Design of terminal angle attack guidance law for interception of maneuvering targets with field of view constraints

Abstract

The present application relates to a kind of interception motor target meets the terminal angle attack guidance law design method of field angle constraint, belong to missile guidance control technical field.The present application is based on three-dimensional interception model, constructs the design goal of guidance rate meeting the field angle of seeker and terminal angle constraint, selects neural network estimation model, designs multiple constraint guidance rate.The present application is difficult to meet the guidance demand of strong motor target confrontation interception missile for traditional zero control miss distance interception guidance law, gives a kind of interception motor target meets the terminal angle attack guidance law of field angle constraint of seeker, can be realized with the desired terminal angle to motor target by interception missile under the condition of meeting the field angle constraint of seeker.

Description

Technical Field

[0001] This invention belongs to the field of missile guidance and control technology, specifically relating to a design method for a terminal angle attack guidance law that satisfies the field of view constraint when intercepting maneuvering targets. Background Technology

[0002] With the increasing maneuverability and penetration capabilities of attack aircraft targets, traditional zero-control miss-range interception guidance laws have reduced the destructive power of interceptor warheads and the probability of successful interception. Therefore, both domestic and international research focuses more on the design of multi-constraint guidance laws, namely, striking the target's key components at the desired attack angle. Furthermore, considering the physical constraints in guidance law design, such as seeker field-of-view constraints and actuator output limitations, terminal guidance laws that consider seeker field-of-view and attack angle constraints for target engagement have become a hot research topic both domestically and internationally.

[0003] However, existing domestic and international research literature on guidance law design for attack angle and field of view constraints mainly focuses on the design of multi-constraint guidance laws for air-to-ground missiles or anti-ship missiles. There is little research on terminal guidance for intercepting maneuvering targets at the desired attack angle under the condition of satisfying the seeker's field of view constraint. The literature "Kim HG, Kim HJ. Field-of-View Constrained Guidance Law for a Maneuvering Target With ImpactAngle Control[J].IEEE Transactions on Aerospace and Electronic Systems,2020(6):56" studies the problem of intercepting maneuvering targets at the desired attack angle under the condition of two-dimensional field of view constraint. The relationship between the terminal desired field of view and the terminal desired attack angle is derived, and the attack angle constraint is transformed into the line of sight constraint. The field of view is constrained by introducing a sign function in the sliding surface, and a stability proof of the field of view and attack angle satisfying the constraints is given. The literature “Wang X, Zhang Y, Wu H. Sliding mode control based impact angle control guidance considering the seeker’s field-of-view constraint[J]. Isa Transactions, 2016, 61” further designs a multi-constraint guidance law for intercepting maneuvering targets by using sliding mode control based on the sufficient condition of satisfying the field-of-view constraint.

[0004] However, the guidance laws for intercepting maneuvering targets in the aforementioned literature that satisfy the seeker's field of view and angle of attack constraints are all designed in a two-dimensional plane. When applied to three-dimensional guidance law design, the coupling between the pitch and yaw channels will affect the guidance accuracy. Therefore, this invention proposes a multi-constraint guidance law for intercepting maneuvering targets based on sliding mode surfaces and filters. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] The technical problem to be solved by the present invention is how to provide a method for designing a terminal angle attack guidance law that satisfies the field of view constraint when intercepting maneuvering targets, so as to solve the problem that the guidance law for intercepting maneuvering targets that satisfies the field of view and attack angle constraints of the seeker is designed in a two-dimensional plane.

[0007] (II) Technical Solution

[0008] To address the aforementioned technical problems, this invention proposes a method for designing a terminal angle attack guidance law that satisfies the field of view constraint when intercepting maneuvering targets. The method includes: constructing a guidance rate design target that satisfies the field of view and terminal angle constraints of the seeker based on a three-dimensional interception model; constructing a neural network estimation model; and designing a multi-constraint guidance rate.

[0009] (III) Beneficial Effects

[0010] This invention proposes a terminal angle attack guidance law design method for intercepting maneuvering targets while satisfying field-of-view constraints. Based on a three-dimensional interception model, this invention constructs a guidance rate design target that satisfies the seeker's field-of-view and terminal angle constraints, selects a neural network estimation model, and designs a multi-constraint guidance rate. Addressing the difficulty of traditional zero-control miss-range interception guidance laws meeting the guidance requirements of interceptor missiles against highly maneuvering targets, this invention presents a terminal angle attack guidance law for intercepting maneuvering targets while satisfying the seeker's field-of-view constraints. This allows the interceptor missile to intercept maneuvering targets at the desired terminal angle while meeting the seeker's field-of-view constraints. Attached Figure Description

[0011] Figure 1 This is the three-dimensional attack model of the present invention;

[0012] Figure 2 The simulation results are shown in the following diagrams: (a) is the three-dimensional interception trajectory diagram; (b) is the overload diagram; (c) is the field of view angle; (d) is the field of view angle constraint diagram; (e) is the sliding surface curve diagram; and (f) is the relative distance diagram. Detailed Implementation

[0013] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0014] This invention belongs to the field of missile guidance and control technology, and specifically relates to the design of the guidance rate for interceptor missiles to intercept maneuvering targets. It can ensure that the interceptor missile intercepts the maneuvering target at the desired terminal angle under the condition of satisfying the field of view constraint of the seeker.

[0015] To address the challenge that traditional zero-control miss-range interception guidance laws are insufficient to meet the guidance requirements of interceptor missiles against highly maneuverable targets, this invention presents a terminal angle attack guidance law design method that satisfies the seeker's field of view constraints when intercepting maneuvering targets. Based on a three-dimensional interception guidance model, this invention proposes a guidance law design target that satisfies the seeker's field of view and terminal angle constraints in a three-dimensional interception scenario. A neural network estimation model for target maneuvering disturbances is constructed, a multi-constraint guidance law sliding surface is designed, a time-varying obstacle avoidance Lyapunov function is defined, and it is proven that the interceptor missile can intercept maneuvering targets with the desired terminal angle under the condition of satisfying the seeker's field of view constraints.

[0016] The technical solution of this invention is as follows: Based on a three-dimensional interception model, a guidance rate design target that satisfies the seeker's field of view and terminal angle constraints is constructed; a neural network estimation model is selected; and a multi-constraint guidance rate is designed. The specific method steps are as follows:

[0017] A. Construction of a 3D Interception Model

[0018] Consider as Figure 1 The three-dimensional interception model shown is illustrated, where M and T represent the interceptor missile and the target, respectively, and four coordinate systems are defined, namely the inertial coordinate system MX. I Y I Z I Line of sight coordinate system MX L Y L Z L The ballistic coordinate system MX of the interceptor missile M Y M Z M and the target's ballistic coordinate system TX T Y T Z T The variable r is the relative distance between the interceptor missile and the target, and the conversion between the inertial frame and the line-of-sight frame is defined by two angles: the line-of-sight tilt angle θ. L and line of sight deflection ψ L The velocity system and line-of-sight system of the interceptor missile are defined as being connected by the forward tilt angle θ of the interceptor missile. M and the pre-positioned deflection angle ψ M Similarly, the conversion is performed between the target's velocity system and line-of-sight system via the target's forward tilt angle θ. T and the pre-positioned deflection angle ψ T Define the parameters. Assume the interceptor missile's velocity is V. M and target speed V T All are constant values. Determined by the interceptor missile's lead angle σ. Mand the forward tilt angle θ of the interceptor missile M and the pre-positioned deflection angle ψ M The geometric relationship between them can be expressed as follows:

[0019] cosσ M =cosθ M ·cosψ M (1)

[0020] Furthermore, the interception kinematics and dynamics can be further described as follows:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Among them, (a yM a zM ) and (a yT a zT These are the normal accelerations of the interceptor missile and the target, respectively.

[0029] To further derive the terminal guidance law for maneuvering targets that satisfies the field of view and terminal angle constraints, we define x1 = θ L -θ LD , x3=ψ L -ψ Ld , Where, θ Ld , ψ Ld Let be the desired field of view angle, and the dynamic equations for the above state variables are expressed as follows:

[0030]

[0031] in, h1=-cosθ M / R, d1=cosθ T ·a zT / R.

[0032]

[0033] in, h2=(sinθ M sinψ M ) / (Rcosθ L h3=-cosψ M / (Rcosθ L ), d2=(cosψ T ·a yT ) / (R·cosθ L )-(sinθ T ·sinψ T ·a zT ) / (R·cosθ L ).

[0034] B. Constructing Guidance Law Design Objectives

[0035] The design objective of the guidance law in a 3D interception scenario, satisfying the seeker's field of view and terminal angle constraints, is as follows:

[0036]

[0037] Where, θ Ld , ψ Ld These are the desired pitch and yaw line-of-sight angles. The maximum forward angle is limited by the seeker's field of view. Furthermore, zero-control miss distance can be achieved when the line-of-sight angular rate approaches zero; therefore, the target conversion design...

[0038]

[0039] Based on the definitions of state variables x1, x2, x3, and x4, the equation satisfies the following formula:

[0040]

[0041] Unlike two-dimensional interception guidance where there is an explicit relationship between the desired terminal attack angle and the terminal line-of-sight angle, in three-dimensional interception scenarios, based on the nonlinear coupling relationship between the pitch and V-yaw channels, it is impossible to derive the explicit geometric relationship between the desired terminal pitch attack angle and the desired terminal yaw attack angle and the terminal line-of-sight tilt and deflection angles. However, for the three-dimensional interception maneuvering target guidance problem, considering the terminal line-of-sight angle constraint can ensure that the terminal line-of-sight angle tracking error and its first derivative converge to zero simultaneously, thereby effectively avoiding the controller chattering problem at the moment of collision.

[0042] C. Constructing a neural network estimation model

[0043] The following neural network is used to estimate the disturbances d1 and d2 caused by the target maneuver.

[0044]

[0045] in, It is an estimation error. yes The estimated value, Φ(Y) i ) is the Gaussian function, C i and σ i These are the width vector of the hidden layer Gaussian function and the coordinate vector of the center point of the Gaussian function, respectively. i It is the input to the neural network. It is ω i The optimal value, i.e.

[0046]

[0047] in, It is compact set, l i m i Let be the dimension of the set of real numbers.

[0048] Assumption 1: Assume that the estimation error is bounded and satisfies the following inequality

[0049]

[0050] Here, ε0 is a positive constant.

[0051] D. Design of multi-constraint guidance rate

[0052] Based on the design objective of equation (13), the following form of sliding surface is first selected.

[0053]

[0054] Where, k1 > 0, 1 < r1 < 2, sign(x2) is the sign function of x2.

[0055] Differentiating equation (17) yields:

[0056]

[0057] Substituting equation (9) into equation (18) yields

[0058]

[0059] Define the time-varying obstacle avoidance Lyapunov function as follows

[0060]

[0061] Differentiating equation (20) yields

[0062]

[0063] in, Based on the set relationship between the lead angle, pitch lead angle, and yaw lead angle, the normal acceleration term of the function in the dynamic model of the lead angle is introduced as follows to avoid controller singularities:

[0064]

[0065] Where T is the time constant of the first-order filter. It is the output of a first-order filter. yes The derivative of is used to... Make an estimate.

[0066] Assumption 1: Assume that the first-order filter shown in equation (22) satisfies the following equation

[0067]

[0068] in, It is a normal number.

[0069] The Z-direction normal overload command is given in the following form:

[0070] a zM =a zMn +a zMI +a zMf +a zMs (twenty four)

[0071] in,

[0072]

[0073]

[0074]

[0075]

[0076] in, It is an estimate of θ1, ε1>0, μ1 and μ2 are both positive constants, and 0<a1<1.

[0077] Furthermore, the following adaptive update law for neural network parameters is given.

[0078]

[0079] Where λ1,k θ1 It is a normal number.

[0080] And another sliding surface of the following form is given.

[0081]

[0082] Where k2 > 0, 1 < r2 < 2, sign(x2) is the sign function of x2.

[0083] Differentiating equation (30) yields

[0084]

[0085] Substituting equation (10) into equation (31) yields

[0086]

[0087] Choose a Lyapunov function of the following form

[0088]

[0089] Differentiating equation (33) and substituting equation (32) into it, we get

[0090]

[0091] in, The normal acceleration a is given below. yM

[0092] a yM =a yMn +a yMl +a yMs (35)

[0093] in:

[0094]

[0095]

[0096]

[0097] in, It is an estimate of θ2, ε5, μ3, μ4 are positive constants, and 0 < a2 < 1.

[0098] The following adaptive update law for neural network parameters is given.

[0099]

[0100] Where λ2>0, k θ2 >0.

[0101] Theorem 1: For the combat scenario of missile intercepting maneuvering targets, considering the interception dynamics model shown in equations (2)-(8), if assumption 1 holds, then the proposed normal overload commands (24), (35) and adaptive update laws (29), (39) can satisfy the missile to intercept the maneuvering target at the desired terminal angle, and satisfy the seeker's field of view constraint during the interception process.

[0102] prove:

[0103] The Lyapunov function is defined as follows:

[0104]

[0105] in, Differentiating equation (40) yields

[0106]

[0107] Substituting the normal overload instructions (24), (35) and the adaptive update laws (29), (39) into equation (41) yields the following:

[0108]

[0109] Equation (42) can be further simplified to

[0110]

[0111] in, a = max(a1, a2),

[0112] According to stability theory, the Lyapunov functions V1, V2, and V3 will converge to zero in a finite time, and V1 is bounded. This proves that the missile will intercept the maneuvering target at the desired terminal angle under the condition that the seeker's field of view is constrained.

[0113] Simulation Analysis

[0114] The effectiveness of the designed multi-constraint interception guidance law was verified by conducting terminal guidance interception simulations under different maneuvering modes. The initial simulation conditions are shown in Table 1, and the target maneuvering mode settings are shown in Table 2. The maximum maneuvering overload amplitude of the interceptor missile was set to... Field of view constraint set to g = 9.8 m / s 2 θ Ld = -25°, ψ Ld= -10°, controller parameters selected as k1 = 0.15, k2 = 0.14, r1 = r2 = 1.5, T = 10, μ1 = 0.1, μ1 = 0.11, μ1 = 0.1, μ1 = 0.1, μ1 = 0.11, μ1 = 0.1, a1 = a2 = 0.45, λ1 = λ2 = 0.5, k θ1 =k θ2 =0.01, the number of nodes in the neural network is 20, b1=0.5, b2=2.

[0115] Table 1 Initial values ​​for simulation

[0116]

[0117]

[0118] Table 2 Different Maneuvering Methods of Targets

[0119]

[0120] Depend on Figure 2 The simulation results show that the designed non-singular multi-constraint guidance law can effectively intercept different maneuvering targets, thus verifying the effectiveness of the designed guidance law.

[0121] This invention addresses the challenge that traditional zero-control miss distance interception guidance laws are insufficient to meet the guidance requirements of interceptor missiles against highly maneuverable targets. It presents a terminal angle attack guidance law for intercepting maneuvering targets while satisfying the seeker's field of view constraints. This law enables the interceptor missile to intercept maneuvering targets at the desired terminal angle while meeting the seeker's field of view constraints.

[0122] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for designing a terminal angle attack guidance law for intercepting a maneuvering target satisfying a field-of-view angle constraint, characterized in that, The method includes: based on the three-dimensional interception model, constructing a guidance rate design target that satisfies the seeker's field of view and terminal angle constraints, constructing a neural network estimation model, and designing a multi-constraint guidance rate; in, The three-dimensional interception model includes: , The interceptor missile and the target are defined separately, and four coordinate systems are defined, namely the inertial coordinate system. Line of sight coordinate system ballistic coordinate system of interceptor missile and the target's ballistic coordinate system ;variable It is the relative distance between the interceptor missile and the target, and defines the conversion between the inertial frame and the line-of-sight frame through two angles: the line-of-sight tilt angle. and line of sight angle The velocity system and line-of-sight system of the interceptor missile are defined as being related by the forward tilt angle of the interceptor missile. and front offset angle Similarly, the conversion is performed between the target's velocity system and line-of-sight system, through the target's forward tilt angle. and front deflection angle Define the parameters; and assume the interceptor missile's velocity. and target speed All are constant values; determined by the interceptor missile's lead angle. and the forward tilt angle of the interceptor missile and front deflection angle The geometric relationship between them is expressed as follows: (1) Furthermore, the interception kinematics and dynamics are described as follows: (2) (3) (4) (5) (6) (7) (8) in, and These are the normal accelerations of the interceptor missile and the target, respectively. The three-dimensional interception model also includes: definition , , , ,in, , Let be the desired field of view angle, and the dynamic equations for the above state variables are expressed as follows: (9) in, , , ; (10) in, , , , ; The guidance law design objectives that satisfy the seeker's field of view and terminal angle constraints include: The guidance law design objectives that satisfy the seeker's field of view and terminal angle constraints in a 3D interception scenario are as follows: (11) in, , These are the desired pitch and yaw line-of-sight angles. The maximum forward angle is limited by the seeker's field of view; and zero-control miss distance can be achieved when the line-of-sight angular rate approaches zero, therefore the target conversion is designed. (12) From state variables , , , By definition, equation (12) satisfies the following equation (13)； The construction of the neural network estimation model includes: using the following neural network to estimate the disturbances caused by the target maneuver. , Make an estimate (14) in, , It is an estimation error. yes The estimated value, It is the Gaussian function. and These are the width vector of the hidden layer Gaussian function and the coordinate vector of the center point of the Gaussian function, respectively. It is the input to the neural network. yes The optimal value, i.e. (15) in, , It is compact, , The dimension of the set of real numbers; The design of multi-constraint guidance rates includes: Based on the design objective of equation (12), the following form of sliding surface is first selected. (17) in, , , , yes The sign function; Differentiating equation (17) yields: (18) Substituting equation (9) into equation (18) yields... (19) Define the time-varying obstacle avoidance Lyapunov function as follows (20) Differentiating equation (20) yields (21) in, To avoid controller singularities, the following first-order filter is introduced. (22) in, It is the time constant of the first-order filter. It is the output of a first-order filter. yes The derivative of is used to... Make an estimate; Assuming the first-order filter shown in equation (22) satisfies the following equation (23) in, It is a positive number; The Z-direction normal overload command is given in the following form: (24) in, (25) (26) (27) (28) in, Yes The estimate, , , All are positive numbers. ; Furthermore, the following adaptive update law for neural network parameters is given. (29) in, , It is a normal number.

2. The method for designing a terminal angle attack guidance law for intercepting maneuvering targets that satisfies field-of-view constraints as described in claim 1, characterized in that, For another form of sliding surface (30) in, , , , yes The sign function; Differentiating equation (30) yields (31) Substituting equation (10) into equation (31) yields (32) Choose a Lyapunov function of the following form (33) Differentiating equation (33) and substituting equation (32) into it, we get (34) in, The following normal acceleration is given. (35) in: (36) (37) (38) in, Yes The estimated value, , , It is a positive number, and ; The following adaptive update law for neural network parameters is given. (39) in, , .

3. The method for designing a terminal angle attack guidance law for intercepting maneuvering targets that satisfies field-of-view constraints as described in claim 2, characterized in that, Assumption 1: Assume that the estimation error is bounded and satisfies the following inequality (16) in, It is a normal number.

4. The method for designing a terminal angle attack guidance law for intercepting maneuvering targets that satisfies field-of-view constraints as described in claim 3, characterized in that, For the combat scenario of missile intercepting maneuvering targets, considering the interception dynamics model shown in equations (2)-(8), if assumption 1 holds, the proposed normal overload command (24), (35) and adaptive update law (29), (39) can satisfy the missile to intercept the maneuvering target at the desired terminal angle, and satisfy the seeker's field of view constraint during the interception process.

5. The method for designing a terminal angle attack guidance law for intercepting maneuvering targets that satisfies field-of-view constraints as described in claim 4, characterized in that, The Lyapunov function is defined as follows: (40) in, , Differentiating equation (40) yields (41) Substituting the normal overload instructions (24), (35) and the adaptive update laws (29), (39) into equation (41) yields the following: (42) Equation (42) is further simplified to (43) in, , , , , According to stability theory, the Lyapunov function , , It will converge to zero in a finite amount of time, and The missile is bounded, thus it will intercept the maneuvering target at the desired terminal angle while satisfying the seeker's field of view constraints.

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