Differential game guidance method for maneuvering target under target information loss

Abstract

The invention relates to the field of control, in particular to a maneuvering target-oriented differential game guidance method under target information loss. The invention discloses a differential game guidance method for a near space high-dynamic target scene under the condition of considering incomplete information of a target. The method comprises the following steps: expressing a tail-section interception problem, taking a vertical plane as a main research plane, and establishing a two-dimensional missile-target relative motion battle model; designing a linear expansion observer to estimate target acceleration information; and then an expression of the zero-control miss distance is given, and a linear quadratic differential game (LQDG) guidance law under incomplete target information is obtained. According to the quadratic differential game (LQDG) guidance law under the linear incomplete target information, the problem of low control accuracy of the interceptor under the incomplete target information in the prior art is solved.

Description

Technical Field

[0001] The invention belongs to the field of control, and in particular relates to a differential game guidance method for a maneuvering target under target information loss. Background Art

[0002] In recent years, hypersonic aircraft 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, the development of more efficient near-space hypersonic aircraft interception technology is the top priority of the current defense system. However, the current near-space hypersonic aircraft interception mission still has technical difficulties such as difficulty in discovery, detection and prediction, tracking and interception. Among them, the high speed and high maneuverability of near-space hypersonic aircraft and the complexity of the near-space environment have led to more severe challenges for the interceptor guidance system. Therefore, in this context, focusing on the interceptor guidance technology and breaking through the current guidance technology bottleneck for the near-space hypersonic aircraft interception mission is the research focus of near-space defense technology.

[0003] For the near-space hypersonic vehicle interception mission, direct collision kill is the most common interception method of the interception system. In order to achieve precise strikes on targets within a limited time, terminal guidance technology needs to have sufficient interception accuracy. In recent years, domestic and foreign experts have conducted a lot of research on terminal guidance technology, with obvious results, but most of the literature designs interception terminal guidance algorithms from the perspective of the interceptor. For unknown target motion information, it is necessary to design the optimal guidance law from the perspective of both the interceptor and the target.

[0004] The present invention establishes a relative motion model of missile-target engagement from the perspectives of both the interceptor and the target, and on this basis uses the zero-control miss amount and the energy consumption of both sides as performance indicators, and designs the optimal guidance algorithms for both sides based on the differential game method under incomplete information. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of low interceptor control accuracy in the prior art. We propose a differential game guidance method for highly dynamic targets in the absence of target information.

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

[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 on the two-dimensional plane. The two-dimensional projectile-target relative motion mathematical model of the present invention takes the vertical plane as the main attack plane and is based on the scenario of the interceptor intercepting the maneuvering target in the near space; the near space refers to the airspace 20 to 100 kilometers from the ground;

[0008] S2: Construct a second-order linear expansion observer, use the second-order linear expansion observer to estimate the information of the maneuvering target, and obtain the observation information;

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

[0010] S4: Based on the guidance system model in state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount and the scalar form of the derivative of the zero-control miss amount obtained in S3, a linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained;

[0011] S5: Execute the linear quadratic differential game (LQDG) guidance law including zero miss amount to control the interceptor.

[0012] The beneficial effects of the present invention are as follows: the present invention proposes a differential game guidance method for the interception mission of high dynamic targets in near space under incomplete information. First, the vertical plane is used as the main attack plane to construct a mathematical model of interceptor-target relative motion, and the differential game theory is used to construct a performance index function that meets the interception constraint, which involves variables such as zero-control miss amount and energy consumption of both parties, and designs a linear quadratic differential game guidance strategy. The present invention aims at the defect of the traditional guidance law that only designs the terminal guidance law from the perspective of the interceptor based on the known target motion information, and provides a linear quadratic differential game guidance strategy for high dynamic targets under incomplete target information, so as to achieve high-precision interception under incomplete information, and verify the effectiveness of the guidance method through interception tests under different maneuvering targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a diagram showing the relative motion relationship between the vertical plane projectile and the target of the present invention;

[0014] Figure 2 This is a schematic diagram of the simulation results of intercepting a non-maneuvering target according to the present invention:

[0015] Figure 2 a is a schematic diagram of the motion trajectory of the projectile at the end of the present invention;

[0016] Figure 2 b is a schematic diagram of the change in velocity of the projectile at the end of the present invention;

[0017] Figure 2 c is a schematic diagram of the change of the sight angle of the end-stage projectile of the present invention;

[0018] Figure 2 d is a schematic diagram of the change in the angular velocity of the sight line of sight in the final stage of the present invention;

[0019] Figure 3 Schematic diagram of observation simulation results of intercepting a sinusoidal maneuvering target according to the present invention;

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

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

[0022] Figure 4 This is a schematic diagram of the simulation results of intercepting a sinusoidal maneuvering target according to the present invention:

[0023] Figure 4 a is a schematic diagram of the change of the sight angle of the end-stage projectile of the present invention;

[0024] Figure 4 b is a schematic diagram of the change in the angular velocity of the sight line of sight at the end of the projectile;

[0025] Figure 4 c is a schematic diagram of the interceptor guidance law and the actual guidance acceleration of the present invention;

[0026] Figure 4 d is a schematic diagram of the change in the zero-control miss amount estimation of the present invention;

[0027] Figure 5 This is a schematic diagram of the simulation results of intercepting a maneuvering target using differential countermeasures according to the present invention:

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

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

[0030] Figure 6 This is a schematic diagram of the simulation results of intercepting a maneuvering target using differential countermeasures:

[0031] Figure 6 a is a schematic diagram of the change of the sight angle of the end-stage projectile of the present invention;

[0032] Figure 6 b is a schematic diagram of the change in the angular velocity of the sight line of sight at the end of the projectile;

[0033] Figure 6 c is a schematic diagram of the interceptor guidance law and the actual guidance acceleration of the present invention;

[0034] Figure 6 d is a schematic diagram of the change in the zero-control miss amount estimation of the present invention. DETAILED DESCRIPTION

[0035] Specific implementation method 1: Combination Figure 1The invention is described, comprising:

[0036] S1: Taking the vertical plane as the main attack plane, a two-dimensional mathematical model of the relative motion between the missile and the target is established according to the interception scenario of both sides in near space.

[0037] S2: Construct a linear expansion observer;

[0038] S3: Based on the two-dimensional projectile-target mathematical model established in S1, the zero-control miss distance is obtained;

[0039] S4: Based on the two-dimensional projectile-target mathematical model established in S1 and the observation information of the linear expansion observer established in S2, the linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained.

[0040] Specific implementation method 2: The difference between this implementation method and specific implementation method 1 is that:

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

[0042] S1.1: Since the interceptor is controlled by direct force and the target is controlled by aerodynamic force, the present invention sets the actuators of the interceptor and the maneuvering target as autopilots.

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

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

[0045]

[0046] Among them, M represents the interceptor, T represents the target, and q ε is the sight angle, is expressed as the velocity of the interceptor in the plumb plane, represents the velocity of the target in the plumb plane, represents the interceptor's ballistic inclination angle, represents the ballistic inclination angle of the maneuvering target, R represents the relative distance between the projectile and the target, and R h It is expressed as the relative distance component of the projectile and the target in the vertical plane, is expressed as the guidance law of the interceptor, represents the guidance law for a maneuvering target; Indicates the rate of change of the relative distance between the projectile and the target. represents the line of sight inclination angular rate, represents the speed change rate of the maneuvering target, represents the rate of change of interceptor speed, represents the ballistic inclination angular rate of the maneuvering target, represents the interceptor trajectory inclination angular rate; It represents the second-order derivative of the relative distance component between the projectile and the target in the vertical plane, l T and l M All 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 Denotes 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, A dynamic model representing a maneuvering target;

[0047] The interceptor ideal guidance law u M It refers to the guidance law that does not take into account the dynamic delay characteristics of the actuator of the interceptor;

[0048] The ideal guidance law u for a maneuvering target T It refers to the guidance law that does not take into account the dynamic delay characteristics of the actuators of the maneuvering target;

[0049] S1.2: Define system state variables According to the system state variables The two-dimensional missile-target relative motion mathematical model (1), (3) and (4) are converted into state space form to obtain the guidance system model in state space form:

[0050]

[0051] Among them, the guidance system matrix in state space form is The guidance system matrix in state space form The guidance system matrix in state space form represents the derivative of the system state variable, and the other steps and parameters are the same as those in the first specific implementation method.

[0052] Specific implementation method three: This implementation method is different from the specific implementation method one in that:

[0053] In S2, a second-order linear expansion observer is constructed, and the information of the maneuvering target is estimated by using the second-order linear expansion observer to obtain observation information; the specific process is:

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

[0055] S2.2: According to the first state variable z1 and the second state variable z2, a second-order linear expansion observer is constructed, and the second-order linear expansion observer is expressed as:

[0056]

[0057] Among them, 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 z2; fal(e1,δ1,δ2) represents the intermediate function;

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

[0059]

[0060] sign() represents the sign function.

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

[0062]

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

[0064] S2.3: Use a second-order linear expansion observer to estimate the target information of the maneuvering target to obtain observation information. Other steps and parameters are the same as those in the first to second embodiments.

[0065] Specific implementation method 4: This implementation method is different from specific implementation methods 1 to 4 in that:

[0066] In S2.3, a second-order linear expansion observer is used to estimate the target information of the maneuvering target to obtain observation information, which is specifically expressed as:

[0067] 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 ,

[0068] S2.2.2: Based on the relative distance R between the projectile and the target and the line of sight inclination angle q at time t ε Get 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:

[0069]

[0070] In the formula, R represents the relative distance between the projectile and the target, q ε Represents the sight angle, R h Indicates the relative distance between the projectile and the target in the vertical plane. Indicates the relative speed of the projectile and target;

[0071] S2.2.3: The relative distance R of the projectile in the vertical plane at time t obtained by the second-order linear expansion observer and S2.2.2 h Relative velocity between projectile and target Observe the maneuvering target at time t and obtain the 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 those in the first to third embodiments.

[0074] Specific implementation method 5: This implementation method is different from specific implementation methods 1 to 4 in that:

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

[0076] S3.1: Based on the guidance system model in the state space form obtained in S1 and the observation information obtained in S2, the zero control miss distance ZEM is constructed and expressed as:

[0077] This paper introduces the zero-control miss amount into the differential game guidance law as a performance indicator, which can be expressed as:

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

[0079] In formula (9), the zero miss distance ZEM is expressed as the state of the interceptor at time t mapped to the time t of the captured target under the action of the zero guidance law: f The miss distance obtained when the interceptor is captured is represented by the distance difference between the interceptor and the maneuvering target at the capture moment; D T represents the transpose of the performance function weight matrix D, wherein the performance function weight matrix D=[1,0,0,0] T , X(t,t f ) is expressed as the state transfer matrix of the guidance system model (5) in state space form, x(t) represents the state variable at time t, and the state variable x(t) at time t is obtained according to the observation information obtained by S2. It can be known from S1.2 that The state variables at time t can be obtained from the observation information z1 and z2;

[0080] The state transfer matrix X(t,t f ) and can be obtained by formulas (10) and (11);

[0081]

[0082] In formula (10), I represents the unit matrix, represents the derivative of the state transfer matrix. In formula (11), L -1 [] represents the inverse Lagrange transform, s represents the 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 Indicates the moment of capturing a maneuvering target;

[0083] The time t at which the maneuvering target is captured f It can be expressed as:

[0084]

[0085] R0 represents the relative distance between the missile and the target when capturing the maneuvering target. It indicates the rate of change of the relative distance between the projectile and the target when capturing the maneuvering target; It indicates the inclination angle of the plumb line trajectory of the maneuvering target at the moment of capturing the maneuvering target. It represents the plumb line of sight angle of the maneuvering target at the moment of capturing the maneuvering target. represents the interceptor's trajectory inclination in the plumb plane at the moment of capturing the maneuvering target, S3.2: Combining equations (9) and (10), we get the derivative of the zero-control miss distance It is expressed as:

[0086]

[0087] S3.3: Combining equations (9), (11) and (13), we can obtain the scalar form of the zero miss distance ZEM (14) and the derivative of the zero miss distance ZEM: The scalar form of (15) is expressed as:

[0088]

[0089] Where: Expressed as a nonlinear time-varying function, Represents a variable in a nonlinear time-varying function.

[0090] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0091] Specific implementation method 6: This implementation method is different from specific implementation methods 1 to 5 in that:

[0092] In S4, according to the guidance system model in the state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount and the scalar form of the derivative of the zero-control miss amount obtained in S3, a linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained. The specific process is:

[0093] S4.1: Construct performance index J and construct performance function. The specific process is as follows:

[0094] The performance index J is expressed by the formula:

[0095]

[0096] The performance function is expressed as:

[0097]

[0098] In formula (16), ZEM(t f ) is the zero-control miss distance of the interceptor and the maneuvering target at the capture moment. This part of the performance index indicates that the designed differential game guidance law reduces the miss distance of the projectile, that is, improves the hit rate.

[0099] It is expressed as the difference in energy consumed by the interceptor and the maneuvering target during the interception process, Q M represents a diagonal matrix, u represents the interceptor guidance law, Q T represents a diagonal matrix, v represents the guidance law of the maneuvering target, and represents that this part of the performance index means that less energy is used to intercept the target, and the target can consume more energy.

[0100] S4.2: According to the guidance system model in the state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount obtained in S3, the scalar form of the derivative of the zero-control miss amount and the performance function obtained in S4.1, a linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained; the other steps and parameters are the same as those in one of the specific implementation modes one to five.

[0101] Specific implementation method 7: This implementation method is different from specific implementation methods 1 to 6 in that:

[0102] In S4.2, according to the guidance system model in the state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount obtained in S3, the scalar form of the derivative of the zero-control miss amount, and the performance index function obtained in S4.1, a linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained; the specific process is:

[0103] S4.2.1: Construct the Hamiltonian function H and define the extreme value conditions based on the Hamiltonian function H.

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

[0105]

[0106] ZEM(t f ) is the derivative of; λ represents a time-varying parameter related to the condition; v * represents the optimal maneuvering target guidance law, u * represents the optimal interceptor guidance law, and the conditions satisfied by the time-varying parameter λ include the transversality condition With the terminal condition λ(t f ), where the transversality condition With the terminal condition λ(t f ) is expressed as:

[0107]

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

[0109]

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

[0111]

[0112] Where: v * represents the optimal maneuvering target guidance law, u * represents the optimal interceptor guidance law, λ(t) represents the time-varying parameter at time t

[0113] S4.2.3: Based on the cross-sectional condition Formula (20) and terminal condition λ(t f ) formula (21), the scalar form of the zero-control miss amount (14), the scalar form of the zero-control miss amount derivative (15), construct formulas (23) and (24);

[0114] λ(t)=P(t)·ZEM(t) (23)

[0115]

[0116] The reason for constructing equations (23) and (24) according to equations (20) and (21) is that it can be determined from equations (20) and (21) that λ has a linear relationship with the zero-control miss amount;

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

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

[0119] S4.2.4: Substituting equation (22) into equation (24), we obtain:

[0120]

[0121] S4.2.5: According to equation (20), equation (25) is simplified to equation (26), which is expressed as:

[0122]

[0123] S4.2.6: Construct an intermediate variable E, E = 1 / P, and construct equation (27) based on the intermediate variable E and variable P. Equation (27) is expressed as:

[0124] PE=1 (27)

[0125] By derivation of formula (27), we can get formula (28), which is expressed as:

[0126]

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

[0128] Simplifying formula (28) gives formula (29), which is expressed as:

[0129]

[0130] S4.2.7: Substituting equation (29) into equation (26) yields equation (30), which is expressed as:

[0131]

[0132] S4.2.8: Integrating equation (30) yields equation (31), which is expressed as:

[0133]

[0134] S4.2.9: Combining equations (21) and (23) yields equation (32), which can be expressed as:

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

[0136] In formula (32), P(t f ) indicates t f Time-varying variables at moments;

[0137] S4.2.10: According to equations (27) and (32), equation (31) can be simplified to equations (33) and (34). The formulas of equations (33) and (34) are expressed as follows:

[0138]

[0139] S4.2.11: Based on P(t) obtained in S4.2.10 and the performance function obtained in S4.1, obtain the optimal interceptor guidance law u with the minimum performance index J * and the optimal maneuvering target guidance law v * , expressed as:

[0140]

[0141] S4.2.12: Set the optimal interceptor guidance law u * (35) is transformed into the linear quadratic differential game (LQDG) guidance law u including the zero miss distance LQDG , expressed as:

[0142]

[0143] Among them, N LQDG Expressed as gain.

[0144] The other steps and parameters are the same as those in the specific implementation modes 1 to 6.

[0145] Combining the simulation analysis of specific implementation methods one to seven

[0146] The present invention takes into account the first-order dynamic characteristics of the autopilot, and the zero miss amount (14) can be divided into the following three parts. The zero miss amount scalar form ZEM is expressed by the formula:

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

[0148] Among them, ZEM0 represents the zero control miss distance in the ideal case without considering the first-order dynamic characteristics, and ZEM M It 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-control miss distance ZEM M According to the interceptor's own measuring device;

[0150] The influence of the first-order dynamic characteristics of the maneuvering target on the zero control miss distance ZEM T It is obtained according to the second-order linear expansion observer;

[0151] Substituting equation (6) into equation (14), we can obtain the ideal zero-control miss distance ZEM0:

[0152]

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

[0154] Table 1 Initial parameters of the vertical plane of the terminal interception of the projectile

[0155]

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

[0157]

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

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

[0160]

[0161] The simulation results are as follows Figure 2-Figure 6 As shown in the figure, the terminal miss distances of the three guidance laws for non-maneuvering targets are 0.065m, 0.293m, and 0.066m respectively; the miss distances for sinusoidal maneuvering targets are 1.286m, 0.469m, and 0.082m respectively; and the miss distances for differential strategy maneuvering targets are 0.098m, 0.079m, and 0.062m respectively. Figure 4 d) and Figure 6 d) It can be seen that the zero-control miss distance fluctuates around 0 over time and is close to 0 at the impact moment.

[0162] From the above results, it can be seen that the proposed differential game guidance law has higher interception accuracy, which proves the effectiveness of the algorithm proposed in the present invention for different maneuvering targets and its superiority over the existing guidance algorithms.

[0163] Depend on Figure 3 and Figure 5 The simulation results of the extended state observer show that for sinusoidal maneuvering targets, the proposed extended state observer can track the target maneuvering acceleration in a timely manner. Figure 3 b) shows the estimation error curve, which further illustrates the effectiveness of the state observer. However, in the differential game maneuver mode, the target adopts the "Bang-Bang" maneuver as shown in Equation (42), which is Figure 5 a) It can be seen that the target acceleration is repeatedly switched, resulting in a time lag in the estimated value, which makes it impossible to track the real acceleration information in time. In this scenario, the state observer is not used to estimate the target information.

[0164] Depend on Figure 2 c), Figure 2 d), Figure 4 a), Figure 4 b), Figure 6 a), and Figure 6 b) It can be seen that during the interception process, the missile-target 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 a preferred embodiment of the present invention. This specification uses individual implementation cases to describe the principles and implementation methods of the present invention in detail. The above implementation cases are only suitable for helping ordinary technicians understand the methods and core ideas of the present invention. At the same time, based on the technical principles of the present invention, technicians can also make several deformations and improvements, which should be regarded as the protection scope of the present invention. The implementation method and application scope of the present invention can be expanded and changed. In summary, the content of this specification should not be understood as a limitation of the present invention.

[0166] The above only describes the preferred embodiments of the present invention. It should be understood that the present invention is not limited to the above specific implementation methods. Although the present invention has been disclosed as above in the preferred embodiments, it is not used to limit the present invention. Any technician familiar with the profession can make some changes or modify the technical contents disclosed above into equivalent embodiments with equivalent changes without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. A differential game guidance method for a maneuvering target in the absence of target information, characterized in that: The following steps are involved: S1: Construct a two-dimensional projectile-target relative motion mathematical model, and transform the two-dimensional projectile-target relative motion mathematical model into a guidance system model in state space form; S2: Construct a second-order linear expansion observer, use the second-order linear expansion observer to estimate the information of the maneuvering target, and obtain the observation information; S3: According to the guidance system model in the state space form obtained in S1 and the observation information obtained in S2, the scalar form of the zero-control miss amount and the scalar form of the derivative of the zero-control miss amount are obtained; S4: Based on the guidance system model in state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount and the scalar form of the derivative of the zero-control miss amount obtained in S3, a linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained; S5: Execute the linear quadratic differential game (LQDG) guidance law including zero miss distance obtained in S4 to control the interceptor.

2. The differential game guidance method for a maneuvering target in the absence of target information according to claim 1, characterized in that: In the S1, a two-dimensional projectile-target relative motion mathematical model is established, and the two-dimensional projectile-target relative motion mathematical model is converted into a guidance system model in a state space form. The specific process is as follows: S1.1: Establish a two-dimensional mathematical model of the relative motion of the projectile and the target in the vertical plane, expressed as follows: Among them, M represents the interceptor, T represents the target, and q ε is the sight angle, Expressed as the interceptor's velocity in the vertical plane, represents the velocity of the target in the plumb plane, represents the interceptor's ballistic inclination angle, represents the ballistic inclination angle of the maneuvering target, R represents the relative distance between the projectile and the target, and R h It is expressed as the relative distance component of the projectile and the target in the vertical plane, is expressed as the guidance law of the interceptor, represents the guidance law for a maneuvering target; Indicates the rate of change of the relative distance between the projectile and the target. represents the line of sight inclination angular rate, represents the speed change rate of the maneuvering target, represents the rate of change of interceptor speed, represents the ballistic inclination angular rate of the maneuvering target, represents the interceptor trajectory inclination angular rate; It represents the second-order derivative of the relative distance component between the projectile and the target in the vertical plane, l T and l M All 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 Denotes 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, A dynamic model representing a maneuvering target; The interceptor ideal guidance law u M It refers to the guidance law that does not take into account the dynamic delay characteristics of the actuator of the interceptor; The ideal guidance law u for a maneuvering target T It refers to the guidance law that does not take into account the dynamic delay characteristics of the actuators of the maneuvering target; S1.2: Define system state variables According to the system state variables The two-dimensional missile-target relative motion mathematical model (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 is The guidance system matrix in state space form The guidance system matrix in state space form represents the derivative of the system state variables.

3. The differential game guidance method for a maneuvering target in the absence of target information according to claim 2 is characterized in that: In S2, a second-order linear expansion observer is constructed, and the information of the maneuvering target is estimated by using the second-order linear expansion observer to obtain observation information; The specific process is: S2.1: Define the first state variable and the second state variable is represents the estimated value of the rate of change of relative distance in the vertical plane, represents the estimated value of the maneuvering target acceleration; S2.2: According to the first state variable z1 and the second state variable z2, a second-order linear expansion observer is constructed, and the second-order linear expansion observer is expressed as: Among them, 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 the intermediate function; The specific formula of the intermediate function fal(e1,δ1,δ2) is expressed as: sign() represents the sign function; S2.3: Use a second-order linear expansion observer to estimate the target information of the maneuvering target and obtain observation information.

4. The differential game guidance method for a maneuvering target in the absence of target information according to claim 3 is characterized in that: In S2.3, a second-order linear expansion observer is used to estimate the target information of the maneuvering target to obtain observation information, which is specifically expressed as: 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 and the line of sight inclination angle q at time t ε Get 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: In the formula, R represents the relative distance between the projectile and the target, q ε Represents the sight angle, R h Indicates the relative distance between the projectile and the target in the vertical plane. Indicates the relative speed of the projectile and target; S2.2.3: The relative distance R of the projectile in the vertical plane at time t obtained by the second-order linear expansion observer and S2.2.2 h Relative velocity between projectile and target Observe the maneuvering target at time t and obtain the observation information at time t; The observation information at the time t includes: z1 and z2.

5. The differential game guidance method for a maneuvering target in the absence of target information according to claim 4, characterized in that: In S3, the scalar form of the zero-control miss amount and the scalar form of the zero-control miss amount derivative are obtained according to the guidance system model in the state space form obtained in S1 and the observation information obtained in S2; the specific process is: S3.1: Based on the guidance system model in the state space form obtained in S1 and the observation information obtained in S2, the zero control miss distance ZEM is constructed and expressed as: ZEM=D T X(t,t f )x(t) (9) In formula (9), the zero control miss distance ZEM is expressed as the state of the interceptor at time t and the estimated capture time t under the action of the zero guidance law f The miss distance obtained when the interceptor is captured is represented by the distance difference between the interceptor and the maneuvering target at the capture moment; D T represents the transpose of the performance function weight matrix D, wherein the performance function weight matrix D=[1,0,0,0] T , X(t,t f ) represents the state transfer matrix of the guidance system model (5) in state space form, 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 by S2. The state transfer matrix X(t,t f ) and can be obtained by formulas (10) and (11); X(t f ,t f )=I (10) In formula (10), I represents the unit matrix, represents the derivative of the state transfer matrix. In formula (11), L -1 [] represents the inverse Lagrange transform, s represents the 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 Indicates the moment of capturing a maneuvering target; The time t at which the maneuvering target is captured f It can be expressed as: R0 represents the relative distance between the missile and the target when capturing the maneuvering target. It indicates the rate of change of the relative distance between the projectile and the target when capturing the maneuvering target; It indicates the inclination angle of the plumb line trajectory of the maneuvering target at the moment of capturing the maneuvering target. It represents the plumb line of sight angle of the maneuvering target at the moment of capturing the maneuvering target. It represents the ballistic inclination angle of the interceptor in the plumb plane at the moment of capturing the maneuvering target. S3.2: Combining equations (9) and (10), we can obtain the derivative of the zero-control miss distance It is expressed as: S3.3: Combining equations (9), (11) and (13), we can obtain the scalar form of the zero miss distance ZEM (14) and the derivative of the zero miss distance ZEM: The scalar form of (15) is expressed as: Where: It is expressed as a nonlinear time-varying function, and l represents the variable in the nonlinear time-varying function.

6. The differential game guidance method for a maneuvering target in the absence of target information according to claim 5, characterized in that: In S4, according to the guidance system model in the state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount and the scalar form of the derivative of the zero-control miss amount obtained in S3, a linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained. The specific process is: S4.1: Construct performance index J and construct performance function. The specific process is as follows: The performance index J is expressed by the formula: The performance function is expressed as: In formula (16), ZEM(t f ) represents the interceptor capturing the maneuvering target at time t f The zero-control miss distance of the projectile, It is expressed as the difference in energy consumed by the interceptor and the maneuvering target during the interception process, Q M represents a diagonal matrix, u represents the interceptor guidance law, Q T represents a diagonal matrix, v represents the guidance law of the maneuvering target; S4.2: Based on the guidance system model in state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount obtained in S3, the scalar form of the derivative of the zero-control miss amount, and the performance function obtained in S4.1, the linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained.

7. The differential game guidance method for a maneuvering target in the absence of target information according to claim 6, characterized in that: In S4.2, according to the guidance system model in the state space form obtained in S1, the observation information obtained in S2, the scalar form of the zero-control miss amount obtained in S3, the scalar form of the derivative of the zero-control miss amount, and the performance index function obtained in S4.1, a linear quadratic differential game (LQDG) guidance law including the zero-control miss amount is obtained; the specific process is: S4.2.1: Construct the Hamiltonian function H and define the extreme value conditions based on the Hamiltonian function H. The Hamiltonian function H is expressed by the formula: ZEM(t f ) is the derivative of; λ represents a time-varying parameter related to the condition; v * represents the optimal maneuvering target guidance law, u * represents the optimal interceptor guidance law, and the conditions satisfied by the time-varying parameter λ include the transversality condition With the terminal condition λ(t f ), where the transversality condition With the terminal condition λ(t f ) is expressed as: The extreme value condition formula (18) is defined according to the Hamiltonian function H, which is expressed as: S4.2.2: Solve the extreme value condition (18) obtained in S4.2.1 to obtain the optimal maneuvering target guidance law v * and the optimal interceptor guidance law u * The calculation formula (22) is: Where: v * represents the optimal maneuvering target guidance law, u * represents the optimal interceptor guidance law, λ(t) represents the time-varying parameter at time t S4.2.3: Based on the cross-sectional condition With the terminal condition λ(t f ), the scalar form of the zero-control miss amount (14), the scalar form of the derivative of the zero-control miss amount (15), construct equations (23) and (24); λ(t)=P(t)·ZEM(t) (23) In formula (23), P(t) represents the time-varying variable at time t; In formula (24), represents the derivative of P(t), S4.2.4: Substituting equation (22) into equation (24), we obtain: S4.2.5: According to equation (20), equation (25) is simplified to equation (26), which is expressed as: S4.2.6: Construct an intermediate variable E, E = 1 / P, and construct equation (27) based on the intermediate variable E and variable P. Equation (27) is expressed as: PE=1 (27) By derivation of formula (27), we can get formula (28), which is expressed as: In formula (28) represents the derivative of the intermediate variable E, Simplifying formula (28) gives formula (29), which is expressed as: S4.2.7: Substituting equation (29) into equation (26) yields equation (30), which is expressed as: S4.2.8: Integrating equation (30) yields equation (31), which is expressed as: S4.2.9: Combining equations (21) and (23) yields equation (32), which can be expressed as: P(t f )=1=E(t f ) (32) In formula (32), P(t f ) indicates t f Time-varying variables at moments; S4.2.10: According to equations (27) and (32), equation (31) can be simplified to equations (33) and (34). 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 with the minimum performance index J is obtained. * and the optimal maneuvering target guidance law v * , expressed as: S4.2.12: Set the optimal interceptor guidance law u * (35) is transformed into the linear quadratic differential game (LQDG) guidance law u including the zero miss distance LQDG , expressed as: Among them, N LQDG Expressed as gain.

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