CN105202972A - Multi-missile cooperative engagement guidance method based on model predictive control technique - Google Patents

Abstract

The invention discloses a multi-missile cooperative engagement guidance method based on a model predictive control technique. Through the adoption of the multi-missile cooperative engagement guidance method, the cooperative engagement problem of missiles is converted into a theoretical trajectory tracking problem on the premise of considering the variable missile speed; the estimation of the residual flight time is avoided; the accuracy and the realizability are improved; meanwhile, the model prediction control technique is adopted, so that an ideal trajectory can be quickly and accurately tracked in the presence of external interference and angle attack and amplitude limit.

Description

A kind of cooperation of many guided missiles based on model predictive control technique method of guidance

Technical field

The present invention relates to technical field of guidance, be specifically related to a kind of many guided missiles based on model predictive control technique cooperation method of guidance.

Background technology

Along with the progress of science and technology, the positive gradual perfection of missile defense systems, the penetration ability of guided missile is subject to serious threat.It is improve the battlefield survival of guided missile and the important means of striking capabilities that many pieces of guided missiles carry out saturation attack to target, is just receiving increasing concern.Therefore, under the prerequisite considering battlefield actual conditions, research can make many pieces of guided missiles arrive target simultaneously, it is significant to have the cooperative guidance method of attack time constraint.

Currently available technology realizes many pieces of guided missiles in solution and arrives in the cooperative guidance technical problem of target simultaneously under the condition with attack time constraint, there will be following problem:

1, the general speed that all can suppose guided missile is constant value, but in real process, be difficult to ensure that missile velocity is constant value, missile velocity can change because of the change of thrust, flying height or external disturbance.

2, the problem need estimated the residual non-uniformity of guided missile.And in practical flight process, the residual non-uniformity of guided missile is also difficult to estimate accurately, when especially becoming when the speed of guided missile, the accurate estimation of residual non-uniformity becomes more difficult.

3, in missile flight process, often can be subject to as various interference such as RANDOM WIND, and prior art is many it is considered that cooperative guidance ideally.

4, the control surface deflection of guided missile is limited, and namely the input of missile control system has non-linear saturability, and then causes angle of attack variation quantitative limitation.And prior art is not considered.

In sum, the many guided missile cooperation guidance of the many considerations of prior art when desirable (noiseless), comparatively simple (speed is constant value).

Summary of the invention

In view of this, the invention provides a kind of many guided missiles based on model predictive control technique cooperative guidance method, can realize cooperative guidance accurately.

Based on many guided missiles cooperation method of guidance of model predictive control technique, for every piece of guided missile, adopt following concrete steps:

The appointment attack time T that step one, setting hit the mark _d, and obtain appointment missile-target distance rate of change according to appointment attack time wherein, r ₀for the distance under original state between guided missile and target;

Step 2, make theoretical missile-target distance rate of change with appointment missile-target distance rate of change equal, according to the barycenter kinetic model of the geometrical relationship played between order Equation of Relative Motion with Small, angle and guided missile, the theoretical flight path of attack time hit specified by derivation guided missile;

Step 3, based on the barycenter kinetics equation playing order Equation of Relative Motion with Small and guided missile, set up the forecast model changed for describing actual missile-target distance;

Step 4, linearisation, discretization and standardization are carried out to forecast model, obtain the canonical form of forecast model;

Step 5, according to performance indications reference representation, set up reaction practical flight track to theoretical path tracking effect, simultaneously the performance index function of reaction controlling amount change size again;

Step 6,

With the maximum amplitude u of the angle of attack _maxas control quantity constraint, the canonical form of the forecast model obtained in step 4 is as profile constraints, the function obtained in step 5, as performance index function, utilizes convex optimization tool, obtains the optimal control sequence under a series of condition meeting minimum performance target function value; And get Section 1 in optimal sequence and substitute into and play order Equation of Relative Motion with Small group, trajectory tilt angle rate of change expression formula, the barycenter kinetic model of guided missile, guided missile resistance expression formula and Missile-Lift expression formula, obtain actual missile-target distance, trajectory tilt angle, the speed of guided missile, the speed angle of lead of guided missile and the angle of sight, and using the actual missile-target distance of acquisition, trajectory tilt angle, the speed of guided missile, the speed angle of lead of guided missile and the angle of sight initial value as subsequent time, then carry out solving of subsequent time optimization problem; Until during actual missile-target distance r < 1000m, proceed to proportional guidance and control.

Especially, the concrete grammar obtaining theoretical flight path is:

21st step: set up and play order Equation of Relative Motion with Small group, and according to appointment missile-target distance rate of change expression formula, obtain missile velocity angle of lead expression formula;

22nd step: according to the domain of definition of anticosine trigonometric function and the restriction of maximum frame corners of setting, segmentation description is carried out to missile velocity angle of lead expression formula, obtain the piecewise function expression formula of missile velocity angle of lead;

23rd step: adopt low pass filter to carry out LPF to missile velocity angle of lead, obtain the speed angle of lead η that low pass filter exports _d;

24th step: according to bullet order relative motion relation, obtain trajectory tilt angle rate of change expression formula;

25th step: barycenter kinetic model and the lift expression formula of setting up guided missile, obtains angle of attack expression formula;

26th step: the lift expression formula of the speed angle of lead expression formula bullet order Equation of Relative Motion with Small obtained, missile velocity angle of lead expression formula, low pass filter exported, trajectory tilt angle rate of change expression formula, barycenter kinetic model, guided missile and angle of attack expression formula simultaneous, obtain theoretical flight path.

Beneficial effect:

The present invention is considering, under the prerequisite that missile velocity is variable, by the cooperation problem of guided missile is converted into theory locus tracking problem, to avoid estimation residual non-uniformity, improve accuracy and the realizability of cooperation.And, adopting model predictive control technique, can, when having external interference and the angle of attack has limit value, realizing carrying out accurate fast tracking to theory locus.

Accompanying drawing explanation

Fig. 1 is present system flow chart.

Fig. 2 is three pieces of guided missile concerted attack target trajectory figure.

Fig. 3 is for playing order relative motion figure.

Fig. 4 guided missile 1 missile-target distance variation diagram;

Fig. 5 is the actual missile-target distance of guided missile 1 section of working in coordination with and expectation missile-target distance difference variation diagram;

Fig. 6 is guided missile 1 speed angle of lead variation diagram;

Fig. 7 is guided missile 1 velocity profile;

Fig. 8 is guided missile 1 angle of attack variation figure.

Detailed description of the invention

To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

The invention provides a kind of many guided missiles based on model predictive control technique cooperative guidance method; As shown in Figure 2, its basic thought is: attack time is specified in setting one, by allowing the missile-target distance rate of change under theoretical case equal the missile-target distance rate of change of specifying, makes the guided missile under theoretical case can at this appointment attack time, many pieces of guided missile hits simultaneously, realize cooperation.Wherein, the missile-target distance of indication is the distance between guided missile to target herein.So, need to estimate the problem of remaining time with regard to avoiding in prior art.In addition, the flight of real missile can be subject to external interference, and the present invention adopts model predictive control technique, realize the theoretical flight path of practical flight trajectory track, thus make guided missile when no matter whether being subject to external interference, target can be arrived at appointment attack time, realize cooperation.

For every piece of guided missile, its concrete grammar is: as shown in Figure 1:

The appointment attack time T that step one, setting hit the mark _d, and obtain appointment missile-target distance rate of change according to appointment attack time

${\stackrel{\&CenterDot;}{r}}_d=-\frac{r_0}{T_d}---\left(1\right)$

Wherein, r ₀for the missile-target distance under original state; Wherein, work in coordination with for realizing each guided missile, the appointment attack time of every piece of guided missile is identical.

Step 2, obtain each guided missile in the theoretical flight path of specifying attack time hit;

As shown in Figure 3: when the speed of target and speed angle of lead known, obtain the theoretical flight path of guided missile if want, first need to obtain about guided missile self and the relevant parameter expression formula of relation between guided missile and target; Again according to each relevant parameter expression formula, simultaneous equations solve and obtain theoretical missile-target distance r _ep, i.e. theoretical flight path.For this reason, the present invention, according to the relevant parameter expression formula of required acquisition, utilizes existing knowwhy, by the form of Simultaneous Equations, obtains final theoretical flight path expression formula; Be specially:

21st step: set up and play order Equation of Relative Motion with Small group:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{r}}_{ep}=v_T{\mathrm{cos\&eta;}}_T-v_M{\mathrm{cos\&eta;}}_M\\ r_{ep}\&CenterDot;\stackrel{\&CenterDot;}{q}=v_M{\mathrm{sin\&eta;}}_M-v_T{\mathrm{sin\&eta;}}_T\end{array}\right.---\left(2\right)$

Wherein, for theoretical missile-target distance rate of change; v _tfor the speed of target T; η _tfor the speed angle of lead of target T; v _mfor the speed of guided missile M; η _mfor the speed angle of lead of guided missile M; Q is the angle of sight;

22nd step: in order to ensure that the guided missile flown along theoretical flight path arrives target at appointment attack time, therefore make theoretical missile-target distance rate of change with appointment missile-target distance rate of change equal; Simultaneous equations (1) and equation group (2), obtain the expression formula of the speed angle of lead of guided missile M:

${\mathrm{\&eta;}}_M=\arccos \frac{v_T{\mathrm{cos\&eta;}}_T-{\stackrel{\&CenterDot;}{r}}_d}{v_M}---\left(3\right)$

Order according to the domain of definition of anticosine trigonometric function and the restriction of maximum frame corners, change formula (3) into piecewise function:

${\mathrm{\&eta;}}_M=\left\{\begin{array}{cc}sign\left({\mathrm{\&eta;}}_0\right)\&CenterDot;{\mathrm{\&eta;}}_{max},& S<{\mathrm{cos\&eta;}}_{max}\\ sign\left({\mathrm{\&eta;}}_0\right)\&CenterDot;\arccos \left(S\right),& {\mathrm{cos\&eta;}}_{max}\&le;S\&le;1\\ 0& S>1\end{array}\right.---\left(4\right)$

Wherein, η ₀for the angle of lead of guided missile initial velocity, η _maxfor considering the speed angle of lead that maximum frame corners limits.

23rd step: because the speed angle of lead and derivative thereof of considering the guided missile M of acquisition do not meet continuity requirement, the present invention adopts low pass filter to carry out filtering to it, is expressed as:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_d=\frac{{\mathrm{\&eta;}}_M-{\mathrm{\&eta;}}_d}{\mathrm{\&tau;}}\\ {\mathrm{\&eta;}}_d\left(0\right)=\mathrm{\&eta;}\left(0\right)\end{array}\right.---\left(5\right)$

Wherein, η _dfor the speed angle of lead that low pass filter exports, τ is filter time constant.

24th step: the geometrical relationship according to playing in order relative motion between angle:

θ＝q-η _M(6)

Wherein, θ is the trajectory tilt angle of guided missile; Therefore in conjunction with formula (5), the trajectory tilt angle rate of change obtaining guided missile is:

$\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=\stackrel{\&CenterDot;}{q}-{\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_d---\left(7\right)$

25th step: the barycenter kinetic model setting up guided missile:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{v}}_M=\frac{P\cos \mathrm{\&alpha;}-X-mg\sin \mathrm{\&theta;}}{m}\\ v_M\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=\frac{Psin\mathrm{\&alpha;}-Y-mgcos\mathrm{\&theta;}}{m}\end{array}\right.---\left(8\right)$

Wherein, m is the quality of guided missile; α is the angle of attack of guided missile, and P is the thrust that guided missile is subject to; X is that guided missile is subject to resistance;

$X=X_0+X^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2---\left(9\right)$

Wherein, X ₀for zero lift drag, for resistance is to the derivative of the angle of attack square.

Y is the lift that guided missile is subject to, and g is acceleration of gravity.The lift caused due to angle of rudder reflection is less, so the lift of guided missile

Y≈Y ^α·α(10)

When the angle of attack is less, make sin α=α, now in conjunction with formula (10), formula (8) then can be changed into:

$\mathrm{\&alpha;}=\frac{{\mathrm{mv}}_M\stackrel{\&CenterDot;}{\mathrm{\&theta;}}+mgcos\mathrm{\&theta;}}{P+Y^{\mathrm{\&alpha;}}}---\left(11\right)$

According to formula (2) to formula (11), now, just obtain about the speed angle of lead η about guided missile _m, trajectory tilt angle rate of change the percentage speed variation of guided missile with the angle of attack of guided missile, also obtain about the theoretical missile-target distance rate of change between guided missile and target and the rate of change of the angle of sight

26th step: by formula (2), formula (3), formula (5), formula (8), formula (10) and formula (11) simultaneous, and then obtain theoretical bullet order missile-target distance r _ep, i.e. theoretical flight path.

Step 3: because theoretical flight path can realize arriving target location at appointment attack time, for this reason, as long as make the theoretical flight path of practical flight track following realize cooperation.Therefore the present invention adopts forecast Control Algorithm, set up the forecast model for describing the actual missile-target distance rate of change of guided missile; Realize real missile and follow the tracks of theoretical flight path.

According to the bullet order Equation of Relative Motion with Small group set up in formula (2), to first expression formula in formula (2) two ends differentiate; Suppose the motion not considering target, i.e. v _tbe zero.Meanwhile, practical flight and the theoretical flight course of guided missile order Equation of Relative Motion with Small form of being hit by a bullet is identical, namely only needs r _epreplace with r.Formula (8) is substituted into the result after differentiate, obtains:

$\stackrel{\&CenterDot;\&CenterDot;}{r}=\frac{{\left(v_M{\mathrm{sin\&eta;}}_M-V_T{\mathrm{sin\&eta;}}_T\right)}^2}{r}-\frac{P\sin \mathrm{\&alpha;}+Y^{\mathrm{\&alpha;}}\mathrm{\&alpha;}-mg\cos \mathrm{\&theta;}}{m}{\mathrm{sin\&eta;}}_M-\frac{P\cos \mathrm{\&alpha;}-X_0-X^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2-mg\sin \mathrm{\&theta;}}{m}{\mathrm{cos\&eta;}}_M---\left(12\right)$

For this reason, the forecast model of actual missile-target distance is set up:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{r}=v_T{\mathrm{cos\&eta;}}_T-v_M{\mathrm{cos\&eta;}}_M\\ \stackrel{\&CenterDot;\&CenterDot;}{r}=\frac{{\left(v_M{\mathrm{sin\&eta;}}_M-V_T{\mathrm{sin\&eta;}}_T\right)}^2}{r}-\frac{P\sin \mathrm{\&alpha;}+Y^{\mathrm{\&alpha;}}\mathrm{\&alpha;}-mg\cos \mathrm{\&theta;}}{m}{\mathrm{sin\&eta;}}_M-\frac{P\cos \mathrm{\&alpha;}-X_0-X^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2-mg\sin \mathrm{\&theta;}}{m}{\mathrm{cos\&eta;}}_M---\left(13\right)\end{array}\right.$

As long as guided missile practical flight track can follow the tracks of theoretical flight path, guided missile can realize cooperation, therefore, sets up the single order about missile-target distance and second-order equation that formula (13) expresses herein.

Step 4, be generally applied to slow time-varying system due to model prediction, it often walks the intensive that solving-optimizing problem causes, the shortcoming that the time is long, be difficult to be applied to fast time-varying system is solved in order to Model Predictive Control can be solved, the present invention adopts convex optimization tool CVXGEN, to solve the problem.In order to the forecast model of convex optimization tool to actual missile-target distance can be adopted to solve, linearisation, discretization and standardization need be carried out to forecast model in advance, namely carry out following routine operation:

41st step: definition status variable $x={\&lsqb;x_1,x_2\&rsqb;}^T={\&lsqb;r,\stackrel{\&CenterDot;}{r}\&rsqb;}^T,f={\&lsqb;f_1,f_2\&rsqb;}^T={\&lsqb;\stackrel{\&CenterDot;}{r},\stackrel{\&CenterDot;\&CenterDot;}{r}\&rsqb;}^T,$ Input u=α, then now, the state-space expression of system can be written as:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ x_2=\frac{{\left(v_M{\mathrm{sin\&eta;}}_M-V_T{\mathrm{sin\&eta;}}_T\right)}^2}{r}-\frac{P\sin \mathrm{\&alpha;}+Y^{\mathrm{\&alpha;}}\mathrm{\&alpha;}-mg\cos \mathrm{\&theta;}}{m}{\mathrm{sin\&eta;}}_M-\frac{P\cos \mathrm{\&alpha;}-X_0-X^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2-mg\sin \mathrm{\&theta;}}{m}{\mathrm{cos\&eta;}}_M\end{array}\right.---\left(14\right)$

42nd step: to formula (14) at theoretical flight path (x _ep, u _ep) place's linearization process, obtain

$\stackrel{\&CenterDot;}{x}=Ax+Bu+C---\left(15\right)$

Wherein, $\begin{array}{ccc}A=\left[\begin{array}{cc}\frac{\&part;f_1}{\&part;x_1}& \frac{\&part;f_1}{\&part;x_2}\\ \frac{\&part;f_2}{\&part;x_1}& \frac{\&part;f_2}{\&part;x_2}\end{array}\right]{|}_{ep}& B=\left[\begin{array}{c}\frac{\&part;f_1}{\&part;u}\\ \frac{\&part;f_2}{\&part;u}\end{array}\right]{|}_{ep}& C=\left[\begin{array}{c}{f}_1-\frac{\&part;f_1}{\&part;x_1}{x}_1-\frac{\&part;f_1}{\&part;x_2}{x}_2-\frac{\&part;f_1}{\&part;u}u\\ f_2-\frac{\&part;f_2}{\&part;x_1}{x}_1-\frac{\&part;f_2}{\&part;x_2}{x}_2-\frac{\&part;f_2}{\&part;u}u\end{array}\right]\end{array}{|}_{ep}$

In matrix, each element expression is:

$\begin{array}{cccc}\frac{\&part;f}{\&part;x_1}=0& \frac{\&part;f_1}{\&part;x_2}=1& \frac{\&part;f_1}{\&part;u}=0& \frac{\&part;f_2}{\&part;x_1}=-\frac{{(v_{m}sin\mathrm{\&eta;}-v_t{\mathrm{sin\&eta;}}_t)}^2}{r^2}\end{array}$

$\begin{array}{cc}\frac{\&part;f_2}{\&part;x_2}=0& \frac{\&part;f_2}{\&part;u}=-\frac{Pcos\mathrm{\&alpha;}+Y^{\mathrm{\&alpha;}}}{m}sin\mathrm{\&eta;}+\frac{Psin\mathrm{\&alpha;}+2{\mathrm{\&alpha;X}}^{{\mathrm{\&alpha;}}^2}}{m}cos\mathrm{\&eta;}\end{array}$

Wherein, parameter v involved in the element of subscript " ep " representation theory parameter and matrix A, B, C _m, η, r and α be the theory locus parameter that step 2 is tried to achieve.

43rd step: utilize Euler method to carry out sliding-model control to formula (15), obtain:

x(k+1)＝A ₁x(k)+B ₁u(k)+C ₁(16)

Wherein, k represents current sample time, matrix A ₁=I+A Δ t, B ₁=B Δ t, C ₁=C Δ t, I are 2 × 2 unit matrixs, and Δ t is the sampling time.

44th step: canonical form formula (16) being written as PREDICTIVE CONTROL:

x(k+i+1|k)＝A ₁(k+i|k)x(k+i|k)+B ₁(k+i|k)u(k+i|k)+C ₁(k+i|k)(17)

Wherein, i=0 ... P, P are the control time domain of Model Predictive Control, and x (k+i|k) represents the prediction of k moment to k+i moment variable.

Step 5, considering that guided missile is in flight course; often can be subject to as various interference such as RANDOM WIND; and the situation that the control surface deflection of guided missile is limited, guided missile is actual plays the tracking of order track to theoretical flight path to adopt the technology that combines with convex optimization of PREDICTIVE CONTROL to realize, thus realizes cooperation.

For realizing the tracking to theoretical flight path, therefore in performance indications, need tracking error item; In order to avoid the too fast change of controlled quentity controlled variable, access control amount in performance indications, is also needed to change item.Meanwhile, according to performance index function reference representation, performance indications are chosen as follows:

$\begin{array}{c}J=\underset{i=1}{\overset{P}{\&Sigma;}}\{{\left(x_1\right(k+i|k)-x_{1ep}(k+i|k\left)\right)}^{T}Q\left(x_1\right(k+i|k)-x_{1ep}(k+i|k\left)\right)+\\ {\left(u\right(k+i|k)-u(k+i-1|k\left)\right)}^T{R}_d\left(u\right(k+i|k)-u(k+i-1|k\left)\right)\}\end{array}---\left(18\right)$

Wherein, x ₁for the actual missile-target distance of guided missile, x _1epfor theoretical missile-target distance, Q and R _dbe respectively corresponding weight matrix, be positive definite matrix.(x in performance index function ₁(k+i|k)-x _ep(k+i|k)) ^tq (x ₁(k+i|k)-x _ep(k+i|k) tracking effect of practical flight track to theoretical flight path) is represented, (u (k+i|k)-u (k+i-1|k)) ^tr _d(u (k+i|k)-u (k+i-1|k)) represents the size of controlled quentity controlled variable change.

Step 6, consider the limited situation causing the restriction of the angle of attack of the control surface deflection of guided missile, amplitude limit is carried out to controlled quentity controlled variable u, even

|u|≤u _max(19)

Wherein, u _maxbeing greater than zero, is the amplitude of controlled quentity controlled variable.

According to formula (17), (18) and (19), the canonical form of Model Predictive Control is written as:

$\begin{array}{c}\begin{array}{cc}\min & J=\underset{i=1}{\overset{P}{\&Sigma;}}\{{\left(x_1\right(k+i|k)-x_{ep}(k+i|k\left)\right)}^{T}Q\left(x_1\right(k+i|k)-x_{ep}(k+i|k\left)\right)+\end{array}\\ {\left(u\right(k+i|k)-u(k+i-1|k\left)\right)}^T{R}_d\left(u\right(k+i|k)-u(k+i-1|k\left)\right)\}\end{array}---\left(20\right)$

$\begin{array}{c}s.t.\left\{\begin{array}{c}x(k+i+1|k)=A_1(k+i\left|k\right)x(k+i|k)+B_1(k+i\left|k\right)u(k+i|k)+C_1(k+i\left|k\right)\\ \left|u(k+i|k)\right|\&le;u_{max}\end{array}\right.\\ i=0...P\end{array}$

Wherein, s.t. represents constraints, and the physical meaning of formula (20) is: at given Q and R _dafterwards, with x (k+i+1|k)=A ₁(k+i|k) x (k+i|k)+B ₁(k+i|k) u (k+i|k)+C ₁(k+i|k) and | u|≤u _maxas constraints, adopt CVXGEN instrument to solve the optimization problem shown in formula (20), obtain can meet optimal control sequence that J is minimum of a value [u (k), u (k+1) ..., u (k+P)] ^t.Wherein, x (k+i+1|k)=A ₁(k+i|k) x (k+i|k)+B ₁(k+i|k) u (k+i|k)+C ₁(k+i|k) A in ₁, B ₁, C ₁matrix obtains according to theoretical flight path parameter, characterizes dynamic constrained.By comprise in formula (17) about x ₁relational expression substitute into formula (20), that plays is theoretical flight path and specifies the restriction of attack time.And | u|≤u _maxit is then the restriction to the angle of attack.Acquisition optimal control sequence [u (k), u (k+1) ..., u (k+P)] ^t;

In order to realize the control to the actual missile-target distance of guided missile, the missile-target distance in kth+1 moment, trajectory tilt angle, the speed of guided missile, the speed angle of lead of guided missile and the angle of sight need be obtained; For this reason, choose optimal control sequence [u (k), u (k+1) ..., u (k+P)] ^tfirst term as input quantity, in the speed v of the Missile Motion parameter in given k moment and missile-target distance r (k), trajectory tilt angle θ (k), guided missile _mthe speed angle of lead η of (k), guided missile _min (k) and angle of sight q (k) situation, substituted in the equation group be made up of formula (2), formula (8), formula (9) and formula (10), by utilizing numerical integration method, obtain missile-target distance r (k+1), the trajectory tilt angle θ (k+1) in kth+1 moment, the speed v of guided missile _m(k+1), the speed angle of lead η of guided missile _mand angle of sight q (k+1), and using the actual missile-target distance, trajectory tilt angle, the speed of guided missile, the speed angle of lead of guided missile and the angle of sight that the obtain initial value as subsequent time, then carry out solving of subsequent time optimization problem (k+1); .Until during actual missile-target distance r < 1000m, proceed to proportional guidance and control.

Embodiment:

As shown in Fig. 4 to 8, suppose the naval vessels that three pieces of same kind guided missiles concerted attack one is static, the position of naval vessels is (x _t, y _t)=(10000m, 0).Guided missile M _iinitial position (the x of (i=1,2,3) _m0, y _m0), initial velocity V _m0, initial trajectory inclination angle theta _m0as shown in table 1.Structure and the aerodynamic data of guided missile are as shown in table 2.

The initial motion parameter of table 1 guided missile

Guided missile	(x m0,y m0)/m	V m0/ms -1	θ m0/°
				Guided missile 1	(0,0)	230	30
Guided missile 2	(50,0)	220	25
				Guided missile 3	(100,0)	210	20

The structure of table 2 guided missile and aerodynamic data

In table 2, S, L are respectively feature area and the characteristic length of guided missile, c _x0, be respectively zero-lift drag coefficient, resistance coefficient to the derivative of the angle of attack square and lift coefficient to the derivative of the angle of attack.

The appointment attack time T of guided missile _d=60s, low pass filter timeconstantτ=0.1s, the control time domain P=30 of Model Predictive Control, the weight Q=10 in performance indications, R _d=0.1, controlled quentity controlled variable amplitude u _max=10 °.

For the antijamming capability of access control system, suppose that in missile flight process, aerodynamic parameter has the perturbation of 20%; For access control system is to the amplitude limit effect of input, suppose that guided missile 1 is owing to launching disturbance, initial velocity becomes 235m/s.Trajectory during three pieces of guided missile cooperations and the change of other kinematic parameter are as shown in Fig. 4 to 8

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. based on many guided missiles cooperation method of guidance of model predictive control technique, it is characterized in that, for every piece of guided missile, adopt following concrete steps:

The appointment attack time T that step one, setting hit the mark _d, and obtain appointment missile-target distance rate of change according to appointment attack time wherein, r ₀for the distance under original state between guided missile and target;

Step 2, make theoretical missile-target distance rate of change with appointment missile-target distance rate of change equal, according to the barycenter kinetic model of the geometrical relationship played between order Equation of Relative Motion with Small, angle and guided missile, the theoretical flight path of attack time hit specified by derivation guided missile;

Step 3, based on the barycenter kinetics equation playing order Equation of Relative Motion with Small and guided missile, set up the forecast model changed for describing actual missile-target distance;

Step 4, linearisation, discretization and standardization are carried out to forecast model, obtain the canonical form of forecast model;

Step 5, according to performance indications reference representation, set up reaction practical flight track to theoretical path tracking effect, simultaneously the performance index function of reaction controlling amount change size again;

Step 6,

With the maximum amplitude u of the angle of attack _maxas control quantity constraint, the canonical form of the forecast model obtained in step 4 is as profile constraints, the function obtained in step 5, as performance index function, utilizes convex optimization tool, obtains the optimal control sequence under a series of condition meeting minimum performance target function value; And get Section 1 in optimal sequence and substitute into and play order Equation of Relative Motion with Small group, trajectory tilt angle rate of change expression formula, the barycenter kinetic model of guided missile, guided missile resistance expression formula and Missile-Lift expression formula, obtain actual missile-target distance, trajectory tilt angle, the speed of guided missile, the speed angle of lead of guided missile and the angle of sight, and using the actual missile-target distance of acquisition, trajectory tilt angle, the speed of guided missile, the speed angle of lead of guided missile and the angle of sight initial value as subsequent time, then carry out solving of subsequent time optimization problem; Until during actual missile-target distance r < 1000m, proceed to proportional guidance and control.

2. many guided missiles cooperation method of guidance as claimed in claim 1, is characterized in that: the concrete grammar obtaining theoretical flight path is:

21st step: set up and play order Equation of Relative Motion with Small group, and according to appointment missile-target distance rate of change expression formula, obtain missile velocity angle of lead expression formula;

22nd step: according to the domain of definition of anticosine trigonometric function and the restriction of maximum frame corners of setting, segmentation description is carried out to missile velocity angle of lead expression formula, obtain the piecewise function expression formula of missile velocity angle of lead;

23rd step: adopt low pass filter to carry out LPF to missile velocity angle of lead, obtain the speed angle of lead η that low pass filter exports _d;

24th step: according to bullet order relative motion relation, obtain trajectory tilt angle rate of change expression formula;

25th step: barycenter kinetic model and the lift expression formula of setting up guided missile, obtains angle of attack expression formula;

26th step: the lift expression formula of the speed angle of lead expression formula bullet order Equation of Relative Motion with Small obtained, missile velocity angle of lead expression formula, low pass filter exported, trajectory tilt angle rate of change expression formula, barycenter kinetic model, guided missile and angle of attack expression formula simultaneous, obtain theoretical flight path.