A method and apparatus for calculating the optimal mid-course guidance law of a dual-pulse air-to-air missile
By using a linear Gaussian pseudospectral model predictive control method to dynamically update the nominal angle of attack and terminal time, the problems of high computational complexity and low accuracy in existing technologies are solved. This enables high-precision calculation of the optimal mid-course guidance law for dual-pulse air-to-air missiles, thereby improving the accuracy of missile target hits.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2023-12-14
- Publication Date
- 2026-08-04
AI Technical Summary
Existing methods for calculating the optimal guidance law for dual-pulse air-to-air missiles involve large computational loads and cannot perform accurate calculations under terminal time-free conditions, resulting in low missile accuracy when hitting targets.
A linear Gaussian pseudospectral model predictive control method is adopted. Through online ballistic integration and linearization, the nominal angle of attack and terminal time are dynamically updated and transformed into a system of linear equations for calculation, which is the calculation model of the optimal guidance law.
It achieves high-precision optimal mid-course guidance law calculation under terminal time freedom conditions, reduces the amount of computation, and improves the accuracy of missile hitting the target.
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Figure CN117631542B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of missile control technology, and more specifically, to a calculation method and apparatus for the optimal mid-course guidance law of a dual-pulse air-to-air missile. Background Technology
[0002] A dual-pulse air-to-air missile flies towards its predicted impact point during the mid-course guidance phase. The state at the end of this phase determines whether the seeker can acquire the target. Therefore, the performance of the mid-course guidance law largely determines whether the missile can hit the target. By establishing appropriate performance indicators and calculating the optimal mid-course guidance law, the missile's performance can be maximized.
[0003] However, the existing methods for calculating the optimal mid-course guidance law are computationally intensive and difficult to apply to missiles. At the same time, the existing calculation methods cannot calculate the optimal mid-course guidance law under the condition of free terminal time. That is, the existing technology sets the terminal time to a fixed value in the process of calculating the optimal mid-course guidance law, rather than a dynamically updated value, resulting in low accuracy of the calculated optimal mid-course guidance law and making it unsuitable for actual missile control. Summary of the Invention
[0004] The purpose of this application is to provide a method and apparatus for calculating the optimal mid-course guidance law of a dual-pulse air-to-air missile, thereby solving the above-mentioned problems existing in the prior art and obtaining a more accurate, more practically applicable, and smaller error-to-actual missile control optimal mid-course guidance law.
[0005] Firstly, a method for calculating the optimal mid-course guidance law of a dual-pulse air-to-air missile is provided, which may include: The basic parameters of the dual-pulse air-to-air missile and the parameter calculation model of the mid-course guidance phase of the dual-pulse air-to-air missile are obtained; wherein, the basic parameters include: the current state vector, the current nominal angle of attack, and the current nominal terminal time; the parameter calculation model includes: dynamic equations and terminal constraints. Based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, the ballistic integral of the dynamic equation is performed to obtain the nominal state vector in the mid-course guidance phase. If the nominal state vector satisfies the terminal constraint condition, then the current nominal angle of attack and the current nominal terminal time are used as the optimal mid-course guidance law output for the mid-course guidance segment; If the nominal state vector does not satisfy the terminal constraint condition, the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using the linear Gaussian pseudospectral model predictive control method to obtain the updated nominal angle of attack and the updated nominal terminal time. The updated nominal angle of attack and the updated nominal terminal time are used as the new current nominal angle of attack and the new current nominal terminal time, respectively, and the execution steps are returned: Based on the current state vector, the current nominal angle of attack and the current nominal terminal time, the ballistic integral of the dynamic equation is performed to obtain the nominal state vector of the mid-guided phase.
[0006] In an optional implementation, based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, the dynamic equations are integrally processed to obtain the nominal state vector for the mid-course guidance phase, including: Using a numerical integration method, with the current state vector as the initial value for integration, and based on the current nominal angle of attack and the current nominal terminal time, the dynamic equation is integrated online to obtain the nominal state vector in the mid-course guidance phase.
[0007] In an optional implementation, the parameter calculation model further includes: first-order necessary conditions for optimal control; The nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using a linear Gaussian pseudospectral model predictive control method to obtain updated nominal angle of attack and updated nominal terminal time, including: Based on the nominal state vector and the current nominal angle of attack, the first-order necessary condition for the optimal control is linearized to obtain the linear differential equation of the state vector correlation quantity; wherein, the state vector correlation quantity includes: the state deviation quantity and the costate vector corresponding to the state vector; The linear differential equations of the state vector correlation quantities are pseudospectrally discretized to obtain the linear algebraic equations of the state vector correlation quantities and the linear algebraic equations of the terminal time correction quantities. The basic parameters are input into the linear algebraic equations of the state vector correlation quantity and the terminal time correction quantity to obtain the state vector correlation quantity and the terminal time correction quantity. Based on the state vector correlation quantity and the correction amount of the terminal time, the current nominal angle of attack and the current nominal terminal time are updated to obtain the updated nominal angle of attack and the updated nominal terminal time.
[0008] In an optional implementation, the linear differential equations of the state vector correlation quantities are pseudospectrally discretized to obtain the linear algebraic equations of the state vector correlation quantities and the linear algebraic equations of the terminal time correction quantities, including: Determine at least one discrete node in the mid-guidance segment; The coordinates of the discrete nodes are transformed; Extract the state vector correlation quantities at the discrete nodes; Based on the state vector correlation at the discrete node, the state vector correlation is fitted using a Lagrange interpolation polynomial to obtain the linear algebraic equations for the state vector correlation at the discrete node and the linear algebraic equations for the terminal time correction at the discrete node.
[0009] In an optional implementation, the linear algebraic equation for the terminal time correction is as follows:
[0010] in, This indicates the fourth stage of the mid-course guidance system. State deviation at each discrete node; This indicates the third stage of the mid-course guidance system. State deviation at each discrete node. Indicates the moment when the mid-guided phase ends. This indicates the end time of the third stage of the mid-course guidance phase. This represents the number of discrete nodes in the fourth stage of the mid-guidance phase. This represents the k-th discrete node. Denotes the coefficients of the Gaussian integral formula. This indicates the fourth stage of the mid-guided phase. k The gradient of the dynamic equations of a discrete node with respect to the state vector. This indicates the fourth stage of the mid-course guidance phase. k State deviation of a discrete node This indicates the fourth stage of the mid-course guidance phase. k The gradient of the dynamic equations of a discrete node with respect to the angle of attack. This indicates the fourth stage of the mid-course guidance phase. k The costate vector of discrete nodes, This represents the missile's dynamic equation vector at the end of the fourth stage of the mid-course guidance phase. This indicates the amount of correction for the terminal time. Indicates the first phase of the mid-guided phase i The first stage k The transpose of the dynamic equations of a discrete node with respect to the gradient of the angle of attack. In the i-th stage of the mid-guidance phase, the... k The nominal angle of attack at a discrete point.
[0011] In an optional implementation, the current nominal angle of attack and the current nominal terminal time are updated based on the state vector correlation quantity and the correction amount of the terminal time to obtain the updated nominal angle of attack and the updated nominal terminal time, including: The state vector related quantities are input into the update formula of the nominal angle of attack to obtain the updated nominal angle of attack; The correction amount of the terminal time is input into the update formula of the nominal terminal time to obtain the updated nominal terminal time.
[0012] In an optional implementation, the formula for updating the nominal angle of attack is as follows: ; in, This represents the nominal angle of attack in the i-th stage of the mid-course guidance phase; In the i-th stage of the mid-guidance phase, the first... k Costate vectors of discrete nodes; Indicates the first guidance phase i The number of discrete nodes in each stage; The formula for updating the nominal terminal time is as follows: ; in, This indicates the nominal terminal time at the end of the mid-guided phase.
[0013] Secondly, a calculation device for the optimal mid-course guidance law of a dual-pulse air-to-air missile is provided, the device including: The acquisition unit is used to acquire the basic parameters of the dual-pulse air-to-air missile and the parameter calculation model of the mid-course guidance phase of the dual-pulse air-to-air missile; wherein, the basic parameters include: the current state vector, the current nominal angle of attack, and the current nominal terminal time; the parameter calculation model includes: dynamic equations and terminal constraints; An integrator unit is used to perform ballistic integration on the dynamic equation based on the current state vector, the current nominal angle of attack, and the current nominal terminal time to obtain the nominal state vector in the mid-course guidance phase. The calculation unit is used to determine whether the nominal state vector satisfies the terminal constraint condition. If the nominal state vector satisfies the terminal constraint condition, the current nominal angle of attack and the current nominal terminal time are output as the optimal mid-course guidance law for the mid-course guidance segment. If the nominal state vector does not satisfy the terminal constraint condition, the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using the linear Gaussian pseudospectral model predictive control method to obtain the updated nominal angle of attack and the updated nominal terminal time. The update unit is used to take the updated nominal angle of attack and the updated nominal terminal time as the new current nominal angle of attack and the new current nominal terminal time, respectively, and return to the execution step: based on the current state vector, the current nominal angle of attack and the current nominal terminal time, perform ballistic integration on the dynamic equation to obtain the nominal state vector of the mid-guided phase.
[0014] Thirdly, an electronic device is provided, which includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; When a processor executes a program stored in memory, it implements any of the steps described in the first aspect above.
[0015] Fourthly, a computer-readable storage medium is provided, wherein a computer program is stored therein, and when executed by a processor, the computer program implements the steps of any of the methods described in the first aspect above.
[0016] The calculation method of this application not only involves very little computation, but also creatively calculates the optimal mid-course guidance law of a dual-pulse air-to-air missile under the condition of terminal time freedom, resulting in a more accurate, more practically applicable optimal mid-course guidance law with smaller error compared to actual missile control.
[0017] This application combines the indirect method, linearization method, Gaussian pseudospectral method, and prediction correction method for optimal control problems, transforming the calculation model of the optimal mid-course guidance law into a set of linear equations. This avoids the two-point boundary value problem in the indirect method and creatively introduces the terminal time correction term into the predictive control formula of the linear Gaussian pseudospectral model, improving the calculation accuracy and precision of the optimal mid-course guidance law and demonstrating strong potential for online application. Attached Figure Description
[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 A flowchart illustrating the calculation method for the optimal mid-course guidance law of a dual-pulse air-to-air missile, provided in this application embodiment; Figure 2 A schematic diagram illustrating a calculation method for the optimal mid-course guidance law of a dual-pulse air-to-air missile, provided as an embodiment of this application; Figure 3 A schematic diagram of the structure of a computational device for the optimal mid-course guidance law of a dual-pulse air-to-air missile, provided in an embodiment of this application; Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation
[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0021] The preferred embodiments of this application are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit this application. Furthermore, the embodiments and features in the embodiments of this application can be combined with each other without conflict.
[0022] Figure 1 This is a flowchart illustrating a method for calculating the optimal guidance law of a dual-pulse air-to-air missile, as provided in an embodiment of this application. Figure 1 As shown, the method may include: Step S110: Obtain the basic parameters of the dual-pulse air-to-air missile and the parameter calculation model of the mid-course guidance phase of the dual-pulse air-to-air missile.
[0023] In this embodiment of the application, the basic parameters include: the current state vector, the current nominal angle of attack, the current nominal terminal time, and the predicted hit position of the missile at the end of the mid-course guidance phase; wherein, the current state vector refers to the current state parameters of the missile expressed in vector form, and the current state parameters of the missile include the missile's longitudinal position, altitude, trajectory inclination angle, velocity, mass, aerodynamic lift of the missile, engine thrust, missile angle of attack, aerodynamic drag of the missile, and a representation of propellant specific impulse.
[0024] In this embodiment, the parameter calculation model includes: dynamic equations, terminal constraints, first-order necessary conditions for optimal control, ballistic performance indicators, and connection conditions for each of the four stages in the mid-course guidance phase.
[0025] In this embodiment, since the dual-pulse air-to-air missile flies towards the predicted impact point during the mid-course guidance phase, the motion of the dual-pulse air-to-air missile (hereinafter referred to as the missile) is simplified to motion in the longitudinal plane. Based on the operating characteristics of the dual-pulse engine, the dynamic process of the dual-pulse air-to-air missile during the mid-course guidance phase is divided into four stages. The first and third stages are active stages, during which the engine operates; the second and fourth stages are passive stages, during which the engine thrust is zero. Thus, the dynamic equations of the dual-pulse air-to-air missile during the four stages of the mid-course guidance phase are as follows: (1) in, t Indicates time, x Indicates the missile's longitudinal position. y Indicates the missile's altitude. Indicates the trajectory inclination angle of the missile. V Indicates the speed of the missile. L This indicates the aerodynamic lift force experienced by the missile. T Indicates engine thrust. m Indicates missile mass, The angle of attack of the missile is represented by , and g is the acceleration due to gravity. D This indicates the aerodynamic drag experienced by the missile; This represents the acceleration due to gravity at sea level. This represents the specific impulse of the propellant; specifically, the missile's longitudinal position, altitude, trajectory inclination, velocity, and mass are the missile's state variables, while the missile's angle of attack is the missile's control variable; both the missile's state variables and its control variables are time-related. t The function.
[0026] In practical applications, the missile's state parameters and dynamic equations are represented in vector form, where the missile's state vector is expressed as follows: (2); in, Represents the missile's state vector; i Indicates the first guidance phase i Each stage; The vector representation of the missile's dynamic equations is as follows: (3) in, The vector representing the missile's dynamic equations is a 5x1 vector, as shown below: (4).
[0027] In this embodiment, the design objective of the mid-course guidance law is to guide the missile to the predicted impact point and ensure good mid-to-terminal guidance handover conditions. Therefore, it is expected that the missile will reach the predicted impact point at the end of mid-course guidance, and the missile's trajectory inclination angle will be the desired value. The terminal constraints are as follows: (5) in, The first row represents the horizontal axis constraint, the second row represents the vertical axis constraint, and the third row represents the trajectory inclination angle constraint. Indicates the moment when the mid-course guidance ends; This indicates the missile's longitudinal position at the end of its mid-course guidance. This indicates the missile's altitude at the end of its mid-course guidance. This indicates the trajectory inclination angle of the missile at the end of mid-course guidance; This represents the x-coordinate of the predicted hit point. This represents the ordinate of the predicted hit point. This represents the desired terminal trajectory inclination angle.
[0028] In practical applications, since it is difficult to strictly satisfy formula (5), it is relaxed to formula (6): (6) in, This indicates the allowable error on the horizontal axis. This indicates the allowable error in the ordinate. This indicates the permissible trajectory tilt angle error.
[0029] In this embodiment, it is desirable that the missile's velocity is as high as possible at the end of the mid-course guidance phase, and that the control curve during the mid-course guidance phase is relatively smooth. Therefore, the following performance indicators are established to measure the quality of the trajectory during the mid-course guidance phase: (7) in, Indicates the performance indicators of ballistics; This indicates the missile's velocity at the end of the mid-course guidance phase; Indicates the moment when the mid-course guidance begins; This indicates the angle of attack of the missile.
[0030] In this embodiment, the design goal of the optimal guidance law is to find an optimal angle-of-attack variation law. According to this angle-of-attack variation law, the missile trajectory not only meets the terminal constraints, but also the corresponding performance indicators It is the smallest among all trajectories that satisfy terminal constraints.
[0031] In this embodiment of the application, the first-order necessary conditions for optimal control of the missile in the mid-course guidance phase are derived from formula (7) as shown in formulas (8) to (13): (8) (9) (10) (11); (12); (13); in, Represents the Hamiltonian function. , As a scalar, Represents the costate vector. With state vector Having the same dimensions; Formula (11) represents the missile's longitudinal position x, missile height y, and missile trajectory inclination angle. The corresponding terminal costate vector; Formula (12) represents the missile's velocity. V Missile quality m and missile angle of attack The corresponding terminal costate vector; Formula (13) represents the Hamiltonian function calculated from the optimal control quantity and the optimal state it determines; Indicates the longitudinal position of the missile Lagrange multipliers; The Lagrange multiplier representing the missile's altitude y; Indicates the missile trajectory inclination angle Lagrange multipliers; This indicates the missile's longitudinal position during the fourth stage of the mid-course guidance phase, at the end of the mid-course guidance phase. The costate vector; This represents the co-state vector of the missile's altitude at the end of the fourth stage of the mid-course guidance phase. This indicates the missile's trajectory inclination angle during the fourth stage of the mid-course guidance phase, at the end of mid-course guidance. The costate vector; This indicates the missile's velocity at the end of the fourth stage of the mid-course guidance phase. V The costate vector; This indicates the missile mass at the end of the fourth stage of the mid-course guidance phase. m The costate vector; This indicates the missile's angle of attack at the end of the fourth stage of the mid-course guidance phase. The costate vector.
[0032] In this embodiment of the application, the original optimal control problem is transformed into a two-point boundary value problem by using the first-order necessary condition for optimal control described above.
[0033] Step S120: Based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, perform ballistic integration on the dynamic equation to obtain the nominal state vector in the mid-course guidance phase.
[0034] In this embodiment, based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, ballistic integration is performed on the dynamic equations to obtain the nominal state vector for the mid-course guidance phase, including: Using the numerical integration method, with the current state vector as the initial value of the integration, and based on the current nominal angle of attack and the current nominal terminal time, the dynamic equation is integrated online to obtain the nominal state vector in the mid-course guidance phase.
[0035] In practical applications, since the initial nominal angle of attack and terminal time are not sensitive, a constant initial nominal angle of attack is chosen. The initial nominal terminal time is selected based on the range. The state vector of the missile at the initial moment of the mid-course guidance phase. As the initial value for integration, the dynamic equation shown in formula (3) is integrated online using numerical integration methods to obtain the nominal state vector of the mid-guided phase. .
[0036] Step S130: Determine whether the nominal state vector of the obtained mid-guided segment satisfies the terminal constraint condition. If it does, then use the current nominal angle of attack and the current nominal terminal time as the optimal mid-guided law output of the mid-guided segment.
[0037] In this embodiment of the application, it is determined whether the nominal state vector of the obtained mid-course guidance phase satisfies the terminal constraint condition, that is, whether the deviation between the nominal state vector of the obtained mid-course guidance phase and the predicted hit position of the missile at the end of the mid-course guidance phase (i.e., the terminal error) exceeds the allowable error range.
[0038] Specifically, the terminal error is calculated using the following formula: (14) in, This indicates the deviation between the nominal ballistic terminal x-coordinate and the predicted impact point x-coordinate. This indicates the deviation between the vertical coordinate of the target trajectory terminal and the vertical coordinate of the predicted impact point; This indicates the deviation between the nominal trajectory inclination angle and the desired trajectory inclination angle; Indicates the x-coordinate of the nominal ballistic terminal; Indicates the nominal ballistic terminal ordinate; Indicates the nominal ballistic inclination angle; if , and All are smaller than the values in formula (6). , and This indicates that the current nominal angle of attack has met the terminal error requirement, i.e., the current angle of attack... Optimal angle of attack .
[0039] Step S140: If the nominal state vector does not meet the terminal constraint conditions, the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using the linear Gaussian pseudospectral model predictive control method to obtain the updated nominal angle of attack and the updated nominal terminal time.
[0040] In this embodiment of the application, the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using a linear Gaussian pseudospectral model predictive control method to obtain the updated nominal angle of attack and the updated nominal terminal time, including: Based on the nominal state vector and the current nominal angle of attack, the first-order necessary conditions for optimal control are linearized to obtain the linear differential equations of the state vector correlation quantities. The linear differential equations of the state vector correlation quantities are then pseudospectrally discretized to obtain the linear algebraic equations of the state vector correlation quantities and the linear algebraic equations of the terminal time correction. The basic parameters are input into these equations to obtain the corrections for the state vector correlation quantities and the terminal time. Based on these corrections, the current nominal angle of attack and the current nominal terminal time are updated to obtain the updated nominal angle of attack and the updated nominal terminal time.
[0041] In this embodiment, the state vector correlation quantities include: state deviation quantities and the costate vector corresponding to the state vector; the linear differential equation of the state vector correlation quantities includes: the costate vector. Linear differential equations and state deviations The linear differential equation.
[0042] Specifically, costate vector Linear differential equations and state deviations The derivation of the linear differential equation is as follows: First, based on the obtained nominal state vector and the current nominal angle of attack, formula (8) is linearized using the first-order Taylor expansion formula, as shown below: (15) in, Represents the nominal state vector of the i-th stage; Let A represent the nominal angle of attack at the i-th stage; let B represent the gradient of the dynamic equation with respect to the state vector; specifically, the expressions for A and B are as follows: (16) (17); Secondly, it is determined that there is a deviation between the missile's actual state vector and its nominal state vector, and there is also a deviation between the missile's actual angle of attack and its nominal angle of attack. The expressions are as follows: (18) (19) in, This represents the state deviation. Indicates the angle of attack deviation; Then, substituting the gradient A of the dynamic equation with respect to the state vector into formula (9), we obtain the costate vector. The linear differential equation is shown below: (20); Substituting equation (19) and the gradient B of the dynamic equation with respect to the angle of attack into equation (10), we obtain the following equation: (twenty one); Substituting equations (16) to (19) and equation (21) into equation (15), we obtain the state deviation. The linear differential equation is as follows: (twenty two).
[0043] In this embodiment of the application, the linear differential equation of the state vector correlation quantity is pseudospectrally discretized to obtain the linear algebraic equation of the state vector correlation quantity and the linear algebraic equation of the terminal time correction quantity, including: Identify at least one discrete node in the mid-guidance segment; transform the coordinates of the discrete node; extract the state vector correlation quantity at the discrete node; based on the state vector correlation quantity at the discrete node, use Lagrange interpolation polynomial fitting to obtain the linear algebraic equations of the state vector correlation quantity at the discrete node and the linear algebraic equations of the terminal time correction quantity at the discrete node.
[0044] Specifically, pseudospectral discretization is performed on the linear differential equations of the state vector correlation quantities to obtain the linear algebraic equations of the state vector correlation quantities and the linear algebraic equations of the terminal time correction quantities, including: First, determine the discrete nodes; specifically, the discrete nodes selected by the Gaussian pseudospectral method are LG points, i.e. N Legendre polynomials N Given a root, different Legendre polynomials of different orders can be selected for different stages of the guidance segment. The discrete nodes of each stage are then denoted as follows: , subscript " j " indicates the first j discrete nodes , ; Indicates the first i The number of discrete nodes in each stage.
[0045] Secondly, a coordinate transformation is performed. Since the LG nodes are all located between [-1, 1], the original time domain needs to be transformed to the range [-1, 1], as shown in the following equation: (twenty three) in, Indicates the time of the segmentation point. This represents the time after the coordinate transformation.
[0046] Furthermore, the parts in formulas (20) and (22) are... t The derivative is replaced with the derivative of The derivative of is used to obtain the following formula: (twenty four) (25) Then, based on the state deviations and costate vectors at discrete nodes, a Lagrange interpolation polynomial is used for fitting. and As shown below: (26) (27) in, and All The expression for the first-order Lagrange interpolation polynomial is: (28) (29) The Lagrange interpolation polynomial has the following properties: (30) (31) Then, compare both sides of the equations (26) and (27). Taking the derivative and taking the values at the discrete nodes, we get: (32) (33) in, , , , ; and It is a differential matrix, that is , , I It is a 6-dimensional identity matrix; and The first element in the differential approximation matrix k The first discrete node corresponding to the l The elements of the column, whose expressions are as follows: (34) (35) in, and The coefficients representing the Gaussian integral formula are constants related to the number of LG nodes; Finally, substituting formula (32) into formula (35) and formula (33) into formula (24), we obtain a set of linear algebraic equations, as shown below: (36) (37) in, and By the i The first stage k The nominal state vector and angle of attack corresponding to each discrete node are calculated. Indicates the first i In the first stage k The nominal angle of attack corresponding to each discrete node.
[0047] In this embodiment of the application, the basic parameters are input into the linear algebraic equations of the state vector correlation quantity and the terminal time correction quantity to obtain the state vector correlation quantity and the terminal time correction quantity, including: By utilizing the connection conditions between the various stages of the mid-course guidance phase, the system of linear algebraic equations of each stage can be connected to achieve simultaneous solution, thereby obtaining the state vector correlation quantity and the terminal time correction quantity.
[0048] Specifically, the derivation process of the linear algebraic equations for the state vector correlation quantities and the terminal time correction quantities is as follows: First, the connection conditions between the various stages of the mid-course guidance phase are determined as follows: (38) (39) In this context, the superscript indicates the stage, and the subscript indicates the position of the corresponding LG point in that stage; Secondly, define the integrated state deviation vector for the i-th stage. and the integrated costate vector of the i-th stage The expression is as follows: (40) (41) Since the timing of the start of mid-course guidance and the missile's state are known, therefore... ; Then, for formulas (36) and (37), the superscript "( i Iterate through numbers 1 to 4, checking the index " k "Traverse from 1 to Substituting into formulas (38) and (39), we obtain the following system of equations: (42) in, Represents the state-state coefficient matrix. Represents the state-costate coefficient matrix. Represents the costate-costate coefficient matrix. Represents the state connection coefficient matrix. Represents the co-state connection coefficient matrix. The vector representing the state constants is expressed as follows: (43) (44) (45) (46) (47) (48) (49) Finally, since Gaussian nodes do not include endpoints, Gaussian integral formulas are needed to estimate the state deviation and costate vector at the endpoints, as shown below: (50) Since the time of each segment point is fixed, formula (50) can be used for the first, second, and third stages, and can be rearranged into the following form: (51) Similarly, for the costate vectors at the segmentation points of the first, second, and third stages of the mid-guidance segment, we have the following expression: (52) For the fourth stage, since the end time of the mid-course guidance phase is uncertain, there will be an additional term for the terminal time correction due to the state deviation at the terminal moment, as shown below: (53) in, The amount of correction to the terminal time is the unknown quantity to be determined; This indicates the fourth stage of the mid-course guidance system. State deviation at each discrete node. This indicates the third stage of the mid-course guidance system. State deviation at each discrete node; Indicates the first phase of the mid-guided phase i The first stage kThe dynamic equations of a discrete node are transposed with respect to the gradient of the angle of attack.
[0049] Similarly, for the costate vector at the terminal time, we have the following expression: (54) in, This represents the terminal costate vector calculated in the previous iteration. The first calculation can be taken as the zero vector.
[0050] From formula (14), it can be seen that for the constrained state component, its terminal state deviation is: (55) From formula (15), it can be seen that for an unconstrained state component, its corresponding terminal costate component is: (56) From formula (13), we know that the Hamiltonian function at the terminal moment on the optimal trajectory is 0, and we have the following equation: (57) Wherein, the state vector and attack angle If all values are taken as nominal values, then formula (57) is a linear equation about the terminal costate vector, which can be simplified to the following form: (58) The above formulas (42), (51), (52), (53), (54), (55), (56), and (58) together form the linear algebraic equations for the state vector correlation quantity and the terminal time correction quantity. The number of equations and the number of unknowns in this system of linear equations are equal. .
[0051] In this embodiment, the linear algebraic equations for the state vector correlation quantity and the terminal time correction quantity are solved to obtain the state deviation quantity at the discrete node. Costate vectors at discrete nodes and the amount of correction for terminal time .
[0052] In this embodiment of the application, the update formulas for the nominal angle of attack and the nominal terminal time are obtained according to formula (21). The co-state vector at each discrete node is input into the update formulas for the nominal angle of attack and the nominal terminal time to obtain the updated nominal angle of attack and the updated nominal terminal time.
[0053] In this embodiment of the application, the formula for updating the nominal angle of attack is as follows: (59).
[0054] In this embodiment, the update formula for the nominal terminal time is as follows: (60).
[0055] Step S150: Use the updated nominal angle of attack and the updated nominal terminal time as the new current nominal angle of attack and the new current nominal terminal time, respectively, and return to execute step S120.
[0056] In one embodiment of this application, such as Figure 2 As shown, the calculation method for the optimal guidance law of a dual-pulse air-to-air missile may include the following steps: Step 1: Model the optimal mid-course guidance law for the dual-pulse air-to-air missile; Step 2: Transform the optimal control problem into a two-point boundary value problem using first-order necessary conditions; Step 3.1: Initialization: Select a suitable nominal angle of attack control law and nominal terminal time; Step 3.2: Integral trajectory prediction: Obtain the nominal state quantity (i.e., state vector) by numerical integration based on the current nominal angle of attack law and nominal terminal time; Step 3.3: Error judgment: Determine whether the terminal state is within the error range. If yes, end the process and output the current nominal control quantity as the optimal control quantity; otherwise, proceed to Step 3.4: Linearize the first-order necessary conditions in Step 2 based on the nominal state and nominal angle of attack; Step 3.5: Discretize the linear differential equations in Step 3.3 using the Gaussian pseudospectral method; Step 3.6: Use connection conditions to combine the discretized first-order necessary conditions of each stage into a set of linear algebraic equations and solve them; Step 3.7: Update the nominal angle of attack law and nominal terminal time based on the solution of the linear equations in Step 3.6, and return to execute Step 3.3.
[0057] Corresponding to the above method, this application also provides a calculation device for the optimal mid-course guidance law of a dual-pulse air-to-air missile, such as... Figure 3 As shown, the calculation device for the optimal mid-course guidance law of this dual-pulse air-to-air missile includes: The acquisition unit 310 is used to acquire the basic parameters of the dual-pulse air-to-air missile and the parameter calculation model of the mid-course guidance phase of the dual-pulse air-to-air missile; wherein, the basic parameters include: the current state vector, the current nominal angle of attack, and the current nominal terminal time; the parameter calculation model includes: the dynamic equation and the terminal constraint conditions; Integrating unit 320 is used to perform ballistic integration on the dynamic equation based on the current state vector, the current nominal angle of attack, and the current nominal terminal time to obtain the nominal state vector in the mid-course guidance phase. The calculation unit 330 is used to determine whether the nominal state vector satisfies the terminal constraint condition. If the nominal state vector satisfies the terminal constraint condition, the current nominal angle of attack and the current nominal terminal time are used as the optimal mid-course guidance law output for the mid-course guidance segment. If the nominal state vector does not satisfy the terminal constraint condition, the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using the linear Gaussian pseudospectral model predictive control method to obtain the updated nominal angle of attack and the updated nominal terminal time. The update unit 340 is used to take the updated nominal angle of attack and the updated nominal terminal time as the new current nominal angle of attack and the new current nominal terminal time, respectively, and return to the execution steps: based on the current state vector, the current nominal angle of attack and the current nominal terminal time, perform ballistic integration on the dynamic equation to obtain the nominal state vector of the mid-guided phase.
[0058] The functions of each unit in the calculation device for the optimal mid-course guidance law of the dual-pulse air-to-air missile provided in the above embodiments of this application can be implemented through the above-described methods and steps. Therefore, the specific working process and beneficial effects of each unit in the calculation device for the optimal mid-course guidance law of the dual-pulse air-to-air missile provided in the embodiments of this application will not be repeated here.
[0059] This application also provides an electronic device, such as... Figure 4 As shown, it includes a processor 410, a communication interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other through the communication bus 440.
[0060] Memory 430 is used to store computer programs; When the processor 410 executes the program stored in the memory 430, it performs the following steps: Obtain the basic parameters of the dual-pulse air-to-air missile and the parameter calculation model for the mid-course guidance phase of the dual-pulse air-to-air missile; the basic parameters include: the current state vector, the current nominal angle of attack, and the current nominal terminal time; the parameter calculation model includes: the dynamic equations and the terminal constraints. Based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, the ballistic integral of the dynamic equation is performed to obtain the nominal state vector in the mid-course guidance phase. Determine whether the nominal state vector satisfies the terminal constraint condition. If the nominal state vector satisfies the terminal constraint condition, then the current nominal angle of attack and the current nominal terminal time are used as the optimal mid-course guidance law output for the mid-course guidance segment. If the nominal state vector does not satisfy the terminal constraint condition, then the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using the linear Gaussian pseudospectral model predictive control method to obtain the updated nominal angle of attack and the updated nominal terminal time. The updated nominal angle of attack and the updated nominal terminal time are used as the new current nominal angle of attack and the new current nominal terminal time, respectively, and the execution steps are returned: Based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, the ballistic integral of the dynamic equation is performed to obtain the nominal state vector of the mid-guided phase.
[0061] The communication bus mentioned above can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.
[0062] The communication interface is used for communication between the aforementioned electronic devices and other devices.
[0063] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.
[0064] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.
[0065] The implementation methods and beneficial effects of the various components of the electronic device in the above embodiments for solving the problem can be found in [reference needed]. Figure 1 The steps in the illustrated embodiments are used to implement the electronic device. Therefore, the specific working process and beneficial effects of the electronic device provided in this application will not be repeated here.
[0066] In another embodiment provided in this application, a computer-readable storage medium is also provided, which stores instructions that, when executed on a computer, cause the computer to perform the calculation method for the optimal centering guidance law of any of the dual-pulse air-to-air missiles in the above embodiments.
[0067] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute the calculation method for the optimal mid-course guidance law of any of the above embodiments for dual-pulse air-to-air missiles.
[0068] Those skilled in the art will understand that the embodiments in this application can be provided as methods, systems, or computer program products. Therefore, the embodiments in this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the embodiments in this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0069] This application describes embodiments of methods, apparatus (systems), and computer program products according to embodiments of this application with reference to flowchart illustrations and / or block diagrams. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0070] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0071] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0072] Although preferred embodiments have been described in this application, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of this application.
[0073] Obviously, those skilled in the art can make various modifications and variations to the embodiments of this application without departing from the spirit and scope of the embodiments of this application. Therefore, if these modifications and variations to the embodiments of this application fall within the scope of the claims in this application and their equivalents, then this application also intends to include these modifications and variations.
Claims
1. A method for calculating the optimal mid-course guidance law of a dual-pulse air-to-air missile, characterized in that, The method includes: The basic parameters of the dual-pulse air-to-air missile and the parameter calculation model of the mid-course guidance phase of the dual-pulse air-to-air missile are obtained; wherein, the basic parameters include: the current state vector, the current nominal angle of attack, and the current nominal terminal time; the parameter calculation model includes: dynamic equations, terminal constraints, and first-order necessary conditions for optimal control; Based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, the ballistic integral of the dynamic equation is performed to obtain the nominal state vector in the mid-course guidance phase. If the nominal state vector satisfies the terminal constraint condition, then the current nominal angle of attack and the current nominal terminal time are used as the optimal mid-course guidance law output for the mid-course guidance segment; If the nominal state vector does not satisfy the terminal constraint condition, the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using a linear Gaussian pseudospectral model predictive control method to obtain updated nominal angle of attack and updated nominal terminal time. This includes: linearizing the first-order necessary condition of the optimal control based on the nominal state vector and the current nominal angle of attack to obtain linear differential equations for state vector correlation quantities; wherein, the state vector correlation quantities include: state deviation and the costate vector corresponding to the state vector; pseudospectrally discretizing the linear differential equations for the state vector correlation quantities to obtain linear algebraic equations for the state vector correlation quantities and linear algebraic equations for terminal time correction; inputting the basic parameters into the linear algebraic equations for the state vector correlation quantities and the linear algebraic equations for terminal time correction to obtain corrections for the state vector correlation quantities and terminal time; updating the current nominal angle of attack and the current nominal terminal time based on the corrections for the state vector correlation quantities and terminal time to obtain updated nominal angle of attack and updated nominal terminal time. The updated nominal angle of attack and the updated nominal terminal time are used as the new current nominal angle of attack and the new current nominal terminal time, respectively, and the execution steps are returned: Based on the current state vector, the current nominal angle of attack and the current nominal terminal time, the ballistic integral of the dynamic equation is performed to obtain the nominal state vector of the mid-guided phase.
2. The method as described in claim 1, characterized in that, Based on the current state vector, the current nominal angle of attack, and the current nominal terminal time, the ballistic integral of the dynamic equation is performed to obtain the nominal state vector in the mid-course guidance phase, including: Using a numerical integration method, with the current state vector as the initial value for integration, and based on the current nominal angle of attack and the current nominal terminal time, the dynamic equation is integrated online to obtain the nominal state vector in the mid-course guidance phase.
3. The method as described in claim 1, characterized in that, Pseudospectral discretization is performed on the linear differential equations of the state vector correlation quantities to obtain the linear algebraic equations of the state vector correlation quantities and the linear algebraic equations of the terminal time correction quantities, including: Determine at least one discrete node in the mid-guidance segment; The coordinates of the discrete nodes are transformed; Extract the state vector correlation quantities at the discrete nodes; Based on the state vector correlation at the discrete node, the state vector correlation is fitted using a Lagrange interpolation polynomial to obtain the linear algebraic equations for the state vector correlation at the discrete node and the linear algebraic equations for the terminal time correction at the discrete node.
4. The method as described in claim 1, characterized in that, The linear algebraic equation for the terminal time correction is as follows: in, This indicates the fourth stage of mid-course guidance. State deviation at each discrete node; This indicates the third stage of the mid-course guidance system. State deviation at each discrete node. Indicates the moment when the mid-guided phase ends. This indicates the end time of the third stage of the mid-course guidance phase. This represents the number of discrete nodes in the fourth stage of the mid-guidance phase. This represents the k-th discrete node. Denotes the coefficients of the Gaussian integral formula. This indicates the fourth stage of the mid-guided phase. k The gradient of the dynamic equations of a discrete node with respect to the state vector. This indicates the fourth stage of the mid-course guidance phase. k The state deviation of a discrete node. This indicates the fourth stage of the mid-course guidance phase. k The gradient of the dynamic equations of a discrete node with respect to the angle of attack. This indicates the fourth stage of the mid-course guidance phase. k The costate vector of discrete nodes, This represents the missile's dynamic equation vector at the end of the fourth stage of the mid-course guidance phase. This indicates the amount of correction for the terminal time. Indicates the first phase of the mid-guided phase i The first stage k The transpose of the dynamic equations of a discrete node with respect to the gradient of the angle of attack. In the i-th stage of the mid-guidance phase, the... k The nominal angle of attack at a discrete point.
5. The method as described in claim 4, characterized in that, Based on the state vector correlation quantity and the correction amount of the terminal time, the current nominal angle of attack and the current nominal terminal time are updated to obtain the updated nominal angle of attack and the updated nominal terminal time, including: The state vector related quantities are input into the update formula of the nominal angle of attack to obtain the updated nominal angle of attack; The correction amount of the terminal time is input into the update formula of the nominal terminal time to obtain the updated nominal terminal time.
6. The method as described in claim 5, characterized in that, The formula for updating the nominal angle of attack is as follows: ； in, This represents the nominal angle of attack in the i-th stage of the mid-course guidance phase; In the i-th stage of the mid-guidance phase, the first... k Costate vectors of discrete nodes; Indicates the first guidance phase i The number of discrete nodes in each stage; The formula for updating the nominal terminal time is as follows: ； in, This indicates the nominal terminal time at the end of the mid-guided phase.
7. A computational device for the optimal mid-course guidance law of a dual-pulse air-to-air missile, characterized in that, The device includes: The acquisition unit is used to acquire the basic parameters of the dual-pulse air-to-air missile and the parameter calculation model of the mid-course guidance phase of the dual-pulse air-to-air missile; wherein, the basic parameters include: the current state vector, the current nominal angle of attack, and the current nominal terminal time; the parameter calculation model includes: dynamic equations, terminal constraints, and first-order necessary conditions for optimal control; An integrator unit is used to perform ballistic integration on the dynamic equation based on the current state vector, the current nominal angle of attack, and the current nominal terminal time to obtain the nominal state vector in the mid-course guidance phase. The calculation unit is used to determine whether the nominal state vector satisfies the terminal constraint condition. If the nominal state vector satisfies the terminal constraint condition, the current nominal angle of attack and the current nominal terminal time are output as the optimal mid-course guidance law for the mid-course guidance segment. If the nominal state vector does not satisfy the terminal constraint condition, the nominal state vector, the current nominal angle of attack, and the current nominal terminal time are updated using a linear Gaussian pseudospectral model predictive control method to obtain updated nominal angle of attack and updated nominal terminal time. This includes: linearizing the first-order necessary condition of the optimal control based on the nominal state vector and the current nominal angle of attack to obtain the state vector phase... The linear differential equations of the state vector correlation quantities are as follows: The state vector correlation quantities include: state deviation and costate vector corresponding to the state vector; the linear differential equations of the state vector correlation quantities are pseudospectral discretized to obtain the linear algebraic equations of the state vector correlation quantities and the linear algebraic equations of the terminal time correction; the basic parameters are input into the linear algebraic equations of the state vector correlation quantities and the linear algebraic equations of the terminal time correction to obtain the state vector correlation quantities and the correction quantities of the terminal time; based on the state vector correlation quantities and the correction quantities of the terminal time, the current nominal angle of attack and the current nominal terminal time are updated to obtain the updated nominal angle of attack and the updated nominal terminal time. The update unit is used to take the updated nominal angle of attack and the updated nominal terminal time as the new current nominal angle of attack and the new current nominal terminal time, respectively, and return to the execution step: based on the current state vector, the current nominal angle of attack and the current nominal terminal time, perform ballistic integration on the dynamic equation to obtain the nominal state vector of the mid-guided phase.
8. An electronic device, characterized in that, The electronic device includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the method of any one of claims 1-6.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method described in any one of claims 1-6.