CN116222310A - Two-pair synchronous region coverage interception method based on RBF_G in three-dimensional space - Google Patents

Two-pair synchronous region coverage interception method based on RBF_G in three-dimensional space Download PDF

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CN116222310A
CN116222310A CN202310393166.3A CN202310393166A CN116222310A CN 116222310 A CN116222310 A CN 116222310A CN 202310393166 A CN202310393166 A CN 202310393166A CN 116222310 A CN116222310 A CN 116222310A
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周荻
白羽
张博伦
何朕
邹昕光
祝月
张锐
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Abstract

A two-to-one synchronous region coverage interception method based on RBF_G in a three-dimensional space belongs to the field of multi-to-one missile synchronous interception. The invention solves the problems that different maneuvering levels and types of the target are not considered and the randomness of normal overload of the target is not considered in the existing synchronous interception method. According to the method, firstly, a calculation method of target interception time by a missile in a three-dimensional space is provided, secondly, a training data set is generated for training and generating an RBF_G network, and then a proportional guidance strategy of a variable proportional coefficient is provided based on a proportional guidance rate, so that an interceptor is allowed to intercept a maneuvering target at expected interception time, even if the target adopts maneuvering of different levels and types, normal overload of the target is a random fixed value, and the missile can realize two-to-one synchronous region coverage interception through the expected interception time and a current time error. The method can be applied to the synchronous interception of the two-to-one guided missiles.

Description

Two-pair synchronous region coverage interception method based on RBF_G in three-dimensional space
Technical Field
The invention belongs to the field of synchronous interception of many-to-one missiles, and particularly relates to a two-to-synchronous area coverage interception method based on RBF_G in a three-dimensional space.
Background
For the problem of synchronous time interception, many scholars have conducted intensive studies before, and a new guidance rate was designed to give a calculation method of interception time (S.R.Kumar and D.Mukherjee, "Terminal time-constrained nonlinear interception strategies against maneuvering targets," Journal of Guidance, control, and Dynamics, vol.44, no.1, pp.200-209,2021.[ Online ]. Available: https:// doi.org/10.2514/1.G 005455). A method based on forward time prediction is proposed to solve the problem of interception of sea-air anti-warships, and guidance strategies proposed based on the scheme can effectively realize attack on accurate targets (M-J.Tahk, S. -W.shim, S. -M.hong, H. -L.Choi and C. -H.Lee, "Impact Time Control Based on Time-to-Go Prediction for Sea-Skimming Antiship Missiles," in IEEE Transactions on Aerospace and Electronic Systems, vol.54, no.4, pp.2043-2052, aug.2018) within a specified time. A Time estimation scheme taking into account the proportional pilot rate of drag is proposed to solve the problem of remaining Time calculation while the missile is flying in the presence of drag (B.zhang, D.Zhou and C.shao, "Closed-Form Time-to-Go Estimation for Proportional Navigation Guidance Considering Drag," in IEEE Transactions on Aerospace and Electronic Systems, vol.58, no.5, pp.4705-4717, oct.2022, doi: 10.1109/TAES.2022.3164863.). An optimal conductivity was proposed to solve the problem of uncertain time-of-flight (Rusnak I. Optimal guidance laws with uncertain time-of-flight [ J ]. IEEE Transactions on Aerospace and Electronic Systems,2000,36 (2): 721-725.). A recursion-based time estimation method is proposed for solving the problem of estimating the remaining flight time of a missile, and a recursion time calculation method for updating the time in a non-iterative manner is proposed. The Recursive method includes an error compensation feature that explicitly calculates the time-out error resulting from a non-zero initial header error (Min-JeaTahk, chang-Kyung Ryoo and Hangju Cho, "repetitive time-to-go estimation for homing guidance missiles," in IEEE Transactions on Aerospace and Electronic Systems, vol.38, no.1, pp.13-24, jan.2002, doi: 10.1109/7.993225.). In literature (C.Y.Wang, X.J.Ding, J.N.Wang, and J.Y. Shan, "A robust threedimensional cooperative guidance law against maneuvering target," Journal of the Franklin Institute, vol.357, no.10, pp.5735-5752, jul.2020.) the relative distance divided by the relative velocity is used, whereas in literature (J.Zhao, R.Zhou, and Z.N. Dong, "Three-dimensional cooperative guidance laws against stationary and maneuvering targets," Chinese Journal of Aeronautics, vol.28, no.4, pp.1104-1120, apr.2015.) the relative distance, the velocity of the target and missile and the heading angle of the missile are used. In many cases, neither of the above estimation methods can accurately estimate the advance time, so that the missile cannot attack the target at the same time under CPN's law.
Many scholars have also made many studies in recent years regarding a many-to-one intercept strategy, an optimal strategy was proposed to solve non-collision gaming in three-dimensional space, in which a feedback strategy based on optimal state was proposed to solve the 2-to-1 intercept problem in three-dimensional space (Garcia E, casbeer D W, pachter m.optimal Strategies for a Class of Multi-Player Reach-Avoid Differential Games in D space [ j ]. IEEE Robotics and Automation Letters,2020, pp (99): 1-1.). One collaborative strategy was proposed for differential gaming of two chasers and One escapement (Garcia E, fuchs Z E, milutinovic D, et al a Geometric Approach for the Cooperative Two-purguer One-Evader Differential Game [ J ], ifacPapersonline,2017,50 (1): 15209-15214.). A two-to-one chase strategy is proposed in which the positional relationship between two pursuers and one escapement is mainly analyzed and the optimal equations of motion for the tracker and the bettor are finally given according to the solution of the HJI equation in differential betting (M.Pachter, A.Von mol, E.Garc. A, D.Casbeer, and D.Milouinovi' c, "Twon-one pursuit," Journal of Guidance, control, and Dynamics, vol.42, pp.1-7,02 2019.). A new non-motorized aircraft defending missile guidance law was proposed to solve the problem of cooperative interception between the chasers, which is based mainly on the concept of dynamic gaming to give the problem of optimal trajectories in real time (Sinha, nandan, kumar, et al, a New Guidance Law for the Defense Missile of NonmaneuverableAircraft [ J ]. IEEE transactions on Control systems technology: A publication of the IEEE Control Systems Society,2015,23 (6): 2424-2431.), a cooperative navigation strategy based on coverage to Control the angle of flight path was proposed to solve the problem of coverage interception (bolan Zhang, di Zhou, junlong Li, and Yuhan Yao Coverage-Based Cooperative Guidance Strategy by Controlling Flight Path Angle, journal of Guidance, control, and Dynamics 2022:5, 972-981).
In terms of stability analysis, a Lyapunov candidate function was proposed for analyzing the stability of neural networks in control systems (Ren X, lewis FL, zhang J.Neal network compensation control for mechanical systems with disturbances [ J)]Automation, 2009,45 (5): 1221-1226. The proposed lyapunov function can be used to analyze the range of values of the weighted norms of the neural network in the presence of disturbances, limited by the parameters of the designed system. A new RBF network is proposed, whose center selection of RBF network is based on l 0 Methods of Norm selection (Wang H, shi Z, wong H T, et al an l0-Norm-Based Centers Selection for Failure Tolerant RBF Networks [ J)]IEEE Access,2019, 7:151902-151914.). For the initial three-dimensional model of the missile, a lyapunov-like method is proposed for analyzing the performance of pure PNG production conductivity in three-dimensional space in terms of interception.
In summary, in view of the existing work discussed at present, the factor that different maneuvering levels and types exist in the target are not considered in the existing synchronous interception method, and the normal overload of the target is set to a fixed value, that is, the randomness of the normal overload of the target is not considered, so that the application effect of the existing synchronous interception method in practice needs to be further improved.
Disclosure of Invention
The invention aims to solve the problems that different maneuvering levels and types of targets are not considered and the randomness of normal overload of the targets is not considered in the existing synchronous interception method, and provides a two-pair synchronous area coverage interception method based on RBF_G in a three-dimensional space.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the method for intercepting the coverage of two pairs of synchronous areas based on RBF_G in the three-dimensional space comprises the following steps:
firstly, establishing a missile interception model in a three-dimensional space, namely establishing a relative kinematics equation of two missiles and a target in the three-dimensional space;
step two, designing a calculation method of target interception time of the missile in the three-dimensional space;
step three, constructing a training set of the RBF_G neural network based on the relative kinematics equation of the step one, and training the RBF_G neural network by utilizing the constructed training set;
and step four, obtaining time deviation according to the synchronous interception time output by the trained RBF_G neural network and the interception time calculated in the step two, then giving a guidance law of synchronous interception through the controller, substituting the time deviation into the guidance law to obtain the normal acceleration of the missile, and giving a final guidance instruction according to the normal acceleration.
The beneficial effects of the invention are as follows:
according to the method, firstly, a calculation method of target interception time by a missile in a three-dimensional space is provided, secondly, a training data set is generated for training and generating an RBF_G network, and then a proportional guidance strategy of a variable proportional coefficient is provided based on a proportional guidance rate, so that an interceptor is allowed to intercept a maneuvering target at expected interception time, even if the target adopts maneuvering of different levels and types, normal overload of the target is a random fixed value, and the missile can realize two-to-one synchronous region coverage interception through the expected interception time and a current time error.
Drawings
FIG. 1 is a block diagram of the overall design of the method of the present invention;
wherein I represents an input layer, R_B represents a radial basis function layer, L represents a linear layer, and O represents an output layer; regularizing and anti-regularizing ballistic data to prevent excessive training errors caused by too large data phase differences;
FIG. 2 is a schematic view of missile interception in three dimensions;
in the figure, (X) I ,Y I ,Z I ) Represents an inertial reference frame, (X) M ,Y M ,Z M ) Representing the projectile coordinate system, a M Representing missile acceleration, a T Representing the target acceleration, gamma T Representing the angle between the normal acceleration and the y-axis in the velocity coordinate system of the target, gamma M Represents the included angle theta between the normal acceleration and the y axis under the velocity coordinate system of the missile L Representing the elevation angle between the P-E view system and the inertial reference frame,
Figure BDA0004176569560000041
representing the inclination angle between the P-E vision line system and the inertial reference coordinate system;
the inertial reference coordinate system takes the mass center of the earth as an origin, takes the straight spring point of the equatorial plane as an x-axis, takes the rotation axis of the earth as a y-axis, and takes the equatorial plane vertical to the x-axis as a z-axis;
the missile body coordinate system takes the mass center of the missile as an origin, takes the symmetry axis of the missile body shell, points to the head of the missile as an x axis, takes the longitudinal symmetry plane of the missile as a y axis and takes the longitudinal symmetry plane of the missile as a z axis;
the speed coordinate system of the target takes the mass center of the target as an origin, takes the speed direction as an x-axis, and a y-axis is positioned on the symmetry plane of the missile and is perpendicular to the x-axis, and a z-axis is determined according to a right-hand rule;
the speed coordinate system of the missile takes the mass center of the missile as an origin, takes the speed direction as an x-axis, and a y-axis is positioned on the symmetrical plane of the missile and is perpendicular to the x-axis, and a z-axis is determined according to a right-hand rule;
the P-E vision line takes the mass center of the missile as an origin, takes the connecting line of the missile and the target as an x-axis, takes the vertical x-axis as a y-axis according to the right-hand rule, and takes the vertical x-axis as a z-axis according to the right-hand rule;
FIG. 3 is a flow chart for generating training data;
FIG. 4 is a two-to-one coverage intercept schematic;
FIG. 5 is a model diagram of an RBF_G neural network;
FIG. 6 is a control block diagram of the guidance system;
FIG. 7 is a screenshot of partial data of an input dataset;
FIG. 8 is a second screenshot of partial data of an input dataset;
FIG. 9 is a screenshot of partial data of an output dataset;
FIG. 10 is a graph of training error versus three algorithms;
FIG. 11 is a graph of prediction accuracy versus three algorithms;
FIG. 12 is a schematic diagram of synchronized area coverage interception;
FIG. 13 is a time error diagram of sync area interception;
FIG. 14 is a schematic diagram of unsynchronized area coverage interception;
fig. 15 is a time error diagram of asynchronous area interception.
Detailed Description
Detailed description of the inventionin the first embodiment, this embodiment will be described with reference to fig. 1 and 5. The method for intercepting two pairs of synchronous region coverage based on RBF_G in the three-dimensional space specifically comprises the following steps:
firstly, establishing a missile interception model in a three-dimensional space, namely establishing a relative kinematics equation of two missiles and a target in the three-dimensional space;
step two, designing a calculation method of target interception time of the missile in the three-dimensional space;
Step three, constructing a training set of the RBF_G neural network based on the relative kinematics equation of the step one, and training the RBF_G neural network by utilizing the constructed training set;
and step four, as shown in fig. 6, obtaining time deviation according to the synchronous interception time output by the trained RBF_G neural network and the interception time calculated in the step two, then giving a guidance law of synchronous interception through the controller, substituting the time deviation into the guidance law to obtain normal acceleration of the missile, and giving a final guidance instruction according to the normal acceleration.
By generating a large amount of missile simulated flight data, the RBF_G neural network is utilized to predict the estimated time of missile interception targets, energy consumption and maximum normal overload. Finally, a set of guidance system is designed to realize the area coverage interception of the possible acceleration of the target projectile. In practical application, the synchronous interception time of the missile to the target is predicted through the RBF_G neural network, and then the time deviation is generated by making a difference with the calculated interception time. Guidance instructions may be generated based on the time offset, which may be regenerated with each iteration update. Finally, the coverage interception of the missile to the target area is realized, and the experimental result shows that the time deviation of each missile reaching the preset position is small enough, so that the coverage interception of the missile synchronous area can be realized.
The second embodiment will be described with reference to fig. 2. The first difference between the present embodiment and the specific embodiment is that the relative kinematic equation of the two missiles and the target in the three-dimensional space is:
assuming the missile and target are point masses, the autopilot and seeker dynamics of the missile are sufficiently fast to be ignored. Further assume that the velocity of the missile and target is constant and that the angle of attack is sufficiently small to be negligible.
Figure BDA0004176569560000051
Figure BDA0004176569560000052
Figure BDA0004176569560000053
Figure BDA0004176569560000054
Figure BDA0004176569560000061
Figure BDA0004176569560000062
Figure BDA0004176569560000063
wherein ,
Figure BDA0004176569560000064
is r i R is the first derivative of i Is the distance between the ith missile and the target, v T Is the velocity vector, θ, of the target T Is the elevation angle between the velocity coordinate system and the P-E line of sight of the target, +.>
Figure BDA0004176569560000065
Is the inclination angle between the velocity coordinate system and the P-E line of sight system of the target, i=1, 2, v Mi Is the velocity vector, θ, of the ith missile Mi Is the elevation angle between the speed coordinate system of the ith missile and the P-E vision system, < ->
Figure BDA0004176569560000066
Is the inclination angle between the speed coordinate system of the ith missile and the P-E sight system, q yMi Is the elevation angle of the sight of the ith missile, q zMi Is the line of sight dip of the ith missile, +.>
Figure BDA0004176569560000067
Is q yMi First derivative of>
Figure BDA0004176569560000068
Is q zMi Is the first derivative of (a);
Figure BDA0004176569560000069
is theta Mi First derivative of A zMi Is the z-axis acceleration component of the ith missile under the own speed coordinate system, A yMi Is the y-axis acceleration component of the ith missile under the own speed coordinate system,/and the speed of the ith missile is equal to or higher than the speed of the ith missile>
Figure BDA00041765695600000610
Is theta T First derivative of A zT Is the z-axis acceleration component of the target in its own velocity coordinate system,/and>
Figure BDA00041765695600000611
is->
Figure BDA00041765695600000612
First derivative of A yT Is the y-axis acceleration component of the target in its own velocity coordinate system.
Other steps and parameters are the same as in the first embodiment.
And a third specific embodiment: the difference between this embodiment and the first or second embodiment is that the specific process of the second step is:
calculating attack time of the missile along a straight line:
Figure BDA0004176569560000071
wherein ,tgoL Representing the attack time of the missile along a straight line,
Figure BDA0004176569560000072
Δy is the relative distance between the missile and the target in the y-axis direction of the inertial reference frame, v M Representative guideVelocity of bullet, a ty For target acceleration a t Projection in the y-axis direction of the target velocity coordinate system, n= 2*v T * Δx, Δx is the relative distance of the missile to the target in the x-axis direction of the inertial reference frame;
at t goL In time, the target moves to a virtual position TF in a speed coordinate system V Calculating virtual position TF under inertial reference system and terminal speed V of target through conversion matrix t ；
Converting the speed of the missile into a virtual P-E vision system to obtain an included angle sigma between the speed of the missile and the P-E vision system MF The missile reaches the virtual point at the following time:
Figure BDA0004176569560000073
wherein, the absolute value is represented, alpha= - (N-2) (N-1), N is a proportionality coefficient, the value is between 2 and 6,
Figure BDA0004176569560000074
yta is the lift-drag coefficient of missile, +.>
Figure BDA0004176569560000075
r represents the distance between the missile and the target;
Figure BDA0004176569560000076
wherein ,Δtgo Is the extension of time caused by the proportional rate arc, V mt2 ＝v M *e Ξ E is the base of the natural logarithm, xi= yta ×n×sign (σ MF )*(0-σ MF ) N-1, sign (·) is a sign function, V t Is the terminal velocity of the object and,
Figure BDA0004176569560000077
is the terminal angle, t, at the moment of interception d ＝t goF -t goL ；
Interception time t goS The method comprises the following steps:
t goS ＝t goL +Δt go
other steps and parameters are the same as in the first or second embodiment.
For both missile 1 and missile 2, the method of the present embodiment is used to calculate the target interception time, for example, when missile 1 is calculated, the corresponding parameters are substituted into the data of missile 1.
The specific embodiment IV is as follows: this embodiment will be described with reference to fig. 3. The difference between this embodiment and one to three embodiments is that the training set for constructing the rbf_g neural network includes the following specific procedures:
step 1, setting a maximum cycle number Num, a stop trajectory simulation flag bit stop_flag, an initial range of missile operation parameters and an initial range of target operation parameters;
Step 2, initializing an initial position of a target and a missile, an elevation angle of a sight angle, a deflection angle of the sight angle, an initial speed, an initial acceleration, an initial distance and estimated interception time; during initialization, taking a value according to the initial range given in the step 1;
step 3, calculating the maximum interception time max (t) of the missile by adopting the method of the step two for the initialization parameters of the step 2 go ) Minimum interception time min (t go )；
Step 4, the minimum interception time min (t go ) Assigning a value to the interception time t go ；
Step 5, judging the interception time t go Whether or not it is smaller than the maximum interception time max (t go ) If t go Less than the maximum interception time max (t go ) Executing the step 6, otherwise returning to the step 2;
step 6, generating ballistic data according to the initialization parameters in the step 2 and the kinematics equation established in the step one, and judging whether the generated ballistic data meets d or not 1 < 1 and d 2 Step 7 is executed if the value is less than 1, otherwise step 19 is executed;
wherein ,d1 Representing the post-completion order of interceptionDistance between tag and 1 st missile, d 2 Representing the distance between the target and the 2 nd missile after the interception is completed;
step 7, judging whether the ballistic data meets the following conditions: maximum normal acceleration a max If the value is less than 100, executing the step 8, and if the value is not met, executing the step 19;
Step 8, judging whether the ballistic data meets the following conditions: r1 is less than 100 and R2 is less than 100, if yes, executing step 9, and if not, executing step 19;
wherein R1 represents the initial distance between the 1 st missile and the target, and R2 represents the initial distance between the 2 nd missile and the target;
step 9, judging whether the ballistic data meets the following conditions: the time_error is less than 0.5, the time_error represents the difference value of the two missile interception times, if the difference value is satisfied, the step 10 is executed, and if the difference value is not satisfied, the step 11 is executed;
step 10, calculating an overall numerical value: total=weight x energy+ (1-weight) a = max Weight represents the weight, energy represents the sum of the energy consumed by the missile and the maximum normal overload; total has no actual physical meaning, is an intermediate value;
if Total < Total min General command Total min Total, save and output ballistic data (i.e., write=1), and then execute step 19; wherein Total is min Representing the minimum value before the current iteration;
if Total is greater than or equal to Total min Step 19 is directly performed;
step 11, let time_up=max (t go )，Time_low＝min(t go ) The interception Time Tgo1 of the 1 st missile is distributed as time_low, and the interception Time Tgo2 of the 2 nd missile is distributed as time_up;
step 12, generating ballistic data according to the relative kinematic equation of the missile and the target in the step one, and judging whether Tgo1 is smaller than max (t go )；
If Tgo is less than max (t go ) Step 13 is executed;
if Tgo is not less than max (t go ) Step 20 is performed;
step 13, assigning the interception Time Tgo2 of the 2 nd missile as time_up;
step 14, judging whether the interception Time Tgo2 of the 2 nd missile is greater than time_low, if Tgo is greater than time_low, executing step 15, otherwise executing step 17;
step 15, judging whether the generated ballistic data meets d 1 < 1 and d 2 < 1, if yes, executing step 16, otherwise executing step 18;
step 16, judging whether the ballistic data meets the following conditions: maximum normal acceleration a max R < 100, R1 < 100 and R2 < 100;
if the maximum normal acceleration a is satisfied max And if the total value is less than 100, R1 is less than 100 and R2 is less than 100, calculating the total value: total=weight x energy+ (1-weight) a = max Weight represents weight and energy represents energy; if Total < Total min General command Total min Total, step 18 is performed after storing and outputting ballistic data, total min Representing the minimum value before the current iteration; if Total is greater than or equal to Total min Step 18 is directly performed;
if the maximum normal acceleration a is not satisfied max Step 18 is performed if R1 is less than 100, and R2 is less than 100;
step 17, tgo 1= Tgo1+dt, and returning to step 12;
step 18, tgo 2= Tgo2-dt, and returning to step 14;
Step 19, re-giving the interception time t go ＝t go +dt, and then returning to step 5, and executing step 20 while returning to step 5;
step 20, judging whether the stored ballistic data are stored in a training set;
if the stored trajectory data is stored in the training set, judging whether the current cycle number turn is smaller than the maximum cycle number Num, if turn is smaller than Num, enabling the cycle number turn=turn+1, and returning to the step 2; if turn=num, then step 21 is performed;
if the stored ballistic data is not stored in the training set, directly returning to the step 2;
and step 21, ending.
The invention performs random on all data within a certain reasonable range, and specifically comprises an initial position, a speed, a sight angle and acceleration. That is, each time the ballistic data is not controllable, which results in a more even distribution of the ballistic in space, and a greater range of consideration. The coverage interception schematic diagram of the two-to-one missile is shown in fig. 4, and two virtual movement points of the target are intercepted by two missiles simultaneously, wherein at the initial moment, other initial parameters except acceleration are consistent. Thus, two missiles can intercept two virtual targets, and synchronous interception of the targets can be realized. If two missiles can intercept two virtual targets with constant acceleration values at the same time, we can default that when the targets fly at one acceleration, the missiles can intercept the targets. Thus, coverage interception of the target can be achieved. The initial aim of the method is achieved, and the problem of interception of the missile is solved.
The parameters initialized in step 2 of this embodiment, i.e., each column of the input dataset are shown in table 1, all missile parameters are capitalized with M1 and M2. All virtual target points are also capitalized with T1 and T2.
TABLE 1 input data
Figure BDA0004176569560000101
Figure BDA0004176569560000111
The first virtual target point and the second virtual target point are identical except acceleration at the initial moment, so that the same data in the first virtual target point and the second virtual target point can be directly assigned to the second virtual target point during initialization assignment.
The output data of the training set is shown in table 2:
TABLE 2 output data
Figure BDA0004176569560000112
Figure BDA0004176569560000121
For the output data set, when the flag is synchronous inter When=1, the first and second targets can be intercepted by the first and second targets, and the time difference is smaller than the expected time difference. t is t M1 ,t M2 Is the predicted time of flight. When synchronizing flag bit flag inter When=0, interception of the first and second targets can be achieved on behalf of the first and second missiles, but the time difference is larger than the expected time difference. Then t M1 ,t M2 The set flight times for missile one and missile two, respectively. The purpose of this is to minimize this time difference even though the two missiles cannot intercept the virtual target point synchronously. The remaining output parameters are consistent. The simulation environment adopted by the invention is shown in table 3:
TABLE 3 simulation Environment
Project Data
CPU E5-2696V4
Memory 128g
Disk capacity 1T
System and method for controlling a system Win10 professional edition
In this embodiment, ballistic data is screened according to performance indexes, and the satisfied data is retained:
1. our aim is to let the missile intercept the target head-on, but if the target cannot be intercepted head-on, i.e. the target is caught head-to-tail, then this is also the intercept trajectory, but not what we expect, so the corresponding data is not preserved.
Here, since "Nan" may occur when the line of sight angle is excessively large, the calculation formula of the line of sight angle is as follows:
Figure BDA0004176569560000122
as the distance between the missile and the target gets closer and closer,
Figure BDA0004176569560000123
the calculated error is very large, and once the head tracking cannot be realized, the head tracking mode is converted into the tail tracking mode, and the view angle is infinite. Thus, when the proportional conductivity is used, the normal overload tends to be infinite and does not meet the condition of constraint on the normal overload, so that data of Nan is deleted in the ballistic iteration process.
2. If the initial positions of the two missiles are too far apart, synchronous interception cannot be realized. In addition, we hope that both missiles are intercepted under the condition of head-tracking, the tail-tracking time is too long, and the data are not in the range of consideration.
3. Only if the time difference between the two missile interception virtual points is smaller than the given time difference, synchronous interception is considered to be realized, otherwise, the corresponding data is not reserved. For data intercepted asynchronously we will recalculate to give the appropriate time of flight, respectively.
Aiming at the problem of interception of guided segments of missile terminals, we do parameter constraint of table 4:
TABLE 4 setting ranges of simulation parameters
Figure BDA0004176569560000131
wherein Nt Is a constant for determining the proportionality coefficient between the maximum allowable time error and the desired difference. Next, we give a definition about the time parameter, as shown in table 5.
TABLE 5 definition of time parameters for missile one and missile two
Definition of time Missile 1 Missile 2
Optimum time t go t go
Calculated missile flight time t gos1 t gos2
Actual missile flight time t m1 t m2
Wherein the optimal time is a human given time parameter, and the reference range is a constant value added or subtracted to the calculated time parameters of the two missiles. The calculated missile flight time is given by an algorithm calculated through three-dimensional space interception time. The actual missile flight time is iterated step by step through the program. The maximum allowable time error range is the difference between the actual missile flight times.
By means of tables 4 and 5, the parameter settings and the desired parameter indicators during the simulation are given, so that the data meeting the requirements can be missed, and the data not meeting the requirements can be deleted, for example, when the missile can be intercepted synchronously, but the required normal overload is too large. Such data cannot be practically applied. Also, although interception can be achieved, the difference in interception time exceeds the maximum allowable time error. The final desire is to be able to acquire enough data for training so that the accuracy of the RBF neural network model is higher. When we have a set of initial data we get a suitable interception time, which can greatly reduce the time spent in practical applications.
Other steps and parameters are the same as in one to three embodiments.
Fifth embodiment: the difference between the present embodiment and one to four embodiments is that the training set constructed is used to train the rbf_g neural network, and the specific process is as follows:
initializing parameters of a radial base layer, parameters of a genetic algorithm, linear layer parameters and deflection of the radial base layer, and initializing training times l=1;
Step (2), inputting input data into an input layer of the RBF_G neural network;
step (3), inputting the output of the input layer into a radial base layer, and generating a radial base layer matrix through radial base function calculation;
step (4), the radial base matrix generated in the step (3) is transmitted into an initial population of a genetic algorithm, and whether the number of the initial population is larger than 2 is judged;
if the initial population number is more than 2, executing the step (5);
otherwise, let l=l+1, return to step (2);
step (5), calculating the second norms of the training error vectors of each individual in the initial population, taking the individual with the smallest second norms of the training error vectors in the initial population as the parent class of the genetic algorithm, and taking the individual with two Fan Shuci small training error vectors in the initial population as the parent class of the genetic algorithm;
each individual in the population comprises a radial basis matrix
Figure BDA0004176569560000141
And training error vector e i ；
Step (6), selecting each row of the parent class and the parent class to randomly generate different constants N ', and performing cross operation according to the constants N';
step (7), randomly generating a natural number M for the first line of the processing result of the step (6), and then carrying out mutation operation on the M-th element of the first line;
and (3) processing each row of the processing result in the step (6) in turn until each row is processed, and generating a new radial base matrix of the subclass;
Step (8), calculating the output of the RBF_G neural network through a linear layer by using the new sub-class radial base matrix generated in the step (7);
step (9), calculating errors according to the output of the step (8), and adding the new radial base matrix of the subclasses into the initial population of the genetic algorithm;
step (10), reversely transferring and updating the parameters of the RBF_G neural network according to the error calculated in the step (9);
and (11) judging whether the set maximum iteration number or the error is smaller than a set threshold value, and ending the training process if the set maximum iteration number or the error is smaller than the set threshold value.
Otherwise, let l=l+1, return to step (2).
Other steps and parameters are the same as in one to four embodiments.
Specific embodiment six: the difference between this embodiment and one to fifth embodiments is that in the step (9), the error is calculated according to the output of the step (8), and the specific process is as follows:
the input data vector X of the rbf_g neural network is expressed as:
X＝[x 1 ,x 2 ,x 3 ,...,x n ] T
wherein ,x1 ,x 2 ,x 3 ,...,x n Input data for 1 st, 2 nd, 3 rd, … th, n-th of X;
the output of the rbf_g neural network is:
Figure BDA0004176569560000151
wherein ,y(xi ) For the actual output value corresponding to the ith input data, q is the number of neurons in the hidden layer, omega j Weights of neurons of the jth hidden layer, b j For the bias of the jth hidden layer neuron,
Figure BDA0004176569560000152
radial basis function for the jth hidden layer neuron,/->
Figure BDA0004176569560000153
dist(x i -c j ) Represents x i and cj Euclidean distance between c j Is the center of the radial basis function, sigma j Is the variance;
the error is:
Figure BDA0004176569560000154
wherein ,Ei Representing the deviation, y' (x), corresponding to the ith input data i ) Representing the actual value of the output corresponding to the ith input data, and m represents the number of neurons of the output.
Other steps and parameters are the same as in one of the first to fifth embodiments.
Seventh embodiment: this embodiment differs from one of the first to sixth embodiments in that the specific process of step (10) is:
Figure BDA0004176569560000155
wherein E.epsilon.1 represents E with number of columns n of 1 and E= [ E ] 1 ,E 2 ,E 3 ,...,E n ] T ，η b For the learning rate of radial base layer deflection vector b, b= [ b ] 1 ,b 2 ,b 3 ,...,b q ] T Δb is the deviation of the radial base layer deflection vector;
after the delta b is calculated, summing the element in the delta b and the corresponding element in the deflection vector b before updating to obtain deflection of the updated hidden layer neuron;
Figure BDA0004176569560000161
wherein ,
Figure BDA0004176569560000162
is a radial basis matrix with row number q and column number n,>
Figure BDA0004176569560000163
E∈(n,1)，η ω as the learning rate of the weight vector ω, Δω is the deviation of the weight vector;
after the delta omega is calculated, summing the elements in the delta omega and the corresponding elements in the weight vector omega before updating to obtain the weight of the updated hidden layer neuron;
Figure BDA0004176569560000164
wherein ,
Figure BDA0004176569560000165
c is j Is a learning rate of Deltac j C is j Deviation of->
Figure BDA0004176569560000166
Is a radial base matrix with 1 row and n columns;
calculation of Δc j Then, Δc is added again j And c before update j Summing to obtain updated c j ；
Figure BDA0004176569560000167
wherein ,
Figure BDA0004176569560000168
is sigma (sigma) j Is a learning rate of DeltaSigma j Is sigma (sigma) j And represents the 2 norms.
Calculating delta sigma j After that, deltaSigma is added again j Sigma before update j Summing to obtain updated sigma j 。
Other steps and parameters are the same as in one of the first to sixth embodiments.
Eighth embodiment: this embodiment differs from one of the first to seventh embodiments in that the proportionality coefficient of the guidance law is:
Nc＝N*(1-E t *t error *R(t)/R(t 0 ))
wherein N is a proportionality coefficient adopted in calculating the interception time, t error Is the difference between the set interception time and the calculated interception time, R (t) represents the distance between the missile and the target at the time t, R (t) 0 ) Representing the distance between the missile and the target at the initial moment, E t Is constant.
Other steps and parameters are the same as those of one of the first to seventh embodiments.
Detailed description nine: this embodiment differs from one to eight of the embodiments in that the normal acceleration of the projectilea M The method comprises the following steps:
a M ＝Nc*Ω×v M
wherein Ω represents the P-E line-of-sight angular rate,
Figure BDA0004176569560000171
for the angular velocity in the y-direction of the P-E line of sight,
Figure BDA0004176569560000172
For angular velocity in z direction, V M Representing missile speed.
Other steps and parameters are the same as in one to eight of the embodiments.
Detailed description ten: this embodiment differs from one of the first to ninth embodiments in that the guidance system is stable when the guidance law satisfies the condition (1) or (2);
condition (1):
Figure BDA0004176569560000173
condition (2):
Figure BDA0004176569560000174
wherein ,ev Is the vector of the error and,
Figure BDA0004176569560000175
estimation error for linear weight, · F Represents F norm, constant sigma > 0, lambda v Is K v Minimum feature value, K v Is the error control gain, +.>
Figure BDA0004176569560000176
M * Is the ideal two norms of the radial base matrix.
Other steps and parameters are the same as in one of the first to ninth embodiments.
Guidance system stability demonstration:
suppose 1: ideal omega * Is bounded and omega * F ≤M * Is omega 1 Can then give
Figure BDA0004176569560000177
wherein
Figure BDA0004176569560000178
Is the estimation error of the linear weight.
Suppose 2: reference error
Figure BDA0004176569560000179
Wherein the constant lambda c ＞0，M＞0，K v Is a given error control gain.
Suppose 3: an adaptive law of parameter ω based on σ correction is given.
Figure BDA00041765695600001710
Where Γ > 0 is the gain matrix and σ > 0 is the scalar parameter.
For proof, please refer to the literature for a detailed proof procedure of 1-3 (Ren X, lewis F L, zhang J.Neal network compensation control for mechanical systems with disturbances [ J ]. Automatics, 2009,45 (5): 1221-1226.).
Theorem one: if the guidance system is stable, any one of the following equations needs to be satisfied.
Figure BDA00041765695600001711
Or->
Figure BDA00041765695600001712
wherein ,λv Is K v Epsilon is a small constant and
Figure BDA00041765695600001818
and (5) correlation.
And (3) proving: we assume that the lyapunov candidate function
Figure BDA0004176569560000181
The derivative of V with respect to time can be obtained:
Figure BDA0004176569560000182
Figure BDA0004176569560000183
Figure BDA0004176569560000184
Figure BDA0004176569560000185
wherein λv > 0 is K v Minimum eigenvalues. Then the first time period of the first time period,
Figure BDA0004176569560000186
Figure BDA0004176569560000187
Figure BDA0004176569560000188
Figure BDA0004176569560000189
thus, we can obtain
Figure BDA00041765695600001810
Figure BDA00041765695600001811
wherein
Figure BDA00041765695600001812
Is a constant. If V.sub.0 needs to be satisfied, we only need +.>
Figure BDA00041765695600001813
Then +.>
Figure BDA00041765695600001814
Then
Figure BDA00041765695600001815
Or->
Figure BDA00041765695600001816
Figure BDA00041765695600001817
So we can rewrite V as
Figure BDA0004176569560000191
Y is the minimum eigenvalue of M. Kappa is the eigenvalue of Γ minimum.
Figure BDA0004176569560000192
Because e v And
Figure BDA0004176569560000196
are all bounded by upper bounds. Then there is also an upper bound for V. Then for the whole control systemIn general, if stable convergence of the system is desired, then only the requirement is satisfied
Figure BDA0004176569560000193
Or->
Figure BDA0004176569560000194
And (5) finishing the verification.
Simulation results
Through the training set data generating part, 3000 groups of data are finally selected, finally, the generated partial data are shown in fig. 7, 8 and 9, the input data meaning of each column is shown in table 6, the output data meaning of each column is shown in table 4, wherein the training set input data total 20 columns comprise initial information of missiles and targets, the training set output data total 11 columns comprise final missile interception time, energy consumption and maximum normal overload. Wherein the partial data of the input data set is shown and the partial data of the output data set is shown.
TABLE 6 definition of parameters
Figure BDA0004176569560000195
Figure BDA0004176569560000201
The training errors of the three algorithms RBF, BP neural network and RBF_G are compared respectively, and as shown in the following figure 10, the training errors of the three algorithms can be obtained, the errors of the three algorithms are large at the beginning of training, but after about 5000 times of training, the training errors of RBF and BP NN are stabilized between 1% and 1.5%, and the training error of RBF_G is less than 0.1%. After 10000 times of data training, the training error of the final RBF is 1.15%, the training error of BP is 1.24%, and the training error of RBF_G is 0.00042%.
Next, we compare the prediction accuracy rates of the three algorithms RBF, BP neural network and rbf_g, and as shown in fig. 11, we can obtain the prediction of the three algorithms, the prediction accuracy rate of BP is 72%, the prediction accuracy rate of RBF is 75%, the prediction accuracy rate of rbf_g is 86%, and the prediction error is mainly caused by the inaccurate energy prediction in the flight phase. But this does not affect our predictions of time of flight, which we mainly use to achieve synchronized coverage interception of missiles to targets in a guidance system.
Finally, a schematic diagram of the synchronous area coverage interception can be realized through the guidance system, as shown in fig. 12, and a two-to-two interception schematic diagram is shown in fig. 12. By means of a small area schematic diagram, we can get the solution proposed by the present invention to achieve area coverage interception, and by means of a time error schematic diagram 13 we can see that the final time error is stable, the estimated flight time is 19.69s. The time of flight of M1 is 20.14s, the time of flight of M2 is 20.63s, and the final time of flight error is 0.49s and less than 0.5s.
For the missile incapable of realizing synchronous interception, the interception time is set respectively, so that the flight time is close enough to achieve the aim of minimum interception time error, as shown in fig. 14, the scheme provided by the invention can realize area coverage interception through a small area schematic diagram, and the final time error is stable and the set flight time is 64.3s and 63.4s respectively as shown in a time error schematic diagram 15. The final M1 time of flight was 64.31s, the final M2 time of flight was 63.64s, and the final time of flight error was 0.67 to greater than 0.5s. Wherein the maximum normal overload of M1 is 31.4647 and-15.2397. The maximum normal overload for M2 is 95.1541 and-80.6831.
The above examples of the present invention are only for describing the calculation model and calculation flow of the present invention in detail, and are not limiting of the embodiments of the present invention. Other variations and modifications of the above description will be apparent to those of ordinary skill in the art, and it is not intended to be exhaustive of all embodiments, all of which are within the scope of the invention.

Claims (10)

1. The method for intercepting the coverage of two pairs of synchronous areas based on RBF_G in the three-dimensional space is characterized by comprising the following steps:
firstly, establishing a missile interception model in a three-dimensional space, namely establishing a relative kinematics equation of two missiles and a target in the three-dimensional space;
step two, designing a calculation method of target interception time of the missile in the three-dimensional space;
step three, constructing a training set of the RBF_G neural network based on the relative kinematics equation of the step one, and training the RBF_G neural network by utilizing the constructed training set;
and step four, obtaining time deviation according to the synchronous interception time output by the trained RBF_G neural network and the interception time calculated in the step two, then giving a guidance law of synchronous interception through the controller, substituting the time deviation into the guidance law to obtain the normal acceleration of the missile, and giving a final guidance instruction according to the normal acceleration.
2. The method for intercepting two pairs of synchronous region coverage based on RBF_G in three-dimensional space according to claim 1, wherein the relative kinematics equation of the two missiles and the target in the three-dimensional space is:
Figure FDA0004176569550000011
Figure FDA0004176569550000012
Figure FDA0004176569550000013
Figure FDA0004176569550000014
Figure FDA0004176569550000015
Figure FDA0004176569550000016
Figure FDA0004176569550000021
wherein ,
Figure FDA0004176569550000022
is r i R is the first derivative of i Is the distance between the ith missile and the target, v T Is the velocity vector, θ, of the target T Is the elevation angle between the velocity coordinate system and the P-E line of sight of the target, +.>
Figure FDA0004176569550000023
Is the inclination angle between the velocity coordinate system and the P-E line of sight system of the target, i=1, 2, v Mi Is the velocity vector, θ, of the ith missile Mi Is the elevation angle between the speed coordinate system of the ith missile and the P-E vision system, < ->
Figure FDA0004176569550000024
Is the inclination angle between the speed coordinate system of the ith missile and the P-E sight system, q yMi Is the elevation angle of the sight of the ith missile, q zMi Is the line of sight dip of the ith missile, +.>
Figure FDA0004176569550000025
Is q yMi First derivative of>
Figure FDA0004176569550000026
Is q zMi Is the first derivative of (a);
Figure FDA0004176569550000027
is theta Mi First derivative of A zMi Is the z-axis acceleration component of the ith missile under the own speed coordinate system, A yMi Is the y-axis acceleration component of the ith missile under the own speed coordinate system,/and the speed of the ith missile is equal to or higher than the speed of the ith missile>
Figure FDA0004176569550000028
Is theta T First derivative of A zT Is the z-axis acceleration component of the target in its own velocity coordinate system,/and>
Figure FDA0004176569550000029
is->
Figure FDA00041765695500000210
First derivative of A yT Is the y-axis acceleration component of the target in its own velocity coordinate system.
3. The method for intercepting two pairs of synchronous area coverage based on rbf_g in three-dimensional space according to claim 2, wherein the specific process of the step two is as follows:
calculating attack time of the missile along a straight line:
Figure FDA00041765695500000211
wherein ,tgoL Representing the attack time of the missile along a straight line,
Figure FDA00041765695500000212
Δy is the inertia of the missile and the targetRelative distance in y-axis direction of sexual reference coordinate system, v M Representing the velocity of the missile, a ty For target acceleration a t Projection in the y-axis direction of the target velocity coordinate system, n= 2*v T * Δx, Δx is the relative distance of the missile to the target in the x-axis direction of the inertial reference frame;
at t goL In time, the target moves to a virtual position TF in a speed coordinate system V Calculating virtual position TF under inertial reference system and terminal speed V of target through conversion matrix t ；
Converting the speed of the missile into a virtual P-E vision system to obtain an included angle sigma between the speed of the missile and the P-E vision system MF The missile reaches the virtual point at the following time:
Figure FDA0004176569550000031
wherein, |·| represents the absolute value, α= - (N-2)/(N-1), N is the scaling factor,
Figure FDA0004176569550000032
yta is the lift-drag coefficient of missile, +.>
Figure FDA0004176569550000033
r represents the distance between the missile and the target;
Figure FDA0004176569550000034
wherein ,Δtgo Is the extension of time caused by the proportional rate arc, V mt2 ＝v M *e Ξ E is the base of the natural logarithm, xi= yta ×n×sign (σ MF )*(0-σ MF ) N-1, sign (·) is a sign function, V t Is the terminal velocity of the object and,
Figure FDA0004176569550000035
is the terminal angle, t, at the moment of interception d ＝t goF -t goL ；
Interception time t goS The method comprises the following steps:
t goS ＝t goL +Δt go 。
4. the method for intercepting two pairs of synchronous region coverage based on RBF_G in three-dimensional space according to claim 3, wherein the specific process of constructing the training set of RBF_G neural network is as follows:
step 1, setting a maximum cycle number Num, a stop trajectory simulation flag bit stop_flag, an initial range of missile operation parameters and an initial range of target operation parameters;
step 2, initializing an initial position of a target and a missile, an elevation angle of a sight angle, a deflection angle of the sight angle, an initial speed, an initial acceleration, an initial distance and estimated interception time;
step 3, calculating the maximum interception time max (t) of the missile by adopting the method of the step two for the initialization parameters of the step 2 go ) Minimum interception time min (t go )；
Step 4, the minimum interception time min (t go ) Assigning a value to the interception time t go ；
Step 5, judging the interception time t go Whether or not it is smaller than the maximum interception time max (t go ) If t go Less than the maximum interception time max (t go ) Executing the step 6, otherwise returning to the step 2;
Step 6, generating ballistic data according to the initialization parameters in the step 2 and the kinematics equation established in the step one, and judging whether the generated ballistic data meets d or not 1 < 1 and d 2 Step 7 is executed if the value is less than 1, otherwise step 19 is executed;
wherein ,d1 Represents the distance between the target and the 1 st missile after the interception is finished, d 2 Representing the distance between the target and the 2 nd missile after the interception is completed;
step 7, judging whether the ballistic data meets the following conditions: maximum normal acceleration a max If the value is less than 100, executing the step 8, and if the value is not met, executing the step 19;
step 8, judging whether the ballistic data meets the following conditions: r1 is less than 100 and R2 is less than 100, if yes, executing step 9, and if not, executing step 19;
wherein R1 represents the initial distance between the 1 st missile and the target, and R2 represents the initial distance between the 2 nd missile and the target;
step 9, judging whether the ballistic data meets the following conditions: the time_error is less than 0.5, the time_error represents the difference value of the two missile interception times, if the difference value is satisfied, the step 10 is executed, and if the difference value is not satisfied, the step 11 is executed;
step 10, calculating an overall numerical value: total=weight x energy+ (1-weight) a = max Weight represents the weight, energy represents the sum of the energy consumed by the missile and the maximum normal overload;
If Total < Total min General command Total min =total, save and output ballistic data, and then execute step 19; wherein Total is min Representing the minimum value before the current iteration;
if Total is greater than or equal to Total min Step 19 is directly performed;
step 11, let time_up=max (t go )，Time_low＝min(t go ) The interception Time Tgo1 of the 1 st missile is distributed as time_low, and the interception Time Tgo2 of the 2 nd missile is distributed as time_up;
step 12, generating ballistic data according to the relative kinematic equation of the missile and the target in the step one, and judging whether Tgo1 is smaller than max (t go )；
If Tgo is less than max (t go ) Step 13 is executed;
if Tgo is not less than max (t go ) Step 20 is performed;
step 13, assigning the interception Time Tgo2 of the 2 nd missile as time_up;
step 14, judging whether the interception Time Tgo2 of the 2 nd missile is greater than time_low, if Tgo is greater than time_low, executing step 15, otherwise executing step 17;
step 15, judging whether the generated ballistic data meets d 1 < 1 andd 2 < 1, if yes, executing step 16, otherwise executing step 18;
step 16, judging whether the ballistic data meets the following conditions: maximum normal acceleration a max R < 100, R1 < 100 and R2 < 100;
if the maximum normal acceleration a is satisfied max And if the total value is less than 100, R1 is less than 100 and R2 is less than 100, calculating the total value: total=weight x energy+ (1-weight) a = max Weight represents weight and energy represents energy; if Total < Total min General command Total min Total, step 18 is performed after storing and outputting ballistic data, total min Representing the minimum value before the current iteration; if Total is greater than or equal to Total min Step 18 is directly performed;
if the maximum normal acceleration a is not satisfied max Step 18 is performed if R1 is less than 100, and R2 is less than 100;
step 17, tgo 1= Tgo1+dt, and returning to step 12;
step 18, tgo 2= Tgo2-dt, and returning to step 14;
step 19, re-giving the interception time t go ＝t go +dt, and then returning to step 5, and executing step 20 while returning to step 5;
step 20, judging whether the stored ballistic data are stored in a training set;
if the stored trajectory data is stored in the training set, judging whether the current cycle number turn is smaller than the maximum cycle number Num, if turn is smaller than Num, enabling the cycle number turn=turn+1, and returning to the step 2; if turn=num, then step 21 is performed;
if the stored ballistic data is not stored in the training set, directly returning to the step 2;
and step 21, ending.
5. The method for intercepting two pairs of synchronous region coverage based on rbf_g in three-dimensional space according to claim 4, wherein said training the rbf_g neural network by using the constructed training set comprises the following specific steps:
Initializing parameters of a radial base layer, parameters of a genetic algorithm, linear layer parameters and deflection of the radial base layer, and initializing training times l=1;
step (2), inputting input data into an input layer of the RBF_G neural network;
step (3), inputting the output of the input layer into a radial base layer, and generating a radial base layer matrix through radial base function calculation;
step (4), the radial base matrix generated in the step (3) is transmitted into an initial population of a genetic algorithm, and whether the number of the initial population is larger than 2 is judged;
if the initial population number is more than 2, executing the step (5);
otherwise, let l=l+1, return to step (2);
step (5), calculating the second norms of the training error vectors of each individual in the initial population, taking the individual with the smallest second norms of the training error vectors in the initial population as the parent class of the genetic algorithm, and taking the individual with two Fan Shuci small training error vectors in the initial population as the parent class of the genetic algorithm;
step (6), selecting each row of the parent class and the parent class to randomly generate different constants N ', and performing cross operation according to the constants N';
step (7), randomly generating a natural number M for the first line of the processing result of the step (6), and then carrying out mutation operation on the M-th element of the first line;
And (3) processing each row of the processing result in the step (6) in turn until each row is processed, and generating a new radial base matrix of the subclass;
step (8), calculating the output of the RBF_G neural network through a linear layer by using the new sub-class radial base matrix generated in the step (7);
step (9), calculating errors according to the output of the step (8), and adding the new radial base matrix of the subclasses into the initial population of the genetic algorithm;
step (10), reversely transferring and updating the parameters of the RBF_G neural network according to the error calculated in the step (9);
and (11) judging whether the set maximum iteration number or the error is smaller than a set threshold value, and ending the training process if the set maximum iteration number or the error is smaller than the set threshold value.
Otherwise, let l=l+1, return to step (2).
6. The method for intercepting two pairs of synchronous region coverage based on rbf_g in three-dimensional space according to claim 5, wherein in said step (9), an error is calculated according to the output of step (8), which comprises the following specific steps:
the input data vector X of the rbf_g neural network is expressed as:
X＝[x 1 ,x 2 ,x 3 ,...,x n ] T
wherein ,x1 ,x 2 ,x 3 ,...,x n Input data for 1 st, 2 nd, 3 rd, … th, n-th of X;
The output of the rbf_g neural network is:
Figure FDA0004176569550000061
wherein ,y(xi ) For the actual output value corresponding to the ith input data, q is the number of neurons in the hidden layer, omega j Weights of neurons of the jth hidden layer, b j For the bias of the jth hidden layer neuron,
Figure FDA0004176569550000062
radial basis function for the jth hidden layer neuron,/->
Figure FDA0004176569550000063
dist(x i -c j ) Represents x i and cj Euclidean distance between c j Is the center of the radial basis function, sigma j Is the variance;
the error is:
Figure FDA0004176569550000071
wherein ,Ei Representing the deviation, y' (x), corresponding to the ith input data i ) Representing the actual value of the output corresponding to the ith input data, and m represents the number of neurons of the output.
7. The method for intercepting two pairs of synchronous area coverage based on rbf_g in three-dimensional space according to claim 6, wherein the specific process of step (10) is as follows:
Figure FDA0004176569550000072
wherein E= [ E 1 ,E 2 ,E 3 ,...,E n ] T ，η b For the learning rate of radial base layer deflection vector b, b= [ b ] 1 ,b 2 ,b 3 ,...,b q ] T Δb is the deviation of the radial base layer deflection vector;
Figure FDA0004176569550000073
wherein ,
Figure FDA0004176569550000074
is a radial base matrix with the number of rows being q and the number of columns being n, eta ω As the learning rate of the weight vector ω, Δω is the deviation of the weight vector;
Figure FDA0004176569550000075
wherein ,
Figure FDA0004176569550000076
c is j Is a learning rate of Deltac j C is j Deviation of->
Figure FDA0004176569550000077
Is a radial base matrix with 1 row and n columns;
Figure FDA0004176569550000078
wherein ,
Figure FDA0004176569550000079
is sigma (sigma) j Is a learning rate of DeltaSigma j Is sigma (sigma) j Is represented by 2 norms.
8. The method for intercepting a two-pair synchronous area coverage based on rbf_g in a three-dimensional space according to claim 7, wherein a proportionality coefficient of said guidance law is:
Nc＝N*(1-E t *t error *R(t)/R(t 0 ))
wherein N is a proportionality coefficient adopted in calculating the interception time, t error Is the difference between the set interception time and the calculated interception time, R (t) represents the distance between the missile and the target at the time t, R (t) 0 ) Representing the distance between the missile and the target at the initial moment, E t Is constant.
9. The method for intercepting a two-pair synchronous area coverage based on rbf_g in three-dimensional space according to claim 8, wherein said missile normal acceleration a M The method comprises the following steps:
a M ＝Nc*Ω×v M
wherein Ω represents the angular velocity of the P-E line of sight, V M Representing missile speed.
10. The method for intercepting a two-pair synchronous area coverage based on rbf_g in a three-dimensional space according to claim 9, wherein the guidance system is stable when the guidance law satisfies the condition (1) or (2);
condition (1):
Figure FDA0004176569550000081
condition (2):
Figure FDA0004176569550000082
wherein ,ev Is the vector of the error and,
Figure FDA0004176569550000083
is the estimated error of the linear weight, I.I F Represents F norm, constant sigma > 0, lambda v Is K v Minimum feature value, K v Is the error control gain, +.>
Figure FDA0004176569550000084
M * Is the ideal two norms of the radial base matrix. />
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