CN109255491B - Collaborative air defense task planning method and system for multi-type air defense weapons - Google Patents

Collaborative air defense task planning method and system for multi-type air defense weapons Download PDF

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CN109255491B
CN109255491B CN201811160508.2A CN201811160508A CN109255491B CN 109255491 B CN109255491 B CN 109255491B CN 201811160508 A CN201811160508 A CN 201811160508A CN 109255491 B CN109255491 B CN 109255491B
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董晨
陆志沣
张宏俊
洪泽华
钱晓超
陈伟
章佳君
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Shanghai Institute of Electromechanical Engineering
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Abstract

The invention provides a planning method and a system for cooperative air defense tasks of multi-type air defense weapons, which estimates the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance indexes of the multi-type air defense weapons and the flight path of an aerial target, determines various constraint conditions, adopts a numerical optimization algorithm, plans the interception time sequence of the multiple weapons on the multiple targets under the constrained condition, obtains the cooperative air defense tasks expressed by the corresponding relation of time period-weapon-target and achieves the optimal interception combat effect.

Description

Collaborative air defense task planning method and system for multi-type air defense weapons
Technical Field
The invention relates to the field of air defense, calculation and calculation, in particular to a collaborative air defense task planning method and a collaborative air defense task planning system for multi-type air defense weapons.
Background
The modern air defense system generally comprises multiple weapons, which form a full air space and multi-layer fire distribution system combining high altitude, hollow, low altitude, long distance, medium distance and short distance.
Operational mission planning is a Dynamic Weapon-Target Allocation Problem, i.e. dividing the total engagement time into series of sufficiently long time periods, allowing all or part of the weapons to shoot targets and observe the effect in each time period until no firing can be continued (see Patrick A Hosein equal to 1990, 2 months, research report "Some analytical Results for the Dynamic Weapon-Target Allocation Problem"), , in a staged optimization manner, to solve the Dynamic Weapon-Target Allocation Problem, forming a mission plan expressed by "time period-Weapon-Target" correspondence, to ground attack (see Yangtze, et al, ballistic report, 2017, stage-on-Target Allocation and decision), missile defense (building, et al, System engineering and electronics, 2016, 8, in "double-deck coordinated guided warfare, scheduling in fire fighting", scheduling, and decision-making), missile defense (building, et al, System engineering and electronics, 2016, in a "system engineering and electronics, 8, in a double-deck coordinated guided fire fight back-fire fighting" and the like), and the use of multiple fire control strategies based on the multiple stage of the fire control, which causes the simultaneous fire-Target Allocation Problem, the multiple fire-Target Allocation Problem, which causes the simultaneous fire-Target Allocation of the multiple-Target Allocation, the multiple stage-Target Allocation Problem, which causes the different fire-Target Allocation Problem of the simultaneous shooting-Target Allocation, the multiple fire-Target Allocation Problem, the multiple fire-Target Allocation, the multiple-Target Allocation Problem, which is easily determined based on the design, the multiple-Target Allocation of the longest fire-Target Allocation Problem, the multiple-Target Allocation of the.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a collaborative air defense mission planning method and system for multi-type air defense weapons.
According to the invention
A collaborative air defense mission planning method for multiple types of air defense weapons, comprising the following steps:
an estimation step: estimating the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance index and each target track of each weapon;
a constraint determining step: determining the quantity constraint of the targets intercepted by the weapons at the same time, the quantity constraint of the weapons intercepted by the targets at the same time, the interception times constraint of the targets and the interception favorable degree of the weapons to the targets;
matrix establishment: establishing an interception starting time matrix, an interception ending time matrix and an interception profitability matrix of each weapon on each target according to the result of the estimation step and the result of the constraint determination step;
a conversion step: converting the collaborative air defense task planning problem of the multi-type air defense weapon into a constrained optimization problem according to the established matrix, wherein the optimization index is the total interception profitability, and the constraint comprises non-time conflict constraint and interception frequency constraint;
solving: and solving the constrained optimization problem by adopting a numerical optimization algorithm to obtain a collaborative air defense task planning scheme of the multi-type air defense weapon.
Preferably, in the constraint determination step, the interception profitability of each weapon on each target is determined by the probability q of each weapon killing each targetijDetermining according to weapon WiFor target TjNumber of interception nijAnd killing probability q calculation for every intercepts, namely:
Figure BDA0001819924780000021
preferably, in the matrix establishing step, the number of weapons W is n, the number of targets T is m, and the interception start time matrix T of each target by each weapon0Intercept end time matrix TfThe interception profitability matrix Q has the form:
Figure BDA0001819924780000022
in the formula, tij0Representative weapon WiFor target TjInterception start time, tijfRepresentative weapon WiFor target TjInterception end time of qijRepresentative weapon WiFor target TjThe degree of interception is favorable.
Preferably, in the solving step, a numerical optimization algorithm is used to solve the constrained optimization problem, and the obtained optimal solution D has the following form:
Figure BDA0001819924780000031
in the formula (d)ij0 or 1, dij1 represents in [ tij0,tijf]By weapon W during time periodiIntercept target Tj，dij0 represents in [ tij0,tijf]Weapon in time period WiNot intercepting target Tj。
Preferably, in the converting step, the time-conflict-free constraint is expressed as:
C(T0*D,Tf*D)-NW0 or less and C ((T)0*D)T,(Tf*D)T)-NT≤0
In the formula, an operator represents that the elements with the same row and column in two matrixes with the same dimension are multiplied respectively;
function C (T)0*D,TfD) for T, respectively0D and TfCalculating non-zero elements t for each row of Dij0And tijfSeveral time periods t of representationij0,tijf]G of the overlapping timesiUsing all giForm a column vector [ g1g2…gn]T；
Column vector NW＝[nW1nW2…nWn]TElement n thereofWiFrom weapons WiSimultaneously intercepting target quantity constraint decisions;
function C ((T)0*D)T,(Tf*D)T) Represents, respectively, to T0D and TfFor each column of D, calculating the non-zero element tij0And tijfSeveral time periods t of representationij0,tijf]Number of overlapping kiUsing all kiForm a column vector [ k1k2…km]T；
Column vector NT＝[nT1nT2…nTm]TElement n thereofTjBy the pair of targets TjWhile intercepting the weapon quantity constraint decision.
Preferably, in the converting step, the interception number constraint is expressed as:
I1×n×(NI*D)-R≥0
in the formula I1×nIs an n-dimensional row vector with elements of 1; n is a radical ofIIs an n x m dimensional matrix with elements nijFrom weapons WiFor target TjDetermining the interception times; r is an m-dimensional row vector of which the element R isjBy the pair of targets TjIs determined by the interception number constraint.
Preferably, in the step of converting, the total interception profitability is expressed as:
I1×n×(Q*D)×Im×1
in the formula Im×1Is an m-dimensional column vector with elements of 1.
Preferably, the constrained optimization problem is represented as:
Figure BDA0001819924780000032
Figure BDA0001819924780000033
that is, matrixes D with 0 or 1 elements are found to satisfy the time conflict-free constraint and the interception times constraint, so that the total interception profitability is maximized, and the triplets (T)0、TfAnd D) representing a collaborative air defense mission planning scheme of the multi-type air defense weapon, namely the corresponding relation of time period-weapon-target.
The invention provides a collaborative air defense mission planning system of multi-type air defense weapons, which comprises:
an estimation module: estimating the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance index and each target track of each weapon;
a constraint determination module: determining the quantity constraint of the targets intercepted by the weapons at the same time, the quantity constraint of the weapons intercepted by the targets at the same time, the interception times constraint of the targets and the interception favorable degree of the weapons to the targets;
a matrix building module: establishing an interception starting time matrix, an interception ending time matrix and an interception profitability matrix of each weapon on each target according to the estimation result and the constraint determination result;
a conversion module: converting the collaborative air defense task planning problem of the multi-type air defense weapon into a constrained optimization problem according to the established matrix, wherein the optimization index is the total interception profitability, and the constraint comprises non-time conflict constraint and interception frequency constraint;
a solving module: and solving the constrained optimization problem by adopting a numerical optimization algorithm to obtain a collaborative air defense task planning scheme of the multi-type air defense weapon.
Preferably, in the constraint determination module, the interception profitability of each weapon on each target and the killing probability q of each weapon on each targetijDetermining according to weapon WiFor target TjNumber of interception nijAnd killing probability q calculation for every intercepts, namely:
Figure BDA0001819924780000041
compared with the prior art, the invention has the following beneficial effects:
1) in the prior art, the combat stages are divided firstly, and then targets are distributed for weapons in each stage, so that firepower gaps among the combat stages are easily caused; according to the interception time periods of each target by each weapon, the time periods which have no time conflict and meet the requirement of shooting times are combined to form the cooperative air defense task of multiple weapons, so that the fighting capacity of each type of air defense weapon can be fully exerted, and the orderly connection of air defense fire power is realized.
2) The method has no time conflict constraint, considers the limitation of the multi-target capability of the weapons on firepower, meets the two requirements that targets are simultaneously shot by a plurality of weapons (such as antiaircraft guns need to simultaneously shoot a plurality of antiaircraft guns to form a bullet screen) and targets are only shot by weapons (such as air defense missiles and different weapons are prevented from interfering with each other), and has the applicability of universal.
3) The interception times constraint of the invention considers the requirement of minimum interception times of each target, ensures that each target has enough interception chance and killing probability, and can avoid the extreme condition that the beneficial degree of total interception is maximized, but the target is in fire prevention due to insufficient shooting times of individual targets.
4) The interception times of the invention restricts the favorable interception degree of each weapon to each target, and can be determined by the killing probability, the inverse number of the interception time and/or the interception cost-effectiveness ratio, so as to realize the optimization target of shortest engagement time and/or the maximum interception cost-effectiveness ratio, meet the requirements of different combat missions, and the method has better flexibility.
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Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a flow chart of a collaborative air defense mission planning method for types of multiple air defense weapons proposed by the present invention;
FIG. 2 is an application scenario of an embodiment of the present invention.
Detailed Description
The present invention is described in detail below with reference to specific examples which will assist those skilled in the art to further the present invention, but not to limit the invention in any way.
As shown in fig. 1, the collaborative air defense mission planning method for kinds of multi-type air defense weapons provided by the invention comprises the following steps:
an estimation step: estimating the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance index and each target track of each weapon;
a constraint determining step: determining the quantity constraint of the targets intercepted by the weapons at the same time, the quantity constraint of the weapons intercepted by the targets at the same time, the interception times constraint of the targets and the interception favorable degree of the weapons to the targets;
matrix establishment: establishing an interception starting time matrix, an interception ending time matrix and an interception profitability matrix of each weapon on each target according to the result of the estimation step and the result of the constraint determination step;
a conversion step: converting the collaborative air defense task planning problem of the multi-type air defense weapon into a constrained optimization problem according to the established matrix, wherein the optimization index is the total interception profitability, and the constraint comprises non-time conflict constraint and interception frequency constraint;
solving: and solving the constrained optimization problem by adopting a numerical optimization algorithm to obtain a collaborative air defense task planning scheme of the multi-type air defense weapon.
In the constraint determining step, the interception profitability of each weapon on each target and the killing probability q of each weapon on each targetijDetermining according to weapon WiFor target TjNumber of interception nijAnd killing probability q calculation for every intercepts, namely:
Figure BDA0001819924780000051
in the matrix establishing step, the number of the weapons W is n, the number of the targets T is m, and the interception starting time matrix T of each weapon to each target0Intercept end time matrix TfThe interception profitability matrix Q has the form:
Figure BDA0001819924780000061
in the formula, tij0Representative weapon WiFor target TjInterception start time, tijfRepresentative weapon WiFor target TjInterception end time of qijRepresentative weapon WiFor target TjThe degree of interception is favorable.
In the solving step, a numerical optimization algorithm is adopted to solve the constrained optimization problem, and the obtained optimal solution D has the following form:
Figure BDA0001819924780000062
in the formula (d)ij0 or 1, dij1 represents in [ tij0,tijf]By weapon W during time periodiIntercept target Tj，dij0 represents in [ tij0,tijf]Weapon in time period WiNot intercepting target Tj。
In the conversion step, the time conflict-free constraint is expressed as:
C(T0*D,Tf*D)-NW0 or less and C ((T)0*D)T,(Tf*D)T)-NT≤0
In the formula, an operator represents that the elements with the same row and column in two matrixes with the same dimension are multiplied respectively;
function C (T)0*D,TfD) for T, respectively0D and TfCalculating non-zero elements t for each row of Dij0And tijfSeveral time periods t of representationij0,tijf]G of the overlapping timesiUsing all giForm a column vector [ g1g2…gn]T；
Column vector NW＝[nW1nW2…nWn]TElement n thereofWiFrom weapons WiSimultaneously intercepting target quantity constraint decisions;
function C ((T)0*D)T,(Tf*D)T) Represents, respectively, to T0D and TfFor each column of D, calculating the non-zero element tij0And tijfSeveral time periods t of representationij0,tijf]Number of overlapping kiUsing all kiForm a column vector [ k1k2…km]T；
Column vector NT＝[nT1nT2…nTm]TElement n thereofTjBy the pair of targets TjWhile intercepting the weapon quantity constraint decision.
The intercept number constraint is expressed as:
I1×n×(NI*D)-R≥0
in the formula I1×nIs an n-dimensional row vector with elements of 1; n is a radical ofIIs an n x m dimensional matrix with elements nijFrom weapons WiFor target TjDetermining the interception times; r is an m-dimensional row vector of which the element R isjBy the pair of targets TjIs determined by the interception number constraint.
The total interception profitability is expressed as:
I1×n×(Q*D)×Im×1
in the formula Im×1Is an m-dimensional column vector with elements of 1.
The constrained optimization problem is represented as:
Figure BDA0001819924780000071
Figure BDA0001819924780000072
that is, matrixes D with 0 or 1 elements are found to satisfy the time conflict-free constraint and the interception times constraint, so that the total interception profitability is maximized, and the triplets (T)0、TfAnd D) representing a collaborative air defense mission planning scheme of the multi-type air defense weapon, namely the corresponding relation of time period-weapon-target.
On the basis of the collaborative air defense mission planning method for the multiple types of air defense weapons, the invention also provides a collaborative air defense mission planning system for the multiple types of multiple types of air defense weapons, which comprises the following steps:
an estimation module: estimating the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance index and each target track of each weapon;
a constraint determination module: determining the quantity constraint of the targets intercepted by the weapons at the same time, the quantity constraint of the weapons intercepted by the targets at the same time, the interception times constraint of the targets and the interception favorable degree of the weapons to the targets;
a matrix building module: establishing an interception starting time matrix, an interception ending time matrix and an interception profitability matrix of each weapon on each target according to the estimation result and the constraint determination result;
a conversion module: converting the collaborative air defense task planning problem of the multi-type air defense weapon into a constrained optimization problem according to the established matrix, wherein the optimization index is the total interception profitability, and the constraint comprises non-time conflict constraint and interception frequency constraint;
a solving module: and solving the constrained optimization problem by adopting a numerical optimization algorithm to obtain a collaborative air defense task planning scheme of the multi-type air defense weapon.
The embodiment is suitable for processing an application scene that 3 air defense missile weapons intercept 5 air targets, and the protection scope of the patent is not limited by the specific implementation of the embodiment.
The embodiment relates to a collaborative air defense mission planning of two types of 3 air defense missile weapons, and the application scene is shown in figure 2, wherein the 3 air defense missile weapons are respectively W1、W2、W3Weapon W2And W3Belongs to the same model and has the same performance as a weapon W1Model , its performance and weapon W2And W3In contrast, the solid line sector area in FIG. 2 indicates W1、W2、W3The interception range of; targets are respectively T1、T2、T3、T4、T5The course of which is shown by the dashed line with arrows in fig. 2.
With reference to fig. 1, the embodiment of the present invention is specifically described as follows:
step 1: and estimating the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance indexes of each weapon and each target track. According to the target T1、T2、T3、T4、T5Speed and its trajectory crossing weapon W1、W2、W3Length of interception Range, estimate weapon W1、W2、W3For target T1、T2、T3、T4、T5The interception start time and the interception end time are shown in the following table:
TABLE 1 interception Start time (unit: s)
T1 T2 T3 T4 T5
W1 4 3 3 3 5
W2 10 9 11 0 0
W3 0 14 12 12 15
TABLE 2 intercept finish time (unit: s)
T1 T2 T3 T4 T5
W1 10 9 11 11 15
W2 15 15 16 0 0
W3 0 18 18 18 18
According to the interception starting time and the interception ending time and the target T1、T2、T3、T4、T5Velocity and weapon W1、W2、W3Velocity of the fired interceptor projectile, estimating weapon W1、W2、W3For target T1、T2、T3、T4、 T5The number of interception is shown in the following table:
TABLE 3 number of intercepts
T1 T2 T3 T4 T5
W1 3 3 3 3 4
W2 2 3 2 0 0
W3 0 2 3 2 1
Step 2: and determining the quantity constraint of the simultaneously intercepted targets of the weapons, the quantity constraint of the simultaneously intercepted weapons of the targets, the number constraint of the intercepted targets and the favorable degree of the interception of the weapons to the targets. According to the weapon W1、W2、W3Performance of which the simultaneous interception target number constraint is n respectivelyW1＝3、nW2＝2、nW32; according to W1、W2、W3For air-defense missile weapons, for avoiding mutual interference between weapons, for target T1、T2、T3、T4、T5The constraint of the number of the simultaneously intercepted weapons is n respectivelyT1＝1、nT2＝1、nT3＝1、nT4＝1、nT51 is ═ 1; assume target T2、T3Is greater than the target T5Degree of threat, target T5Is greater than the target T1、T4The more times the target with higher threat degree is intercepted, according to the target T1、T2、T3、T4、T5Degree of threat of, set to target T1、T2、 T3、T4、T5The interception times are respectively restricted as r1＝2、r2＝4、r3＝4、r4＝2、r5And (3), setting the probability of killing the target by the weapon for times of interception, and calculating the favorable degree of the target interception by the weapon according to the interception times as shown in the following table:
TABLE 4 advantageous degree of interception
T1 T2 T3 T4 T5
W1 0.94 0.94 0.94 0.94 0.97
W2 0.84 0.94 0.84 0 0
W3 0 0.84 0.94 0.84 0.6
And step 3: and establishing an interception starting time matrix, an interception ending time matrix and an interception profitability matrix of each weapon on each target. According to the calculation results of the interception starting time, the interception ending time and the interception profitability in the steps, an interception starting time matrix T0Intercept end time matrix TfThe interception profitability matrix Q is as follows:
Figure BDA0001819924780000091
and 4, step 4: and converting the collaborative air defense task planning problem into a constrained optimization problem, wherein the optimization index is the total interception profitability, and the constraint comprises non-time conflict constraint and interception frequency constraint. The constrained optimization problem is represented by the calculation of the previous steps as:
Figure BDA0001819924780000093
Figure BDA0001819924780000094
in the formula: d is a 3X 5 dimensional matrix with an element Dij0 or 1, the value of which is to be optimized; t is0、TfQ is 3 as described in step 3X 5 dimensional matrix; n is a radical ofWIs a 3-dimensional column vector, NTIs a 5-dimensional column vector, NIIs a 3 × 5 dimensional matrix, and R is a 5 dimensional row vector with the following values:
Figure BDA0001819924780000095
I1×nis a 3-dimensional row vector, Im×1Is a 5-dimensional column vector whose values are as follows:
Figure BDA0001819924780000101
and 5: and solving the constrained optimization problem by adopting a numerical optimization algorithm to obtain a collaborative air defense task planning scheme of the multi-type air defense weapon. In this embodiment, a genetic algorithm is used to solve the constrained optimization problem, and the optimal solution is obtained as follows:
then the triplet (T)0、TfAnd D) representing a cooperative air defense mission scheme of the multi-type air defense weapon, which specifically comprises the following steps:
to W1Assign it to intercept T from 3s to 9s2Intercepting T in 3 s-11 s3Intercepting T in 5 s-15 s5；
To W2Assign it to intercept T between 10s and 15s1Intercepting T in 9 s-15 s2；
To W3Assign it to intercept T from 12s to 18s3Intercepting T in 12 s-18 s4；
In the above task scheme, W1The number of the intercepted targets does not exceed 3, W2And W3The number of the intercepted targets does not exceed 2; for T1、T2、T3、T4、T5The number of simultaneously intercepted weapons per target does not exceed 1; for T1、T2、T3、T4、T5Respectively interception times of2 times, 6 times, 2 times and 4 times; the above conditions satisfy the time conflict-free constraint and the interception times constraint, the total interception profitability is 6.41, and the maximized optimization target is realized.
One skilled in the art will appreciate that, in addition to the system and its various devices, modules, and units provided by the present invention being implemented as pure computer-readable program code, the system and its various devices, modules, and units provided by the present invention can be implemented with the same functions by completely logically programming method steps in the form of logic , switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (5)

  1. The cooperative air defense mission planning method for the multi-type air defense weapons is characterized by comprising the following steps:
    an estimation step: estimating the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance index and each target track of each weapon;
    a constraint determining step: determining the quantity constraint of the targets intercepted by the weapons at the same time, the quantity constraint of the weapons intercepted by the targets at the same time, the interception times constraint of the targets and the interception favorable degree of the weapons to the targets;
    matrix establishment: establishing an interception starting time matrix, an interception ending time matrix and an interception profitability matrix of each weapon on each target according to the result of the estimation step and the result of the constraint determination step;
    a conversion step: converting the collaborative air defense task planning problem of the multi-type air defense weapon into a constrained optimization problem according to the established matrix, wherein the optimization index is the total interception profitability, and the constraint comprises non-time conflict constraint and interception frequency constraint;
    solving: solving the constrained optimization problem by adopting a numerical optimization algorithm to obtain a collaborative air defense task planning scheme of the multi-type air defense weapon;
    in the constraint determining step, the interception profitability of each weapon on each target and the killing probability q of each weapon on each targetijDetermining according to weapon WiFor target TjNumber of interception nijAnd killing probability q calculation for every intercepts, namely:
    Figure FDA0002217405550000011
    in the matrix establishing step, the number of the weapons W is n, the number of the targets T is m, and the interception starting time matrix T of each target by each weapon0Intercept end time matrix TfThe interception profitability matrix Q has the form:
    Figure FDA0002217405550000012
    in the formula, tij0Representative weapon WiFor target TjInterception start time, tijfRepresentative weapon WiFor target TjInterception end time of qijRepresentative weapon WiFor target TjFavorable degree of interception;
    in the solving step, a numerical optimization algorithm is adopted to solve the constrained optimization problem, and the obtained optimal solution D has the following form:
    in the formula (d)ij0 or 1, dij1 represents in [ tij0,tijf]By weapon W during time periodiIntercept target Tj，dij0 represents in [ tij0,tijf]Weapon in time period WiNot intercepting target Tj；
    In the converting step, the constraint without time conflict is expressed as:
    C(T0*D,Tf*D)-NW0 or less and C ((T)0*D)T,(Tf*D)T)-NT≤0
    In the formula, an operator represents that the elements with the same row and column in two matrixes with the same dimension are multiplied respectively;
    function C (T)0*D,TfD) for T, respectively0D and TfCalculating non-zero elements t for each row of Dij0And tijfSeveral time periods t of representationij0,tijf]G of the overlapping timesiUsing all giForm a column vector [ g1g2… gn]T；
    Column vector NW＝[nW1nW2… nWn]TElement n thereofWiFrom weapons WiSimultaneously intercepting target quantity constraint decisions;
    function C ((T)0*D)T,(Tf*D)T) Represents, respectively, to T0D and TfFor each column of D, calculating the non-zero element tij0And tijfSeveral time periods t of representationij0,tijf]Number of overlapping kiUsing all kiForm a column vector [ k1k2… km]T；
    Column vector NT＝[nT1nT2… nTm]TElement n thereofTjBy the pair of targets TjWhile intercepting the weapon quantity constraint decision.
  2. 2. The cooperative air defense mission planning method for a multiple-type air defense weapon according to claim 1, wherein in the transforming step, the interception number constraint is expressed as:
    I1×n×(NI*D)-R≥0
    in the formula I1×nIs an n-dimensional row vector with elements of 1; n is a radical ofIIs an n x m dimensional matrix with elements nijFrom weapons WiFor target TjDetermining the interception times; r is an m-dimensional row vector of which the element R isjBy the pair of targets TjIs determined by the interception number constraint.
  3. 3. A cooperative air defense mission planning method for a multiple-type air defense weapon according to claim 2, wherein in the transforming step, the total interception profitability is expressed as:
    I1×n×(Q*D)×Im×1
    in the formula Im×1Is an m-dimensional column vector with elements of 1.
  4. 4. A collaborative air defense mission planning method for a multiple-type air defense weapon according to claim 3, characterized in that the constrained optimization problem is expressed as:
    Figure FDA0002217405550000021
    Figure FDA0002217405550000022
    that is, matrixes D with 0 or 1 elements are found to satisfy the time conflict-free constraint and the interception times constraint, so that the total interception profitability is maximized, and the triplets (T)0、TfAnd D) representing a collaborative air defense mission planning scheme of the multi-type air defense weapon, namely the corresponding relation of time period-weapon-target.
  5. The cooperative air defense mission planning system for the multiple types of air defense weapons of the types is characterized by comprising:
    an estimation module: estimating the interception starting time, the interception ending time and the interception times of each weapon on each target according to the performance index and each target track of each weapon;
    a constraint determination module: determining the quantity constraint of the targets intercepted by the weapons at the same time, the quantity constraint of the weapons intercepted by the targets at the same time, the interception times constraint of the targets and the interception favorable degree of the weapons to the targets;
    a matrix building module: establishing an interception starting time matrix, an interception ending time matrix and an interception profitability matrix of each weapon on each target according to the estimation result and the constraint determination result;
    a conversion module: converting the collaborative air defense task planning problem of the multi-type air defense weapon into a constrained optimization problem according to the established matrix, wherein the optimization index is the total interception profitability, and the constraint comprises non-time conflict constraint and interception frequency constraint;
    a solving module: solving the constrained optimization problem by adopting a numerical optimization algorithm to obtain a collaborative air defense task planning scheme of the multi-type air defense weapon;
    in the constraint determination module, the interception profitability of each weapon on each target and the killing probability q of each weapon on each targetijDetermining according to weapon WiFor target TjNumber of interception nijAnd killing probability q calculation for every intercepts, namely:
    Figure FDA0002217405550000031
    in the matrix establishing module, the number of the weapons W is n, the number of the targets T is m, and the interception starting time matrix T of each weapon to each target0Intercept end time matrix TfThe interception profitability matrix Q has the form:
    Figure FDA0002217405550000032
    in the formula, tij0Representative weapon WiFor target TjInterception start time, tijfRepresentative weapon WiFor target TjInterception end time of qijRepresentative weapon WiFor target TjFavorable degree of interception;
    in the solving module, a numerical optimization algorithm is adopted to solve the constrained optimization problem, and the obtained optimal solution D has the following form:
    Figure FDA0002217405550000033
    in the formula (d)ij0 or 1, dij1 represents in [ tij0,tijf]By weapon W during time periodiIntercept target Tj，dij0 represents in [ tij0,tijf]Weapon in time period WiNot intercepting target Tj；
    In the conversion module, the constraint without time conflict is expressed as:
    C(T0*D,Tf*D)-NW0 or less and C ((T)0*D)T,(Tf*D)T)-NT≤0
    In the formula, an operator represents that the elements with the same row and column in two matrixes with the same dimension are multiplied respectively;
    function C (T)0*D,TfD) for T, respectively0D and TfCalculating non-zero elements t for each row of Dij0And tijfSeveral time periods t of representationij0,tijf]G of the overlapping timesiUsing all giForm a column vector [ g1g2… gn]T；
    Column vector NW＝[nW1nW2… nWn]TElement n thereofWiFrom weapons WiSimultaneously intercepting target quantity constraint decisions;
    function C ((T)0*D)T,(Tf*D)T) Represents, respectively, to T0D and TfEach column of D, calculate notZero element tij0And tijfSeveral time periods t of representationij0,tijf]Number of overlapping kiUsing all kiForm a column vector [ k1k2… km]T；
    Column vector NT＝[nT1nT2… nTm]TElement n thereofTjBy the pair of targets TjWhile intercepting the weapon quantity constraint decision.
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