance law, and the candidate values ​​of the equivalent navigation coefficients are calculated. The candidate values ​​of the equivalent navigation coefficients are subjected to amplitude limiting to obtain the equivalent navigation coefficients that meet the engineering constraints; Based on the equivalent navigation coefficients that satisfy engineering constraints, the commanded angular velocity of the pursuing fixed-wing UAV is calculated. The heading of the pursuing fixed-wing UAV is then updated in conjunction with the maximum turning radius or angular velocity saturation constraints, thereby achieving online interception of the target rotary-wing UAV.

[0013] Furthermore, in the process of calculating the candidate values ​​of the equivalent navigation coefficients, if the line-of-sight angular rate is zero, it is necessary to switch to a degenerate solution form based on the elements of the feedback matrix.

[0014] Furthermore, the expression for the proportional guidance law is as follows: In the above formula, This indicates the lateral acceleration command from the pursuing party. This represents the equivalent proportionality coefficient. Indicates the line-of-sight angular rate. This indicates the closing velocity.

[0015] The beneficial effects of this invention are as follows: This invention obtains the rendezvous state variables and constructs a locally linearized relative lateral dynamic equation based on the two-dimensional relative motion relationship between the pursuing fixed-wing UAV and the target rotary-wing UAV. Furthermore, it describes the locally linearized relative lateral dynamic equation as a finite-time zero-sum linear quadratic differential game. Based on the rendezvous state variables, it constructs approximate state vectors for lateral deviation and lateral velocity, and calculates the optimal lateral control variable for the pursuing UAV. Addressing the pursuit-escape confrontation problem during the UAV dynamic rendezvous process, it constructs a finite-time linear quadratic differential game model using rendezvous information such as the relative distance, closing velocity, and line-of-sight angular rate at the current moment. Finally, it calculates the optimal lateral control variable for the pursuing UAV. The parameters are correlated with the proportional guidance law, and the command angular velocity of the pursuing fixed-wing UAV is calculated to achieve online interception of the target rotary-wing UAV. The optimal control result of the finite-time linear quadratic differential game is converted into the equivalent navigation coefficient of proportional guidance, which takes into account both game optimization capability and the convenience of proportional guidance engineering implementation. In this embodiment, the rendezvous information such as relative distance, closing velocity, and line-of-sight angular rate are used as inputs to construct a pursuit-escape relative lateral motion model online, solve the finite-time Riccati equation, obtain the optimal lateral control quantity of the pursuer in the game sense, and map this control quantity into the equivalent navigation coefficient K in the form of proportional guidance, thereby realizing real-time adjustment of the heading angular velocity of the fixed-wing UAV. Attached Figure Description

[0016] Figure 1 This is a flowchart of the steps of the maneuvering target interception method based on linear quadratic differential game proportional guidance of the present invention; Figure 2 This is a schematic diagram illustrating the solution of the equivalent scaling factor provided in a specific embodiment of the present invention; Figure 3 This is a schematic diagram of the LQDG-PN algorithm flow provided in a specific embodiment of the present invention; Figure 4 This is a schematic diagram of the two-dimensional intersection geometry between a fixed-wing UAV and a target, provided in a specific embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the impact of different Q values ​​on the system under a straight path, provided in a specific embodiment of the present invention. Figure 6 This is a schematic diagram comparing interception trajectories under different state weight matrices Q, provided in a specific embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the influence of different Q values ​​on intermediate quantities of the system under a straight path, provided in a specific embodiment of the present invention. Detailed Implementation

[0017] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.

[0018] First, it should be noted that, in addressing the problems of existing technologies where fixed navigation coefficient proportional guidance is difficult to adapt to changes in target maneuverability and differential game control is difficult to directly implement in engineering, this invention proposes a fixed-wing UAV target interception method based on equivalent proportional guidance using finite-time linear quadratic differential game theory. This method uses intersection information such as relative distance, closing velocity, and line-of-sight angular rate as input to construct an online pursuit-escape relative lateral motion model, solves the finite-time Riccati equation, obtains the optimal lateral control quantity of the pursuer in a game-theoretic sense, and maps this control quantity to an equivalent navigation coefficient K in the form of proportional guidance, thereby achieving real-time adjustment of the fixed-wing UAV's heading angular velocity.

[0019] Reference Figure 1 and Figure 2 This invention provides a method for intercepting maneuvering targets based on proportional guidance of linear quadratic differential game, the method comprising the following steps: S100. Based on the two-dimensional relative motion relationship between the pursuing fixed-wing UAV and the target rotary-wing UAV, obtain the rendezvous state variables and construct the relative lateral dynamic equation after local linearization. The rendezvous state variables include relative distance, closing velocity and line-of-sight angular rate. Specifically, the position information, velocity, and normal acceleration of the pursuing fixed-wing UAV and the target rotary-wing UAV are set respectively to determine the rendezvous geometry. Based on the rendezvous geometry, the relative distance and line-of-sight angular rate between the pursuing fixed-wing UAV and the target rotary-wing UAV are determined. Based on the inertial coordinate system, and combined with the position information and velocity of the pursuing fixed-wing UAV and the target rotary-wing UAV, the kinematic equations of the pursuing and target UAVs are constructed. Based on the kinematic equations of the pursuing and target UAVs, the heading angles of the pursuing and target UAVs are introduced, the relative position vectors of the pursuing and target UAVs are defined, and the closed velocity is obtained. Based on the assumptions of small-angle linearization and short-time scale, the nonlinear pursuit problem is approximated into a relative lateral motion problem. The lateral deviation and lateral velocity are taken as state variables to construct the locally linearized relative lateral dynamic equations.

[0020] In this embodiment, a two-dimensional relative motion relationship is established between the pursuing fixed-wing UAV and the target, and the relative distance is obtained. Closing speed angular velocity of line of sight Isostatic variables.

[0021] Consider the dynamic rendezvous process of a fixed-wing UAV and a rotary-wing UAV in a two-dimensional plane. Let the fixed-wing UAV be the pursuing UAV. The position coordinates are The speed is The normal acceleration is Rotary-wing drones are the target. The position coordinates are The speed is The normal acceleration is The line of sight connecting the pursuer and the pursuer constitutes the line of sight, and its length is defined as the relative distance. Line of sight and inertial coordinate system The angle between axes is defined as the line-of-sight angle. Therefore, we can conclude that: The above variables and intersection diagram Figure 4 Maintaining consistency in the symbols used is fundamental to subsequent system dynamics modeling and guidance law construction.

[0022] Furthermore, to facilitate the establishment of an analytical guidance model, the following two assumptions are made: Assumption 1: Small-angle linearization assumption. During a rendezvous, the relative line-of-sight angle deviation between the pursuing and fleeing parties is relatively small, and the lateral motion is secondary to the longitudinal closing motion. Therefore, the relative motion can be linearized around the local line-of-sight direction.

[0023] Assumption 2: Short timescale assumption. Within a single navigation coefficient update cycle or a finite prediction time domain, the relative distance... With closing speed The change is relatively slow and can be regarded as a piecewise constant or slowly changing parameter, thus establishing a dynamic game model with local freezing.

[0024] Therefore, in the inertial coordinate system, the kinematic equations of the pursuing party and the target party are as follows: in, and These are the heading angles of the pursuing and target sides, respectively. The relative position vector is defined as: The closing velocity can then be expressed as: in, This indicates that the system is in a convergent intersection state.

[0025] Under the assumptions of small-angle linearization and short time scale, the nonlinear pursuit problem is approximated as a relative lateral motion problem. A lateral deviation is considered. and lateral speed For the state variables, construct the state vector, whose expression is: The relative transverse dynamic equation after local linearization can then be written as: in: In the formula, For the lateral control input of the pursuing party, The target's lateral maneuver input is used. This model shows that the pursuer's control aims to reduce lateral deviation, while the target's maneuver attempts to increase it, creating a zero-sum antagonistic relationship in the lateral path. This state-space expression is consistent with the relative lateral model used in the simulation program.

[0026] S200. The relative lateral dynamic equation after local linearization is described as a finite-time zero-sum linear quadratic differential game. Based on the intersection state variables, the approximate state vectors of lateral deviation and lateral velocity are constructed, and the optimal lateral control quantity of the pursuing party is obtained. Specifically, based on the relative lateral dynamics equation after local linearization, the guidance confrontation between the pursuer and the target is described as a finite-time zero-sum linear quadratic differential game. Based on the finite-time zero-sum linear quadratic differential game, a performance index function is constructed by setting the state weight matrix, the pursuer's control weight, the target's control weight, and the prediction time domain. Based on the performance index function, the pursuer's control matrix and the target's control matrix are set to form an equivalent confrontation matrix, and the Riccati differential equation is integrated in reverse to obtain the feedback matrix at the current time. Based on the intersection state variables, an approximate state vector of lateral deviation and lateral velocity is constructed, and combined with the feedback matrix at the current time, the optimal lateral control quantity of the pursuer is obtained.

[0027] In this embodiment, a finite-time linear quadratic differential game model is constructed, and a state weight matrix is ​​set. The pursuing side controls the weight. Target control weight and prediction time domain .

[0028] More specifically, based on the aforementioned relative lateral dynamics, the guidance confrontation between the pursuer and the target is described as a finite-time zero-sum linear quadratic differential game. The pursuer aims to reduce lateral deviation, lateral velocity, and terminal miss tendency, while suppressing control energy consumption; the target, on the other hand, aims to increase lateral deviation through maneuvering evasion to disrupt the rendezvous process. To this end, a performance index function is constructed, the expression of which is: in, For finite prediction time domain, The state weight matrix is... To allow the pursuing side to control the weight, Control the weights for the target party. This is the terminal weight matrix. This reflects the system's level of attention to lateral deviation and lateral velocity. and This then describes the control costs for the pursuing and the target sides respectively. The program also uses... , , and As the main modeling parameter.

[0029] The equivalent adversarial matrix is ​​formed by the control matrix of the pursuer and the control matrix of the target, and the Riccati differential equation is integrated in reverse to obtain the feedback matrix P0 at the current moment. Based on the current rendezvous state, the approximate state vectors of lateral deviation and lateral velocity are constructed to obtain the optimal lateral control quantity of the pursuer.

[0030] More specifically, according to the theory of linear quadratic differential games, let the value function take the form of a quadratic form, and its expression is: Substituting into the Hamilton–Jacobi–Isaacs equation, we obtain the matrix. Satisfied Riccati differential equation: The terminal conditions are: By performing inverse integration on the terminal conditions, the feedback matrix at the current time step can be obtained. Furthermore, based on the saddle point optimality condition, the optimal control for the pursuer and the target can be obtained as follows: in, This represents the optimal lateral control quantity of the pursuing party in a game-theoretic context, comprehensively reflecting the combined impact of state deviation, target maneuver, and control costs on guidance decisions. The simulation program achieves equivalent control solutions based on the aforementioned Riccati equations and optimal feedback relationships.

[0031] S300: The optimal lateral control quantity of the pursuer is mapped to the proportional guidance law, and the command angular velocity of the pursuer's fixed-wing UAV is calculated to achieve online interception of the target rotary-wing UAV.

[0032] Specifically, the optimal lateral control quantity of the pursuer is mapped to the proportional guidance law to calculate the equivalent navigation coefficient candidate value; the equivalent navigation coefficient candidate value is subjected to amplitude limiting processing to obtain the equivalent navigation coefficient that meets the engineering constraints; based on the equivalent navigation coefficient that meets the engineering constraints, the command angular velocity of the pursuer fixed-wing UAV is calculated, and the heading of the pursuer fixed-wing UAV is updated in combination with the maximum turning radius or angular velocity saturation constraint to achieve online interception of the target rotary-wing UAV.

[0033] In this embodiment, the optimal lateral control quantity is mapped to the proportional guidance law to calculate the equivalent navigation coefficient candidate value; when λ̇ approaches zero, the solution is switched to a degenerate solution form based on feedback matrix elements; the equivalent navigation coefficient candidate value is subjected to amplitude limiting to obtain the equivalent navigation coefficient K that satisfies the engineering constraints, and is maintained or refreshed at a certain update cycle; the command angular velocity of the fixed-wing UAV is calculated using K, and the UAV's heading is updated in combination with the maximum turning radius or angular velocity saturation constraint to achieve online interception of the target.

[0034] To align with the proportional navigation system commonly used in engineering, the optimal lateral control obtained through differential game theory is equivalently mapped to the navigation coefficients in proportional navigation. The proportional navigation law can be expressed as: in, To provide lateral acceleration for the pursuing party, This is the equivalent proportionality coefficient. The line-of-sight angular rate is given.

[0035] If we denote the optimal control quantity obtained by differential game theory as... Then the equivalent navigation coefficient at the current moment can be defined as: This allows traditional proportional guidance with fixed navigation coefficients to be extended to state-dependent time-varying guidance parameters. It should be noted that when... When the value approaches zero, the equivalent navigation coefficient at the current moment may become numerically unstable. Therefore, in actual calculations, degenerate representation and amplitude limiting strategies are required to ensure the stability of the navigation coefficient solution.

[0036] Furthermore, such as Figure 3 As shown, this embodiment of the invention first performs a validity check on the input parameters. When the relative distance... When it is less than or equal to zero, it is corrected to a very small positive number; when the closing velocity If the value is too small, immediately set the equivalent navigation coefficient to zero and exit the current solution to avoid numerical anomalies caused by the denominator approaching zero; , and Set a minimum threshold to ensure stable solutions to the Riccati equation.

[0037] Subsequently, a relative lateral motion model of the pursuing and fleeing parties is established. Let the state matrix A be in second-order integral form, and let the control matrices of the pursuing and the target describe the effects of their lateral maneuvers on the system state. Based on... , , Construct adversarial terms and use terminal matrices As a boundary condition, the finite-time Riccati differential equation is integrated in reverse to obtain the feedback matrix P0 at the current time.

[0038] Next, based on the current relative distance and line-of-sight angular rate, approximate quantities for lateral deviation and lateral velocity are constructed to form a state vector. The optimal lateral control quantity of the pursuing party is calculated using the feedback matrix P0, and then mapped to the proportional guidance control form to obtain the equivalent navigation coefficient candidate value. When the absolute value of the line-of-sight angular rate is small, the degenerate mapping formula based on the P0(2,2) element is used to calculate the equivalent navigation coefficient candidate value.

[0039] In engineering implementation, lower and upper limits are set for candidate values ​​of the equivalent navigation coefficients to obtain the equivalent navigation coefficients K that satisfy the aircraft's maneuver constraints; simultaneously, K does not need to be recalculated in every sampling period, but is refreshed according to a preset update cycle. During the guidance phase, based on K, The command angular velocity of the fixed-wing UAV is calculated from the filtered line-of-sight angular rate, and angular velocity saturation processing is performed. Finally, the heading and position information are updated until the acquisition conditions are met or the target successfully returns.

[0040] Finally, the embodiments of the present invention will be further described and illustrated with reference to the accompanying drawings: like Figure 4 As shown, this embodiment addresses the initial patrol position of the fixed-wing UAV, the target point selection of the rotary-wing UAV, and the state weight matrix. Under randomly varying conditions, 20,000 Monte Carlo cycle simulations were conducted. The simulation results are shown in Table 1 below: Table 1. Statistical results of 20,000 sets of cyclic simulations numerical values 19579 0.97895 0.02105 0.872137 57.5188 Based on cyclic simulations, a single set of typical simulation results is further selected to conduct a detailed analysis of the evolution of the rendezvous trajectory, the change in relative distance, and the response process of the equivalent proportional coefficient, as detailed below. Figure 5 , Figure 6 as well as Figure 7 As shown in Table 2, to more intuitively illustrate the algorithm's mechanism of action and guiding performance, the simulation data are as follows: Table 2 Comparison of system simulation results under different state weight matrices Specifically, such as Figure 5 As shown, under the three sets of state weight matrices Q=[1,1], Q=[1,10], and Q=[10,1], the flight trajectories of the pursuing fixed-wing UAVs are basically overlapping. They all originate near their own patrol area, enter the interception phase after detecting the target, and continuously approach the target rotary-wing UAV along similar paths, ultimately rendezvousing near the target waypoint. Simultaneously, their relative distance curves are also basically consistent, continuously decreasing over time and approaching zero at the end of the rendezvous. (Equivalent scaling factor) and its candidate values The value remains essentially zero before entering the guidance phase, increases rapidly after entering the guidance phase, and then shows a segmented decreasing trend as the interception process progresses. Among them, the peak value of the proportional coefficient under the conditions of Q=[1,10] and Q=[10,1] is significantly higher than that under the condition of Q=[1,1], indicating that although different state weight matrices have little impact on the changes in macroscopic trajectory and distance, they will significantly affect the distribution of the internal gain of the guidance law and the control strength in the middle and later stages.

[0041] like Figure 6 As shown, under the three sets of state weight matrices, the trajectory of the pursuer remains highly consistent in overall shape, with only minor differences appearing in local areas at the end of the rendezvous phase. Local magnification results indicate that the pursuer's terminal correction path deviates slightly when approaching the target under different weight parameters. This suggests that the state weight matrix has a limited impact on the overall interception path, but it does affect the minor geometric correction process at the terminal stage. In other words, the state weight matrix does not significantly change whether the pursuer can reach the vicinity of the target, nor does it significantly alter the overall flight path, but it adjusts the internal control allocation of the guidance law, causing varying degrees of local convergence differences in the terminal approach process.

[0042] like Figure 7 As shown, the lateral deviation, line-of-sight angular rate, commanded angular velocity, and actual angular velocity curves under the three sets of state weight matrices generally exhibit the same overall trend. The lateral deviation initially experiences a significant change before gradually converging to near zero, indicating that all three sets of parameters effectively compress the lateral error. The line-of-sight angular rate remains relatively constant for most of the time, only showing a significant fluctuation at the end before rapidly decaying, indicating that the state weight matrix has a certain regulatory effect on changes in terminal line-of-sight rotation. Both the commanded and actual angular velocities show significant adjustments initially during the guidance engagement phase, followed by terminal alignment through reverse compensation, and finally returning to a stable state. The differences between the different state weight matrices are mainly reflected in the magnitude of the terminal peak, the descent speed, and the strength of the local dynamic response. This suggests that the main role of this parameter is not reflected in the external flight trajectory, but rather in the internal dynamic adjustment characteristics of the guidance law and the terminal correction capability.

[0043] Compared with the prior art, the embodiments of the present invention have the following advantages: 1) The optimal control result of the finite-time linear quadratic differential game is converted into the proportional guidance equivalent navigation coefficient, which takes into account both the game optimization capability and the convenience of proportional guidance engineering implementation.

[0044] 2) The equivalent navigation coefficient K can be adjusted online according to changes in relative distance, closing velocity and line-of-sight angular rate, making it more suitable for dealing with maneuvering targets than the fixed navigation coefficient scheme.

[0045] 3) By setting parameters such as Q, Rp, RT and Tf, the system's attention to lateral deviation, lateral velocity and control cost can be explicitly adjusted. The physical meaning of the parameters is clear, which is convenient for engineering tuning.

[0046] 4) By using zero line-of-sight angular rate degradation solution and piecewise preservation update mechanism, the numerical stability and real-time implementation of the algorithm are improved.

[0047] 5) This technical solution can be directly embedded into existing fixed-wing UAV flight control or guidance software, and is suitable for scenarios such as anti-UAV interception, patrol and early warning, and border protection.

[0048] In summary, compared with the prior art, the embodiments of the present invention have the following distinguishing technical features: 1) Online solution mechanism for equivalent proportional coefficients based on finite-time linear quadratic differential game: Addressing the pursuit-escape confrontation problem during UAV dynamic rendezvous, a finite-time linear quadratic differential game model is constructed using rendezvous information such as relative distance, closing velocity, and line-of-sight angular rate at the current moment. The optimal lateral control quantity of the pursuer is obtained by solving the corresponding Riccati equation. Based on this, an equivalent mapping relationship between the optimal control quantity and the proportional guidance law is further established, generating the equivalent proportional coefficients in real time. Unlike traditional proportional guidance where navigation coefficients are fixed or preset, the proportional coefficients in this invention can be adjusted online according to changes in the rendezvous situation, thus possessing stronger adaptive capabilities and the ability to counter target maneuvers.

[0049] 2) Equivalent Conversion Method from Optimal Control Quantity to Proportional Guidance Parameters: This embodiment does not directly use the control quantity obtained from game theory to drive the aircraft. Instead, it further converts the optimal lateral control quantity into an equivalent proportional coefficient that can be directly invoked under the proportional guidance framework. This allows the complex game optimization results to be embedded in the traditional proportional guidance structure for engineering applications. This conversion method combines the adversarial advantages of the optimal control method with the advantages of a clear proportional guidance law structure and simple implementation, forming a technical path of "game optimization - equivalent mapping - proportional guidance execution".

[0050] 3) Segmented update control mechanism for UAV rendezvous: During UAV flight, the guidance parameters are not completely resolved for each discrete step. Instead, the equivalent proportional coefficient is periodically refreshed according to a preset update cycle, and it remains involved in guidance control within adjacent update intervals. This mechanism ensures that the guidance parameters can dynamically change according to the battlefield situation, while avoiding the computational burden of repeated solutions at every moment, thus improving the real-time performance and engineering deployability of the algorithm.

[0051] 4) Constraint Processing and Robust Design Methods for Practical Flight Control: The algorithm incorporates systematic constraint processing and robust design to address various special operating conditions that may arise during UAV dynamic rendezvous. For example, when the relative distance is too small, the closing velocity is too low, or the line-of-sight angular rate is close to zero, key variables are corrected or alternative calculation methods are used; when the obtained equivalent proportional coefficient is too large or too small, amplitude limiting is implemented; when the guidance command exceeds the aircraft's maximum turning capability, the command angular velocity is saturated and constrained. These designs enable the invention not only to theoretically solve for guidance parameters but also to maintain numerical stability and control feasibility in practical UAV control systems.

[0052] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for intercepting maneuvering targets based on linear quadratic differential game proportional guidance, characterized in that, Includes the following steps: Based on the two-dimensional relative motion relationship between the pursuing fixed-wing UAV and the target rotary-wing UAV, the rendezvous state variables are obtained and the relative lateral dynamic equations after local linearization are constructed. The rendezvous state variables include relative distance, closing velocity and line-of-sight angular rate. The relative lateral dynamic equation after local linearization is described as a finite-time zero-sum linear quadratic differential game. Based on the intersection state variables, an approximate state vector of lateral deviation and lateral velocity is constructed, and the optimal lateral control quantity of the pursuer is obtained. By mapping the optimal lateral control quantity of the pursuer to the proportional guidance law and calculating the command angular velocity of the pursuer's fixed-wing UAV, online interception of the target rotary-wing UAV is achieved.

2. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 1, characterized in that, The step of obtaining the rendezvous state variables and constructing the locally linearized relative lateral dynamic equations based on the two-dimensional relative motion relationship between the pursuing fixed-wing UAV and the target rotary-wing UAV specifically includes: Set the position, velocity, and normal acceleration of the pursuing fixed-wing UAV and the target rotary-wing UAV respectively, and determine the intersection geometry. Based on the intersection geometry, determine the relative distance and line-of-sight angular rate between the pursuing fixed-wing UAV and the target rotary-wing UAV; Based on the inertial coordinate system, and combining the position and velocity information of the pursuing fixed-wing UAV and the target rotary-wing UAV, the kinematic equations of the pursuing and target UAVs are constructed. Based on the kinematic equations of the pursuer and the target, the heading angles of the pursuer and the target are introduced, the relative position vectors of the pursuer and the target are defined, and the closing velocity is obtained. Based on the assumptions of small-angle linearization and short-time scale, the nonlinear pursuit problem is approximated as a relative lateral motion problem. The lateral deviation and lateral velocity are taken as state variables, and the relative lateral dynamic equations after local linearization are constructed.

3. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 2, characterized in that, The kinematic equations of the pursuing and target sides are expressed as follows: In the above formula, Indicates the speed of the pursuing fixed-wing drone. Indicates the speed of the target rotary-wing drone. Indicates the heading angle of the pursuing party. Indicates the heading angle of the target. This indicates that the pursuing fixed-wing drone was in velocity components in the direction, This indicates that the pursuing fixed-wing drone was in velocity components in the direction, Indicates the target rotary-wing drone in velocity components in the direction, Indicates the target rotary-wing drone in The velocity component in the direction.

4. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 2, characterized in that, The step of describing the locally linearized relative lateral dynamic equation as a finite-time zero-sum linear quadratic differential game, constructing approximate state vectors of lateral deviation and lateral velocity based on the intersection state variables, and obtaining the optimal lateral control quantity for the pursuing side specifically includes: Based on the relative lateral dynamics equation after local linearization, the guidance confrontation between the pursuer and the target is described as a finite-time zero-sum linear quadratic differential game. Based on finite-time zero-sum linear quadratic differential game, a performance index function is constructed by setting the state weight matrix, the pursuer's control weight, the target's control weight, and the prediction time domain. Based on the performance index function, the pursuing party's control matrix and the target party's control matrix are set to form an equivalent adversarial matrix, and the Riccati differential equation is integrated in reverse to obtain the feedback matrix at the current time. Based on the rendezvous state variables, construct approximate state vectors for lateral deviation and lateral velocity, and combine them with the feedback matrix at the current moment to obtain the optimal lateral control variable for the pursuing party.

5. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 4, characterized in that, The specific expression for the performance index function is as follows: In the above formula, Represents a performance metric function. Represents the finite prediction time domain. Represents the state weight matrix. This indicates that the pursuing side controls the weight. Indicates the target party's control weight. Represents the terminal weight matrix. Represents the system state vector. This represents the control input of the pursuing party. This represents the control input from the target side.

6. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 4, characterized in that, The specific expression of the Riccati differential equation is as follows: In the above formula, Indicates the target party's control weight. Represents the terminal weight matrix. Represents the state weight matrix. This represents the first derivative of matrix P with respect to time, i.e., the rate of change of the Riccati matrix with respect to time. The Riccati matrix, representing the coefficient matrix corresponding to the optimal value function, is used to characterize the impact of state variables on performance indicators during game optimization. This represents the system state matrix, used to describe the natural evolution of the system state under no control input. This represents the control input matrix of the pursuing party, used to describe how the pursuing party's control input affects changes in the system state. This represents the target control input matrix, which describes how the target control quantity affects changes in the system state.

7. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 4, characterized in that, The expression for the optimal lateral control quantity of the pursuing party is as follows: In the above formula, This represents the feedback matrix at the current moment. This indicates that the pursuing side controls the weight. Indicates the target party's control weight. Indicates the current time The system state vector, Indicates the current time The optimal control input for the pursuing side. Indicates the current time The optimal control input for the target side. This represents the attacking control input matrix. This represents the target control input matrix.

8. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 1, characterized in that, The step of mapping the optimal lateral control quantity of the pursuer to the proportional guidance law and calculating the command angular velocity of the pursuer's fixed-wing UAV to achieve online interception of the target rotary-wing UAV specifically includes: The optimal lateral control quantity of the pursuing party is mapped to the proportional guidance law, and the candidate values ​​of the equivalent navigation coefficients are calculated. The candidate values ​​of the equivalent navigation coefficients are subjected to amplitude limiting to obtain the equivalent navigation coefficients that meet the engineering constraints; Based on the equivalent navigation coefficients that satisfy engineering constraints, the commanded angular velocity of the pursuing fixed-wing UAV is calculated. The heading of the pursuing fixed-wing UAV is then updated in conjunction with the maximum turning radius or angular velocity saturation constraints, thereby achieving online interception of the target rotary-wing UAV.

9. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 8, characterized in that, In the process of calculating the candidate values ​​of the equivalent navigation coefficients, if the line-of-sight angular rate is zero, it is necessary to switch to the degenerate solution form based on the elements of the feedback matrix.

10. The maneuvering target interception method based on linear quadratic differential game proportional guidance according to claim 8, characterized in that, The specific expression for the proportional guidance law is as follows: In the above formula, This indicates the lateral acceleration command from the pursuing party. This represents the equivalent proportionality coefficient. Indicates the line-of-sight angular rate. This indicates the closing velocity.

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