A differential game guidance method for a maneuvering target in the case of missing target information

Abstract

The present application relates to the field of control, in particular to a kind of target information missing under the differential game guidance method for maneuvering target.The present application discloses a kind of differential game guidance method for near space high dynamic target scene under considering target incomplete information.The method comprises the following steps: the terminal interception problem is expressed, and the vertical plane is taken as the main research plane, and a two-dimensional missile-target relative motion engagement model is established;A linear extended observer is designed to estimate the target acceleration information;Then, the expression of zero-control miss distance is given, and the linear quadratic differential game (LQDG) guidance law under incomplete target information is obtained.The linear quadratic differential game (LQDG) guidance law under incomplete target information of the present application solves the problem of low control accuracy of interceptor under incomplete target information in the prior art.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of control, and particularly relates to a differential game guidance method for a maneuvering target under target information loss. BACKGROUND

[0002] In recent years, hypersonic vehicle technology has developed rapidly, and the corresponding hypersonic defense system has also received more and more attention. In view of the shortcomings of existing aerospace defense technology, developing more efficient near-space hypersonic vehicle interception technology is the top priority of the current defense system. However, there are still technical difficulties in the current near-space hypersonic vehicle interception task, such as difficulty in discovery, detection and prediction, tracking and interception. Among them, the high speed and high maneuverability of the near-space hypersonic vehicle and the complexity of the near-space environment make the interceptor guidance system face more severe challenges. Therefore, under this background, focusing on the guidance technology of the interceptor, breaking through the current bottleneck of the guidance technology is the research focus of the near-space defense technology.

[0003] Direct collision and killing is the most common interception method for the current interception system. In order to achieve accurate attack on the target within a limited time, the terminal guidance technology needs to have sufficient interception accuracy. In recent years, domestic and foreign experts have carried out a lot of research on terminal guidance technology, and have achieved obvious results, but most of the literature designs the interception terminal guidance algorithm from the perspective of the interceptor. For unknown target motion information, the optimal guidance law of the interceptor and the target needs to be designed from the perspective of both sides.

[0004] The present application establishes a relative motion model of the interceptor and the target from the perspective of both sides, and designs the optimal guidance algorithm of both sides based on the differential game method under incomplete information, with zero-control miss distance and energy consumption of both sides as performance indicators. SUMMARY

[0005] The present application aims to solve the problem of low control accuracy of the interceptor in the prior art. We propose a differential game guidance method for high dynamic targets under target information loss.

[0006] S1: constructing a two-dimensional projectile-target relative motion mathematical model, and converting the two-dimensional projectile-target relative motion mathematical model into a state space form guidance system model;

[0007] The two-dimensional projectile-target relative motion mathematical model is used to describe the mathematical model of the relative motion of the interceptor and the maneuvering target in the two-dimensional plane. The two-dimensional projectile-target relative motion mathematical model of the present application takes the vertical plane as the main attack plane, and is based on the scene of the interceptor intercepting the maneuvering target in the near space. The near space refers to the airspace 20-100 kilometers away from the ground.

[0008] S2: Constructing a second-order linear extended observer, using the second-order linear extended observer to estimate the information of the maneuvering target, and obtaining observation information;

[0009] S3: According to the state space form of the guidance system model obtained in S1 and the observation information obtained in S2, obtaining the scalar form of the zero-control miss distance and the scalar form of the derivative of the zero-control miss distance;

[0010] S4: According to the state space form of the guidance system model obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss distance obtained in S3 and the scalar form of the derivative of the zero-control miss distance, obtaining a linear quadratic differential game (LQDG) guidance law containing the zero-control miss distance;

[0011] S5: Executing the linear quadratic differential game (LQDG) guidance law containing the zero-control miss distance to control the interceptor.

[0012] The beneficial effects of the present application are: the present application proposes a differential game guidance method for near space high dynamic target interception task under incomplete information. First, the vertical plane is used as the attack main plane, the interceptor-target relative motion mathematical model is constructed, and the performance index function meeting the interception constraint is constructed by using the differential game theory, which involves zero-control miss distance and energy consumption of both parties, and a linear quadratic differential game guidance strategy is designed. The present application gives a linear quadratic differential game guidance strategy for high dynamic target under incomplete target information, which overcomes the defect that the traditional guidance law only designs the terminal guidance law from the perspective of the interceptor based on the known target motion information, realizes high-precision interception under incomplete information, and verifies the effectiveness of the guidance method through interception test under different maneuvering targets. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 is the relative motion relationship diagram of the present application;

[0014] Figure 2 is the simulation result schematic diagram of the present application for intercepting a non-maneuvering target;

[0015] Figure 2 a is the schematic diagram of the motion trajectory of the present application in the terminal section;

[0016] Figure 2 b is the schematic diagram of the velocity change of the present application in the terminal section;

[0017] Figure 2 c is the schematic diagram of the line-of-sight angle change of the present application in the terminal section;

[0018] Figure 2 d is the schematic diagram of the line-of-sight angle rate change of the present application in the terminal section;

[0019] Figure 3 is the simulation result schematic diagram of intercepting the sine maneuver target of the present application;

[0020] Figure 3 a is the target acceleration observation result schematic diagram of the present application;

[0021] Figure 3 b is the target acceleration observation error change schematic diagram of the present application;

[0022] Figure 4 is the simulation result schematic diagram of intercepting the sine maneuver target of the present application;

[0023] Figure 4 a is the schematic diagram of the change of the line-of-sight angle of the terminal-stage projectile and target of the present application;

[0024] Figure 4 b is the schematic diagram of the change of the line-of-sight angle rate of the terminal-stage projectile and target of the present application;

[0025] Figure 4 c is the schematic diagram of the interceptor guidance law and the real guidance acceleration of the present application;

[0026] Figure 4 d is the schematic diagram of the change of the zero-control miss distance estimation of the present application.

[0027] Figure 5 is the simulation result schematic diagram of intercepting the differential game maneuver target of the present application;

[0028] Figure 5 a is the target acceleration observation result schematic diagram of the present application;

[0029] Figure 5 b is the target acceleration observation error change schematic diagram of the present application;

[0030] Figure 6 is the simulation result schematic diagram of intercepting the differential game maneuver target of the present application;

[0031] Figure 6 a is the schematic diagram of the change of the line-of-sight angle of the terminal-stage projectile and target of the present application;

[0032] Figure 6 b is the schematic diagram of the change of the line-of-sight angle rate of the terminal-stage projectile and target of the present application;

[0033] Figure 6 c is the schematic diagram of the interceptor guidance law and the real guidance acceleration of the present application;

[0034] Figure 6 d is the schematic diagram of the change of the zero-control miss distance estimation of the present application. DETAILED DESCRIPTION

[0035] DETAILED DESCRIPTION ONE: in combination Figure 1The application is illustrated, including:

[0036] S1: Establish a two-dimensional projectile-target relative motion mathematical model according to the interception scene of the two parties in the adjacent space with the vertical plane as the main attack plane.

[0037] S2: Construct a linear extended observer;

[0038] S3: Obtain the zero-control miss distance according to the two-dimensional projectile-target mathematical model established in S1;

[0039] S4: Obtain the linear quadratic differential game (LQDG) guidance law containing the zero-control miss distance according to the observation information of the two-dimensional projectile-target mathematical model established in S1 and the linear extended observer established in S2.

[0040] Specific implementation method two: The difference between this implementation method and the specific implementation method one is that,

[0041] The two-dimensional projectile-target relative motion mathematical model is established in S1, and the two-dimensional projectile-target relative motion mathematical model is converted into a state space form guidance system model, and the specific process is:

[0042] S1.1: Since the interceptor adopts direct force control and the target adopts aerodynamic force control, the actuator of the interceptor and the maneuvering target is set as an autopilot,

[0043] The dynamic characteristics of the actuators of the interceptor and the maneuvering target are both expressed as first-order dynamics delay characteristics,

[0044] A two-dimensional projectile-target relative motion mathematical model is established in the vertical plane, which is expressed by a formula as:

[0045]

[0046] Wherein, M represents the interceptor, T represents the target, q ε is the line-of-sight angle, is the velocity of the interceptor in the plumb plane, is the velocity of the target in the plumb plane, is the trajectory angle of the interceptor, is the trajectory angle of the maneuvering target, and R represents the projectile-target relative distance, R h is the projectile-target relative distance component in the vertical plane, is the guidance law of the interceptor, is the guidance law of the maneuvering target; is the projectile-target relative distance rate of change, is the line-of-sight angle rate, is the maneuvering target velocity rate of change, is the interceptor velocity rate of change, represents the angular rate of the ballistic angle of the maneuvering target, represents the angular rate of the ballistic angle of the interceptor, represents the second derivative of the relative distance between the interceptor and the maneuvering target in the vertical plane, T and l M both represent intermediate variables, u M represents the ideal guidance law of the interceptor, u T represents the ideal guidance law of the maneuvering target, τ M represents the first-order delay parameter of the interceptor, τ T represents the first-order delay parameter of the maneuvering target; represents the dynamic model of the interceptor, represents the dynamic model of the maneuvering target;

[0047] the ideal guidance law of the interceptor u M refers to the guidance law without considering the dynamic delay characteristics of the actuator of the interceptor;

[0048] the ideal guidance law of the maneuvering target u T refers to the guidance law without considering the dynamic delay characteristics of the actuator of the maneuvering target;

[0049] S1.2: Define the system state variables According to the system state variables The two-dimensional relative motion mathematical model of the interceptor and the maneuvering target is converted into a state space form, and a state space form of the guidance system model is obtained:

[0050]

[0051] wherein the state state space form of the guidance system matrix the state state space form of the guidance system matrix the state state space form of the guidance system matrix represents the derivative of the system state variable, and the other steps are the same as in the first embodiment.

[0052] The third embodiment is different from the first embodiment in that,

[0053] The second-order linear extended observer is constructed in S2, and the information of the maneuvering target is estimated by using the second-order linear extended observer to obtain the observation information; the specific process is as follows:

[0054] S2.1: Define the first state variable and the second state variable represents the estimated value of the relative distance change rate in the vertical plane, represents the acceleration estimation value of the maneuvering target;

[0055] S2.2: constructing a second-order linear extended observer according to the first state variable z1 and the second state variable z2, which is expressed as:

[0056]

[0057] wherein e1 is the observation error; β1, β2 are gain coefficients; δ1, δ2 > 0 are gain parameters, represents the derivative of z1, represents the derivative of z2; fal(e1, δ1, δ2) represents an intermediate function;

[0058] The specific formula of the intermediate function fal(e1, δ1, δ2) is:

[0059]

[0060] sign() represents a sign function.

[0061] The expression of the sign function sign() is:

[0062]

[0063] x represents the independent variable of the sign function.

[0064] S2.3: estimating the target information of the maneuvering target by using the second-order linear extended observer to obtain observation information. The other steps and parameters are the same as one of the first to fourth embodiments.

[0065] The fourth embodiment is different from the first to fourth embodiments in that,

[0066] The estimation of the target information of the maneuvering target by using the second-order linear extended observer in S2.3 to obtain observation information is specifically expressed as:

[0067] S2.2.1: measuring the missile-target relative distance R and the line-of-sight angle q at time t by using the measuring device of the interceptor itself ε ,

[0068] S2.2.2: obtaining the missile-target relative distance R h and the missile-target relative velocity in the vertical plane at time t according to the missile-target relative distance R and the line-of-sight angle q at time t ε The specific process is:

[0069]

[0070] where R represents the relative distance between the interceptor and the target, q ε represents the line-of-sight angle, R h represents the relative distance between the interceptor and the target in the vertical plane, represents the relative velocity between the interceptor and the target;

[0071] S2.2.3: obtaining the relative distance between the interceptor and the target in the vertical plane R h and the relative velocity between the interceptor and the target at time t according to the second-order linear extended observer, S2.2.2; observing the maneuvering target at time t to obtain observation information at time t;

[0072] the observation information at time t includes z1 and z2

[0073] the other steps and parameters are the same as one of the first to third embodiments.

[0074] the fifth embodiment is different from the first to fourth embodiments in that,

[0075] the state space form of the guidance system model obtained according to S1 and the observation information obtained according to S2 in the S3 are used to obtain the scalar form of the zero-control miss distance and the scalar form of the derivative of the zero-control miss distance; the specific process is as follows:

[0076] S3.1: constructing the zero-control miss distance ZEM according to the state space form of the guidance system model obtained according to S1 and the observation information obtained according to S2, which is expressed by the formula:

[0077] introducing the zero-control miss distance into the differential game guidance law as a performance index in the present specification, which can be expressed as:

[0078] ZEM=D T X(t,t f )x(t) (9)

[0079] in the formula (9), the zero-control miss distance ZEM is expressed as the miss distance obtained by mapping and estimating the state of the interceptor at time t to the time t f when the zero guidance law is used to capture the target, the miss distance represents the distance difference between the interceptor and the maneuvering target at the capture time; D T represents the transpose of the performance function weight matrix D, the performance function weight matrix D = [1, 0, 0, 0] T , X(t,t f ) is expressed as the state transition matrix of the state space form of the guidance system model formula (5), x(t) is the state variable at time t, the state variable x(t) at time t is obtained according to the observation information obtained according to S2, the state variable x(t) at time t is obtained according to the observation information obtained according to S2, and it is known from S1.2 that The state variable at time t can be obtained from the observation information z1, z2;

[0080] The state transition matrix X(t, t f ) can be obtained from equations (10) and (11);

[0081]

[0082] In equation (10), I represents a unit matrix, represents the derivative of the state transition matrix, and in equation (11), L -1 represents the Laplace inverse transform, s represents a differential operator, t go = t f -t represents the remaining flight time, A represents the guidance system matrix in the state space form; t f represents the time of capturing the maneuvering target;

[0083] The time t f of capturing the maneuvering target is represented by equation (12):

[0084]

[0085] R0 represents the relative distance between the missile and the target at the time of capturing the maneuvering target, represents the rate of change of the relative distance between the missile and the target at the time of capturing the maneuvering target; represents the ballistic angle of the maneuvering target in the lead plane at the time of capturing the maneuvering target, represents the line-of-sight angle of the maneuvering target in the lead plane at the time of capturing the maneuvering target, represents the ballistic angle of the interceptor in the lead plane at the time of capturing the maneuvering target, S3.2: The derivative of the zero-control miss distance is obtained by combining equations (9) and (10) and is represented as:

[0086]

[0087] S3.3: The scalar form (14) of the zero-control miss distance ZEM and the scalar form (15) of the derivative of the zero-control miss distance are obtained by combining equations (9), (11) and (13), and are specifically represented as:

[0088] In the equation:

[0089] is represented as a nonlinear time-varying function, represents the variable in the nonlinear time-varying function.

[0090] The other steps and parameters are the same as one of the first to fourth embodiments.

[0091] ​Embodiment six: the embodiment is different from the first to fifth embodiments in that,

[0092] The state space form of the guidance system model obtained according to S1, the observation information obtained in S2, the scalar form of the zero-control miss distance and the scalar form of the derivative of the zero-control miss distance obtained in S3, and the performance function obtained in S4.1, are used to obtain a linear quadratic differential game (LQDG) guidance law containing the zero-control miss distance, and the specific process is as follows:

[0093] S4.1: constructing a performance index J and constructing a performance function, and the specific process is as follows:

[0094] The performance index J is expressed by a formula as follows:

[0095]

[0096] The performance function is expressed by a formula as follows:

[0097]

[0098] In formula (16), ZEM(t f ) represents the zero-control miss distance between the interceptor and the maneuvering target at the capture time, and this part of the performance index represents that the designed differential game guidance law reduces the miss distance between the interceptor and the target, that is, improves the hit,

[0099] represents the difference between the energy consumed by the interceptor and the energy consumed by the maneuvering target during the interception process, and Q M represents a diagonal matrix, u represents the guidance law of the interceptor, Q T represents a diagonal matrix, v represents the guidance law of the maneuvering target, and represents that this part of the performance index represents that the target can consume more energy with less energy,

[0100] S4.2: according to the state space form of the guidance system model obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss distance obtained in S3, the scalar form of the derivative of the zero-control miss distance, and the performance function obtained in S4.1, a linear quadratic differential game (LQDG) guidance law containing the zero-control miss distance is obtained; other steps and parameters are the same as one of the first to fifth embodiments.

[0101] Embodiment seven: the embodiment is different from the first to sixth embodiments in that,

[0102] The state space form of the guidance system model obtained according to S1, the observation information obtained in S2, the scalar form of the zero-control miss distance obtained in S3, the scalar form of the derivative of the zero-control miss distance, and the performance index function obtained in S4.1, are used to obtain a linear quadratic differential game (LQDG) guidance law containing the zero-control miss distance; and the specific process is as follows:

[0103] S4.2.1: Construct the Hamiltonian function H, and define the extremum condition according to the Hamiltonian function H,

[0104] The Hamiltonian function H is expressed by formula:

[0105]

[0106] denotes the derivative of ZEM(t f ); λ denotes a time-varying parameter related to the condition; v * denotes the optimal maneuvering target guidance law, u * denotes the optimal interceptor guidance law, and the condition satisfied by the time-varying parameter λ includes the intersection condition and the terminal condition λ(t f ); wherein the intersection condition and the terminal condition λ(t f ) are expressed as:

[0107]

[0108] The extremum condition formula (18) defined according to the Hamiltonian function H is expressed as:

[0109]

[0110] S4.2.2: Solve the extremum condition formula (18) obtained in S4.2.1 to obtain the calculation formula (22) of the optimal maneuvering target guidance law v * and the optimal interceptor guidance law u * .

[0111]

[0112] In the formula, v * denotes the optimal maneuvering target guidance law, u * denotes the optimal interceptor guidance law, and λ(t) denotes the time-varying parameter at t

[0113] S4.2.3: According to the intersection condition formula (20) and the terminal condition λ(t f ) formula (21), the scalar form (14) of the zero-control miss distance and the scalar form (15) of the derivative of the zero-control miss distance, construct formulas (23) and (24);

[0114] λ(t) = P(t) · ZEM(t) (23)

[0115]

[0116] The reason for constructing the formula (23), (24) according to the formula (20), (21) is that the linear relationship between the lambda and the zero control off-target amount can be determined by the formula (20), (21);

[0117] In the formula (23), P(t) represents a time-varying variable at t moment;

[0118] In the formula (24), represents the derivative of P(t),

[0119] S4.2.4: Substituting the formula (22) into the formula (24) can obtain:

[0120]

[0121] S4.2.5: Simplifying the formula (25) into the formula (26) according to the formula (20), the formula (26) is expressed as:

[0122]

[0123] S4.2.6: Constructing an intermediate variable E, E=1 / P, constructing the formula (27) according to the intermediate variable E and the variable P, the formula (27) is expressed as:

[0124] PE=1 (27)

[0125] Deriving the formula (27) to obtain the formula (28), the formula (28) is expressed as:

[0126]

[0127] In the formula (28) represents the derivative of the intermediate variable E,

[0128] Simplifying the formula (28) to obtain the formula (29), the formula (29) is expressed as:

[0129]

[0130] S4.2.7: Substituting the formula (29) into the formula (26) can obtain the formula (30), the formula (30) is expressed as:

[0131]

[0132] S4.2.8: Integrating the formula (30) can obtain the formula (31), the formula (31) is expressed as:

[0133]

[0134] S4.2.9: Associating the formula (21) and the formula (23) can obtain the formula (32), the formula (32) is expressed as:

[0135] P(tf ) = 1 = E(t f ) (32)

[0136] In formula (32), P(t f ) represents a time-varying variable at time t f ;

[0137] S4.2.10: According to formula (27), (32), formula (31) can be simplified into formula (33) and formula (34), which are expressed as:

[0138]

[0139] S4.2.11: According to P(t) obtained in S4.2.10 and the performance function obtained in S4.1, the optimal interceptor guidance law u * and the optimal maneuvering target guidance law v * are obtained when the performance index J is minimum, which are expressed as:

[0140]

[0141] S4.2.12: The optimal interceptor guidance law u * (35) is converted into a linear quadratic differential game (LQDG) guidance law u LQDG containing a zero-control miss distance, which is expressed as:

[0142]

[0143] Wherein, N LQDG is expressed as a gain.

[0144] The other steps and parameters are the same as one of the first to seventh embodiments.

[0145] Simulation analysis combined with the first to seventh embodiments

[0146] The present application considers the first-order dynamic characteristics of the autopilot, and the zero-control miss distance (14) can be divided into the following three parts, and the zero-control miss distance scalar form ZEM is expressed as:

[0147] ZEM = ZEM0+ ZEM T + ZEM M (39)

[0148] Wherein, ZEM0represents the zero-control miss distance in the ideal case without considering the first-order dynamic characteristics, ZEM M represents the influence of the first-order dynamic characteristics of the interceptor on the zero-control miss distance; ZEM T represents the influence of the first-order dynamic characteristics of the maneuvering target on the zero-control miss distance,

[0149] The influence of the first-order dynamic characteristics of the interceptor on the zero-effort miss ZEM M According to the measurement device of the interceptor itself;

[0150] The influence of the first-order dynamic characteristics of the motor target on the zero-effort miss ZEM T According to the second-order linear extended observer;

[0151] Substitute formula (6) into formula (14), the zero-effort miss ZEM0in the ideal case can be obtained:

[0152]

[0153] In this part, simulation analysis is performed for different motor targets, and the effectiveness of the differential game countermeasure guidance strategy proposed is verified. The initial simulation conditions of the interceptor and the target are shown in Table 1, the guidance period sampling is 0.05s, the weight parameters in the guidance algorithm formula (35), (36) are designed as Q M = 0.001, Q T = 1, the state observer parameters are set as β1= 2, β2= 100, δ1= 0.5, δ2= 0.005, the first-order dynamic delay parameters are designed as τ M = 0.05s, τ T = 0.1s. Considering the saturation characteristics of the actuator, the upper limits of the interceptor and target accelerations are set as u max = 200m / s 2 , v max = 50m / s 2 .

[0154] Table 1 Initial parameters of the interceptor and target in the terminal segment of the vertical plane

[0155]

[0156] Considering whether the target performs game maneuver, three groups of simulation scenarios are set for analysis: 1) the target does not perform maneuver; 2) the target performs sinusoidal maneuver, as shown in formula (41); 3) the target performs differential countermeasure maneuver, as shown in formula (42). In addition, two kinds of guidance methods are added for comparison with the designed differential countermeasure method, the augmented proportional guidance law is shown in formula (44), and the navigation ratio is set as N APN = 6, and the norm type differential countermeasure guidance law is shown in formula (43).

[0157]

[0158] v NDG = v max sign(ZEM) (42)

[0159] uNDG = u max sign(ZEM) (43)

[0160]

[0161] The simulation results are shown in Figures 2-6 , the miss distances of the three guidance laws are 0.065m, 0.293m, 0.066m respectively for the non-maneuvering target, 1.286m, 0.469m, 0.082m respectively for the sinusoidal maneuvering target, and 0.098m, 0.079m, 0.062m respectively for the differential game maneuvering target. Figure 4 d) and Figure 6 d) show that the zero-effort miss fluctuates around 0 with time and approaches to 0 at the impact time.

[0162] From the above results, the proposed differential game guidance law has higher interception accuracy, which proves the effectiveness of the proposed algorithm for different maneuvering targets and the superiority compared with existing guidance algorithms.

[0163] From Figure 3 and Figure 5 the simulation results of the extended state observer, for the sinusoidal maneuvering target, the proposed extended state observer can track the target maneuvering acceleration Figure 3 b) shows the estimation error curve, which further illustrates the effectiveness of the state observer. However, in the differential game maneuvering mode, the target adopts the "Bang-Bang" maneuver as shown in equation (42), and Figure 5 a) shows that the target acceleration exists repeated switching phenomenon, which leads to the time delay behavior of the estimated value, and cannot track the real acceleration information in time. In this scenario, the state observer is not used to estimate the target information.

[0164] From Figure 2 c), Figure 2 d), Figure 4 a), Figure 4 b), Figure 6 a), and Figure 6 b) can be seen that during the interception process, the line-of-sight angle and its rate of change can converge to stability in time, which shows the stability of the proposed differential game guidance system.

[0165] The above is the preferred embodiment of the present application, the description of the present application uses individual cases to describe the principles and methods of the present application in detail, the above cases are only applicable to help ordinary technical personnel understand the method and core idea of the present application. At the same time, on the basis of the technical principles of the present application, the technical personnel can also make some deformations and improvements, which should be regarded as the protection scope of the present application, and the implementation method and application range of the present application can be expanded and changed. In summary, the content of the present application should not be understood as a limitation of the present application.

[0166] The above is the preferred embodiment of the present application, the description of the present application uses individual cases to describe the principles and methods of the present application in detail, the above cases are only applicable to help ordinary technical personnel understand the method and core idea of the present application. At the same time, on the basis of the technical principles of the present application, the technical personnel can also make some deformations and improvements, which should be regarded as the protection scope of the present application, and the implementation method and application range of the present application can be expanded and changed. In summary, the content of the present application should not be understood as a limitation of the present application.

Claims

1. A differential game-playing guidance method for maneuvering targets under conditions of missing target information, characterized in that, Includes the following steps: S1: Construct a two-dimensional mathematical model of the relative motion between the projectile and the target, and transform the two-dimensional mathematical model of the relative motion between the projectile and the target into a guidance system model in state-space form; S2: Construct a second-order linear extended observer and use it to estimate the information of the maneuvering target to obtain the observation information; S3: Based on the state-space form of the guidance system model obtained in S1 and the observation information obtained in S2, the scalar form of the zero-control miss quantity and the scalar form of the derivative of the zero-control miss quantity are obtained; S4: Based on the state-space form of the guidance system model obtained in S1, the observation information obtained in S2, and the scalar form of the zero-control miss quantity and the scalar form of the derivative of the zero-control miss quantity obtained in S3, the linear quadratic differential game (LQDG) guidance law containing the zero-control miss quantity is obtained. S5: The linear quadratic differential game (LQDG) guidance law control interceptor obtained by executing S4, which includes zero-control miss quantity.

2. The differential game guidance method for maneuvering targets under conditions of missing target information, as described in claim 1, is characterized in that, In step S1, a two-dimensional mathematical model of the relative motion between the projectile and the target is established, and this model is then transformed into a state-space guidance system model. The specific process is as follows: S1.1: Establish a two-dimensional mathematical model of the relative motion between the projectile and the target in the vertical plane, expressed by the following formula: Where M represents the interceptor, T represents the target, and q ε For the angle of view, Expressed as the velocity of the interceptor in the vertical plane. Indicates the velocity of the target within the plumb line. Indicates the trajectory inclination angle of the interceptor. The trajectory inclination of the maneuvering target is represented by R, which is the relative distance between the projectile and the target. h Represented as the relative distance component between the projectile and the target in the vertical plane. This is expressed as the guidance law of the interceptor. Guidance laws representing maneuvering targets; This represents the rate of change of the relative distance between the projectile and the target. Indicates the angular rate of the line of sight tilt. Indicates the rate of change of speed of a maneuvering target. Indicates the rate of change of the interceptor's velocity. Indicates the angular rate of inclination of a maneuvering target. Indicates the interceptor's trajectory inclination angle and angular rate; The second derivative of the relative distance component between the projectile and the target in the vertical plane, l T and l M Both represent intermediate variables. u M This represents the ideal guidance law for the interceptor, u T τ represents the ideal guidance law for a maneuvering target. M Let τ be the first-order delay parameter of the interceptor. T The first-order delay parameter represents the maneuvering target; Represents the dynamic model of the interceptor. A dynamic model representing a maneuvering target; The ideal guidance law of the interceptor u M This refers to a guidance law that does not consider the dynamic delay characteristics of the interceptor's actuator; The ideal guidance law for maneuvering targets u T This refers to a guidance law that does not consider the dynamic delay characteristics of the actuators of the maneuvering target; S1.2: Define system state variables Based on system state variables The two-dimensional mathematical model of the relative motion between the projectile and the target (1), (3) and (4) are converted into state-space form to obtain the guidance system model in state-space form: Among them, the guidance system matrix in state-space form State-space form of guidance system matrix State-space form of guidance system matrix It represents the derivative of the system state variable.

3. The differential game guidance method for maneuvering targets under conditions of missing target information, as described in claim 2, is characterized in that... In S2, a second-order linear extended observer is constructed, and the information of the maneuvering target is estimated using the second-order linear extended observer to obtain the observation information; The specific process is as follows: S2.1: Define the first state variable The second state variable is This represents an estimate of the rate of change of relative distance within the vertical plane. This represents the estimated acceleration of a maneuvering target. S2.2: Based on the first state variable z1 and the second state variable z2, construct a second-order linearly extended observer, which is expressed as: Where e1 is the observation error; β1 and β2 are the gain coefficients; and δ1 and δ2 > 0 are the gain parameters. Denotes the derivative of z1. The derivative of z2 is represented by fal(e1,δ1,δ2); fal(e1,δ1,δ2) represents the intermediate function. The specific formula for the intermediate function fal(e1,δ1,δ2) is as follows: sign() represents the sign function; S2.3: The target information of the maneuvering target is estimated by using a second-order linear extended observer to obtain the observation information.

4. The differential game guidance method for maneuvering targets under conditions of missing target information, as described in claim 3, is characterized in that... In S2.3, a second-order linear extended observer is used to estimate the target information of the maneuvering target, and the observation information is obtained, specifically expressed as follows: S2.2.1: The relative distance R between the missile and the target and the line-of-sight angle q at time t are measured by the interceptor's own measuring device. ε , S2.2.2: Based on the relative distance R between the projectile and the target at time t and the line-of-sight angle q ε Obtain the relative distance R between the projectile and the target in the vertical plane at time t. h Relative velocity between projectile and target The specific process is as follows: In the formula, R represents the relative distance between the projectile and the target, and q ε R represents the angle of inclination of the line of sight. h Indicates the relative distance between bullets and targets in the vertical plane. Indicates the relative velocity between the projectile and the target; S2.2.3: The relative distance R between the projectile and the target in the vertical plane at time t, obtained from the second-order linear extended observer and S2.2.

2. h Relative velocity between projectile and target The maneuvering target at time t is observed to obtain the observation information at time t; The observation information at time t includes z1 and z2.

5. The differential game guidance method for maneuvering targets under conditions of missing target information, as described in claim 4, is characterized in that... In step S3, based on the state-space form of the guidance system model obtained in S1 and the observation information obtained in S2, the scalar form of the zero-control miss quantity and the scalar form of the zero-control miss quantity derivative are obtained; the specific process is as follows: S3.1: Construct the zero-control miss distance ZEM based on the state-space form of the guidance system model obtained in S1 and the observation information obtained in S2, expressed by the formula: ZEM=D T X(t,t f )x(t) (9) In equation (9), the zero-control miss distance ZEM represents the state of the interceptor at time t, under the action of the zero guidance law, to estimate the time t at which the target is captured. f The miss distance obtained at the time of acquisition, whereby the miss distance represents the distance difference between the interceptor and the maneuvering target at the moment of acquisition; D T This represents the transpose of the performance function weight matrix D, where D = [1, 0, 0, 0]. T , X(t,t f The state transition matrix of the guidance system model (5) in state-space form is represented by x(t), where x(t) represents the state variable at time t. The state variable x(t) at time t is obtained based on the observation information obtained in S2. The state transition matrix X(t,t) f And can be obtained from formulas (10) and (11); X(t f ,t f )=I (10) In equation (10), I represents the identity matrix. Let L denote the derivative of the state transition matrix, in equation (11), L -1 [] denotes the inverse Laplace transform, s denotes the differential operator, and t go =t f -t represents the remaining flight time, and A represents the guidance system matrix in state-space form; t f Indicates the moment when a maneuvering target is captured; The time t for capturing the maneuvering target f This can be expressed as formula (12): R0 represents the relative distance between the missile and the target at the moment of target acquisition. This indicates the rate of change of the relative distance between the missile and the target at the moment of target acquisition; Indicates the trajectory inclination angle of the maneuvering target in the plumb plane at the moment of target acquisition. Indicates the line-of-sight angle of the maneuvering target in the plumb plane at the moment of target acquisition. This indicates the interceptor's trajectory inclination in the plumb plane at the moment of interception of a maneuvering target. S3.2: Combining equations (9) and (10), the derivative of the zero-control miss distance is obtained. Represented as: S3.3: Combining equations (9), (11) and (13), we obtain the scalar form (14) of the zero-control miss distance ZEM and the derivative of the zero-control miss distance. The scalar form (15) is specifically represented as: In the formula: It is represented as a nonlinear time-varying function, where l represents the variable in the nonlinear time-varying function.

6. The differential game guidance method for maneuvering targets under conditions of missing target information, as described in claim 5, is characterized in that... In step S4, based on the state-space form of the guidance system model obtained in S1, the observation information obtained in S2, and the scalar form of the zero-control miss quantity and its derivative obtained in S3, a linear quadratic differential game (LQDG) guidance law containing the zero-control miss quantity is obtained. The specific process is as follows: S4.1: Construct the performance metric J and the performance function. The specific process is as follows: The performance index J is expressed by the formula: The performance function is expressed by the formula: In equation (16), ZEM(t) f ) represents the interceptor's state at time t when it acquires the maneuvering target. f The zero-control miss distance of the missile target. Q represents the energy difference between the interceptor and the maneuvering target during the interception process. M Let Q represent a diagonal matrix, u represent the interceptor guidance law, and Q represent the direction of the interceptor. T Let v denote a diagonal matrix, and v denote the guidance law for maneuvering targets. S4.2: Based on the state-space form of the guidance system model obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss quantity obtained in S3, the scalar form of the derivative of the zero-control miss quantity, and the performance function obtained in S4.1, the linear quadratic differential game (LQDG) guidance law containing the zero-control miss quantity is obtained.

7. The differential game guidance method for maneuvering targets under missing target information as described in claim 6, characterized in that, In S4.2, based on the state-space form of the guidance system model obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss quantity obtained in S3, the scalar form of the derivative of the zero-control miss quantity, and the performance index function obtained in S4.1, a linear quadratic differential game (LQDG) guidance law containing the zero-control miss quantity is obtained; the specific process is as follows: S4.2.1: Construct the Hamiltonian function H, and define the extremum conditions based on the Hamiltonian function H. The Hamiltonian function H is expressed by the formula: ZEM(t) represents f The derivative of ); λ represents the time-varying parameter related to the conditions; v * U represents the optimal maneuvering target guidance law. * The optimal interceptor guidance law is given by the time-varying parameter λ, which satisfies conditions including the cross-section condition. With terminal condition λ(t) f ); where, the transverse condition With terminal condition λ(t) f This can be expressed as a formula: The extremum condition (18) defined according to the Hamiltonian function H is expressed as: S4.2.2: Solve the extreme value condition (18) obtained from S4.2.1 to obtain the optimal maneuvering target guidance law v. * and the optimal interceptor guidance law u * The calculation formula (22) is as follows: In the formula: v * U represents the optimal maneuvering target guidance law. * Let λ(t) represent the optimal interceptor guidance law, and let λ(t) represent the time-varying parameters at time t. S4.2.3: Based on the cross section condition With terminal condition λ(t) f ), scalar form of zero-control miss quantity (14), scalar form of zero-control miss quantity derivative (15), constructive formulas (23), (24); λ(t)=P(t)·ZEM(t) (23) In equation (23), P(t) represents the time-varying variable at time t; In equation (24), The derivative of P(t) is... S4.2.4: Substituting equation (22) into equation (24) yields: S4.2.5: Based on equation (20), equation (25) is simplified to equation (26), which is expressed as: S4.2.6: Construct intermediate variable E, E = 1 / P. Based on intermediate variable E and variable P, construct equation (27), which is expressed as: PE = 1 (27) Differentiating equation (27) yields equation (28), which can be expressed as: In formula (28) The derivative of the intermediate variable E. Simplifying equation (28) yields equation (29), which can be expressed as: S4.2.7: Substituting equation (29) into equation (26) yields equation (30), which can be expressed as: S4.2.8: Integrating equation (30) yields equation (31), which is expressed as: S4.2.9: Combining equations (21) and (23), we can obtain equation (32), which can be expressed as: P(t f )=1=E(t f ) (32) In equation (32), P(t) f ) represents t f Time-varying variables at any given moment; S4.2.10: According to equations (27) and (32), equation (31) can be simplified to equations (33) and (34), and the formulas of equations (33) and (34) are expressed as follows: S4.2.11: Based on P(t) obtained in S4.2.10 and the performance function (17) obtained in S4.1, the optimal interceptor guidance law u is obtained when the performance index J is minimized. * And the optimal maneuvering target guidance law v * This can be expressed as a formula: S4.2.12: Apply the optimal interceptor guidance law u * (35) Transformed into a linear quadratic differential game (LQDG) guidance law containing zero-control miss distance u LQDG This can be expressed as a formula: Where, N LQDG This is represented as gain.

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