A method of space-time synchronous coordinated guidance of missile based on uncontrollable axial velocity constraint

Abstract

The present invention discloses a method for space-time synchronous coordinated guidance of a missile based on the uncontrollable constraint of axial velocity. The method takes the remaining range and velocity of a reference trajectory as coordination variables, utilizes a preset distance control method, takes the relative distance between the missile and the target and the elevation angle of sight as control targets, and realizes the tracking and control capability of the missile on the distance and the elevation angle of sight by converting the under-actuated problem under the uncontrollable axial velocity into a full-actuated control problem in a step-by-step form.

Description

Technical Field

[0001] The invention relates to the technical field of missile guidance control, in particular to a missile time-space synchronous coordinated guidance method based on uncontrollable axial velocity constraints. Background Art

[0002] As the development of aerospace weapon system technology at home and abroad is becoming more and more advanced, different from the previous combat style of relying on a single missile to participate in attacking the target, the coordinated completion of combat missions by multiple missiles has gradually become the focus of attention in the military field at home and abroad. Among them, the guidance law affects the guidance accuracy of the missile and determines whether the missile can successfully intercept the target. Therefore, the research on the coordinated guidance law of multiple missiles has great practical engineering significance, and it is necessary to study the design of the coordinated guidance law of multiple missiles.

[0003] At present, the research on cooperative guidance law with angle constraints is mostly focused on finite time convergence. However, the upper limit of convergence time of finite time control is limited because it depends on the initial conditions of the system. In comparison, fixed time stability has the advantage that the upper limit of convergence time does not depend on initial conditions. Therefore, the application of fixed time convergence theory to guidance law design has attracted the attention of scholars at home and abroad. The constructed fixed time convergence guidance law has good guidance performance and a wide range of applications.

[0004] Common coordination variables for multi-missile coordinated interception are the remaining time or the missile-target distance and lead angle. Comparing these two coordination strategies, we can find that: (1) the remaining time strategy can not only meet the simultaneity of multiple missiles but also realize the coordinated guidance with attack time constraints, but the online estimation accuracy of the remaining time affects the interception result; (2) the remaining distance and lead angle strategies need to determine the lead missile as the tracking object, but there is no need to estimate the remaining time online. An implicit constraint of multi-missile coordinated interception is that the consistency protocol of the coordination variables needs to be completed before the missile-target intersection.

[0005] In the framework of three-dimensional space-time synchronization, if the axial velocity of the missile is uncontrollable, then the control of the relative distance between the missile and the target and the line of sight angle between the two missiles and the target becomes an underactuated problem. Switching control is often used in underactuated designs, but it will bring about the problems of complicated switching and oscillation of control laws. Existing three-dimensional collaborative guidance research for fixed targets with uncontrollable axial velocity often only focuses on the control of the missile-target distance to achieve simultaneous strikes, but rarely limits the missile strike angle. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method for time-space synchronous coordinated guidance of a missile based on the uncontrollable constraint of axial speed, taking the remaining range and speed of a reference trajectory as coordination variables, utilizing a preset distance control method, taking the relative distance between the missile and the target and the elevation angle of sight as control targets, and realizing the tracking and control capability of the missile on the distance and the elevation angle of sight by converting the under-actuated problem under the uncontrollable axial speed into a full-actuated control problem in a step-by-step form.

[0007] In order to solve the above technical problems, the present invention provides a missile space-time synchronous coordinated guidance method based on axial velocity uncontrollable constraint, comprising the following steps:

[0008] Step 1: Design a two-dimensional reference motion trajectory that meets the time-space synchronization characteristics and has a segmented form: an adjustment segment and a straight segment. The adjustment segment realizes the spatial predetermined attack angle adjustment, and the straight segment maintains the predetermined attack angle until the guidance task is completed;

[0009] Step 2: Design a collaborative strategy that satisfies the consistency of arrival time in the two-dimensional reference motion trajectory, that is, to make the remaining flight distance S dg,i At the same time, it converges to 0;

[0010] Step 3: Establish an error model between the two-dimensional reference motion trajectory and the longitudinal plane guidance system to ensure that the longitudinal plane guidance motion trajectory conforms to the two-dimensional reference motion trajectory;

[0011] Step 4: Design a kinematic tracking control strategy to achieve convergence of the kinematic tracking error and the speed compensation amount within a preset distance;

[0012] Step 5: Design a dynamic tracking control strategy to achieve convergence of the dynamic tracking error within a preset distance;

[0013] Step 6: Design a switching strategy for control force distribution to obtain an ideal control force distribution;

[0014] Step 7: Combining the reference trajectory and coordination strategy in step 2, the control strategy in step 4, the control strategy in step 5, and the switching strategy in step 6, if there is a suitable reference speed V d,i Assign so that μ i (x 2,i ) and u i No saturation occurs Then the synchronization of space and time can be achieved, completing the simultaneous attack of multiple missiles from different viewing angles.

[0015] Preferably, in step 1, a missile kinematic model in a three-dimensional guidance mode is established:

[0016]

[0017] Among them, for missile Mi , R i Indicates the distance between the projectile and the target, q θ,i Indicates the elevation angle of the missile's sight. V represents the azimuth of the missile-target line of sight. m,i represents the missile speed, θ m,i and a mθ,i Indicates the missile's current altitude angle and control acceleration. and Indicates the current position angle of the missile and its control acceleration.

[0018] Preferably, in step 1, a two-dimensional reference trajectory motion model of the i-th missile is defined

[0019]

[0020] Among them, R d,i Indicates the reference distance, V d,i represents the reference speed, q d,i represents the reference sight angle, η d,i represents the reference lead angle, and R d,i (0) = R 0,i ,q d,i (0) = q θ0,i , subscript 0 represents the initial time, and subscript d represents the reference trajectory;

[0021] Define a new distance-related variable r d,i =f r,i (R d,i ) and two specified quantities r c,i and r f,i , f r,i (R d,i ) is the distance scale function, the subscript c represents the dividing point between the adjustment segment and the straight segment state, and the subscript f represents the final state, which satisfies the following conditions:

[0022]

[0023] When f′ r,i (R d,i ) = df r,i (R d,i ) / dR d,i and f″ r,i (R d,i ) = df′ r,i (R d,i ) / dR d,i When r d,i Relationship with time t:

[0024]

[0025] Preferably, when in the adjustment section R d,i ∈[R c,i ,R 0,i ], we get:

[0026]

[0027] Consider the reference trajectory obeying the following segmentation form: when R d,i ∈(R c,i ,R 0,i ], so that:

[0028]

[0029] Among them, k d1,i =N 1,i N 2,i , k d2,i =N 1,i +N 2,i -1,N 1,i and N 2,i is the reference trajectory adjustment coefficient, N 1,i <N 2,i , and N 1,i , N 2,i is a positive integer, so we get:

[0030]

[0031] Preferably, when in the straight line segment R d,i ∈[0,R c,i ], the reference trajectory maintains linear motion, that is, maintains q d,i =q f,i ; The maximum lead angle in the reference trajectory motion is obtained

[0032]

[0033] The final total distance of the reference trajectory S df,i From the following we get:

[0034]

[0035] Proof S df,i and V d,i are not related, which provides the possibility for spatial and temporal synchronization control;

[0036] Based on the principle of straight path and shortest distance difference, the design parameter R is optimized. c,i ,N 1,i ,N 2,i

[0037]

[0038] Preferably, in step 2, the remaining flight distance S dg,i At the same time, it converges to 0, and the remaining range is dynamically expressed as:

[0039]

[0040] Therefore, the following collaborative strategy is designed:

[0041]

[0042] in, represents the control amount for the coordinated regulation of the remaining distance, represents the control amount for tracking error compensation feedback, It indicates the component of reference speed affected by control input. Indicates the component of the reference speed affected by the feedback compensation amount;

[0043] Select the adjustment amount Strategy to achieve coordinated consistency convergence of the remaining distance and meet the reference speed Approaching the true speed V m,i :

[0044]

[0045] Among them, λ d1 and λ d2 In the collaborative network, the consistency adjustment parameters are all constant values ​​greater than 0. V d,max,i =V m,i The function f(·) satisfies: (i) (iii)f(0)=0.

[0046] Preferably, the distance tracking error R is defined as e,i =R i -R d,i , the line of sight tracking error q e,i =q θ,i -q d,i , define a new state variable x 1e,i =[R e,i q e,i ] T , μ i (x 2,i )=[μ R,i μ q,i ] T ,in μ q,i = sinθ m,i , and define the input variables Under the constraint of fixed missile speed, the kinematic virtual command Subject to the constraints of the triangular relationship, that is, Defining Error and Among them, sat is a saturation function, which is defined as sat(·,b)=sign(·)min(|·|,b). According to the composition of the reference trajectory in the coordination strategy, Define the function:

[0047]

[0048] in, and Respectively represent the total force in the control input and feedback compensation. Relative kinematics and dynamics model of a single missile:

[0049]

[0050] B 1,i (x 1,i )=-diag{V m,i ,V m,i / R i}

[0051]

[0052] Although the speed-limited space-time synchronous collaborative guidance loses the freedom of missile speed adjustment, the speed limit of the reference trajectory serves as an additional adjustment means to compensate for the control effect.

[0053] Preferably, in step 4, x is implemented 1e,i and At the preset distance R 0,i -R d,i =R 0,i -R p1,i Before convergence, define the state variable z i =[z 1,i z 2,i ] T , where z 1,i =x 1e,i , Define the time-varying T c1,i Scaling function:

[0054]

[0055] Select the shape The Lyapunov candidate function of x is designed 2,i and Preset distance control law:

[0056]

[0057] Based on the above state of z, the Lyapunov function V z,i The derivatives of time and distance are transformed into:

[0058]

[0059] when No saturation occurs And the dynamic tracking converges Then V z,i At a distance R d,i Reduce to R p1,i Convergence before.

[0060] Preferably, in step 5, e 2,i At the preset distance R 0,i -R d,i =R 0,i -R p2,i , R p2,i >R p1,i Preconvergence, definition Select the shape of V e2,i =||e 2,i Lyapunov candidate function for ||

[0061] Select the desired control law as follows:

[0062]

[0063] Lyapunov function V e2,i The derivative of is expressed as:

[0064]

[0065] Preferably, in step 6, b 3,i = cosθ m,i / V m,i , and get the ideal control force distribution:

[0066]

[0067] For and The tracking control takes both into account and As the first priority, choose the control law:

[0068]

[0069] Among them, ε is a sufficiently small quantity to avoid singularity in calculation;

[0070] V d,i Gradually converges to V m,i and remain unchanged, so μ R,i The command signal will converge to 1, which requires Gradually converges to 0, through R c,i Selection to adjust the flatness of the yaw direction of the missile trajectory in three-dimensional space.

[0071] The beneficial effects of the present invention are as follows: (1) The present invention designs a distributed cooperative guidance law with the remaining range and speed of the reference trajectory as coordination variables, and adopts two forms of preset distance control for the kinematics and dynamics of a single missile respectively, and compensates for the error caused by the projection constraint in the system by secondary adjustment of the reference speed; (2) The present invention adopts a time-space synchronous cooperative guidance law design framework with uncontrollable axial speed, which satisfies the limitation of the missile strike angle while achieving target strike; (3) The present invention reduces the dimension of the reference trajectory in the three-dimensional time-space synchronous framework, takes the relative distance between the missile and the target and the elevation and low angle of sight as the control target, and then transforms the transformed time-space synchronous cooperative guidance into a full-drive control problem; takes the relative speed in the reference trajectory as an additional degree of freedom, and ensures the missile's control ability to track the distance and the elevation and low angle of sight and adjusts the flatness of the yaw direction of the missile trajectory in three-dimensional space; under the premise of constraining the missile constant speed, the present invention does not adopt the coordination variable of the remaining time, and integrates the fixed time convergence strategy to realize multi-missile cooperative guidance under time-space synchronization, and the present invention can be applied to a multi-missile cooperative guidance system. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0073] FIG. 2( a ) is a projectile-target interception curve diagram of the present invention when striking a fixed target.

[0074] FIG. 2( b ) is a diagram showing the missile-target interception distance when the present invention strikes a fixed target.

[0075] FIG. 2( c ) is a diagram showing the elevation angles of the missile-target sight line of sight when the present invention is used to strike a fixed target.

[0076] FIG. 2( d ) is a diagram showing the azimuth angles of the projectile when striking a fixed target according to the present invention.

[0077] FIG. 2( e ) is a diagram of the guidance distance control signal when the present invention is used to strike a fixed target.

[0078] FIG. 2( f ) is a diagram of the guidance azimuth control signal when the present invention is used to strike a fixed target. DETAILED DESCRIPTION

[0079] Considering the coordinated guidance of four missiles in a team, the initial conditions and expected terminal interception conditions of the four missiles are shown in Table 1:

[0080] Table 1 Multi-missile coordinated interception scenario design

[0081]

[0082] The communication topology of multi-missile coordination is undirected and interconnected. A method for space-time synchronous coordinated guidance of missiles based on uncontrollable axial velocity constraints includes the following steps:

[0083] Step 1: Design a two-dimensional reference trajectory that meets the characteristics of time-space synchronization and has a segmented form: an adjustment segment and a straight segment. The adjustment segment realizes the spatial predetermined attack angle adjustment, and the straight segment maintains the predetermined attack angle until the guidance task is completed.

[0084] Establish the missile kinematic model in three-dimensional guidance mode:

[0085]

[0086] Design reference trajectory, which is expressed as follows:

[0087]

[0088] Among them, R d,i (0) = R 0,i ,q d,i (0) = q θ0,i .

[0089] Define a new distance-related variable r d,i =f r,i (R d,i ), f r,i (R d,i )=R c,i -R d,i and two specified quantities r c,i and r f,i , the following conditions are met:

[0090]

[0091] When f′ r,i (R d,i ) = df r,i (R d,i ) / dR d,i and f″ r,i (R d,i ) = df′ r,i (R d,i ) / dR d,i When r d,i Relationship with time t:

[0092]

[0093] Therefore, when in the adjustment section R d,i ∈[R c,i ,R 0,i ], we can get:

[0094]

[0095] Furthermore, consider that the reference trajectory obeys the following segmentation form: when R d,i ∈(R c,i ,R 0,i ], to make the target system in r d,i Reduce to r c,i Previous high and low sight angles q d,i Achieve the expected q f,i , then we need to make:

[0096]

[0097] Among them, k d1,i =N 1,i N 2,i , k d2,i =N 1,i +N 2,i -1. From this we can get:

[0098]

[0099] When in the straight line segment R d,i ∈[0,R c,i ], the reference trajectory maintains linear motion, that is, maintains q d,i =q f,i .

[0100] Furthermore, the maximum lead angle in the reference trajectory motion can be obtained

[0101]

[0102] The final total distance of the reference trajectory S df,i It can also be obtained from:

[0103]

[0104] It can be proved that S df,i and V d,i are not related, which provides the possibility for spatial and temporal synchronous control.

[0105] Based on the principle of straight path and shortest distance difference, the design parameter R is optimized. c,i ,N 1,i ,N 2,i

[0106]

[0107] Optimize missile reference path parameters: R c,1 =0km, N 1,1 =2,N 2,1 =2; R c,2 =0km, N 1,2 =2,N 2,2 =3; R c,3 =3.38km, N 1,3 =2,N 2,3 =3; R c,4 =0.53km, N 1,4 =2,N 2,4 =3.

[0108] Step 2: Design a coordination strategy based on the remaining distance. In order to achieve the simultaneity of guidance in the space and time synchronization framework, the remaining range S between each missile and the target should be dg,i At the same time, it converges to 0, and its dynamics can be expressed as:

[0109]

[0110] Therefore, the following collaborative strategy is designed:

[0111]

[0112] in, represents the control amount for the coordinated regulation of the remaining distance, represents the control amount for tracking error compensation feedback, It indicates the component of reference speed affected by control input. Indicates the component of the reference speed affected by the feedback compensation amount.

[0113] Select the adjustment amount Strategy to achieve coordinated consistency convergence of the remaining distance and meet the reference speed Approaching the true speed V m,i :

[0114]

[0115] Among them, λ d1 =10,λ d2 =0.05.

[0116] Step 3: Establish an error model between the two-dimensional reference motion trajectory and the longitudinal plane guidance system to ensure that the longitudinal plane guidance motion trajectory conforms to the two-dimensional reference motion trajectory;

[0117] Correlate the actual motion of the missile with the reference trajectory and define the distance tracking error R e,i =Ri -R d,i , the line of sight tracking error q e,i =q θ,i -q d,i , define a new state variable x 1e,i =[R e,i q e,i ] T , μ i (x 2,i )=[μ R,i μ q,i ] T , μ q,i = sinθ m,i , and define the input variables Under the constraint of fixed missile speed, the kinematic virtual command Subject to the constraints of the triangular relationship, that is, Defining Error and

[0118] According to the composition of the reference trajectory in the coordination strategy Define the function:

[0119]

[0120] Relative kinematic and dynamic models of a single missile:

[0121]

[0122] B 1,i (x 1,i )=-diag{V m,i ,V m,i / R i},

[0123]

[0124] Step 4: Design a kinematic tracking control strategy to achieve convergence of the kinematic tracking error and the speed compensation amount within a preset distance;

[0125] In order to achieve x 1e,i and At the preset distance R 0,i -R d,i =R 0,i -R p1,i Before convergence, define the state variable z i =[z 1,i z 2,i ] T where z 1,i =x1e,i , Define the time-varying T c1,i Scaling function:

[0126]

[0127] Select the shape The Lyapunov candidate function of V z,i Derivative with distance:

[0128]

[0129] Designx 2,i and Preset distance control law:

[0130]

[0131] Based on the above state of z, the Lyapunov function V z,i The derivative with respect to distance becomes:

[0132]

[0133] when No saturation occurs And the dynamic tracking converges Then V z,i At a distance R d,i Reduce to R p1,i Previously converged;

[0134] Step 5: Design a dynamic tracking control strategy to achieve convergence of the dynamic tracking error within a preset distance;

[0135] In order to achieve e 2,i At the preset distance R 0,i -R d,i =R 0,i -R p2,i , R p2,i >R p1,i Preconvergence, definition Select the shape of V e2,i =‖e 2,i ‖ and calculate the desired control law:

[0136]

[0137] Then the Lyapunov function V e2,i The derivative of can be expressed as:

[0138]

[0139] Then V e2,i At a distance R d,i Reduce to R p2,i Previously converged;

[0140] Step 6: Design a switching strategy for control force distribution to obtain an ideal control force distribution;

[0141] remember b 3,i = cosθ m,i / V m,i , and get the ideal control force distribution:

[0142]

[0143] For and The tracking control takes both into account and As the first priority, choose the control law:

[0144]

[0145] Among them, ε is a sufficiently small quantity to avoid singularity in calculation;

[0146] Step 7: Combining the reference trajectory and coordination strategy in step 2, the control strategy in step 4, the control strategy in step 5, and the switching strategy in step 6, if there is a suitable reference speed V d,i Assign so that μ i (x 2,i ) and u i No saturation occurs Then the synchronization of space and time can be achieved, completing the simultaneous attack of multiple missiles from different viewing angles.

[0147] First, the reference trajectory in the three-dimensional space-time synchronization framework is reduced in dimension, and the relative distance between the missile and the target and the elevation angle of sight are used as the control targets. Then, the transformed space-time synchronization cooperative guidance is transformed into a full-drive control problem. Secondly, a distributed cooperative guidance law with the remaining range and speed of the reference trajectory as coordination variables is designed to avoid the estimation of the remaining time. Then, two forms of preset distance control are used for the kinematics and dynamics of a single missile respectively, and the system tracking control error is compensated by secondary adjustment of the reference speed. Then, the reference speed in the reference trajectory is used as an additional degree of freedom to ensure the missile's ability to control the distance and elevation angle of sight and adjust the flatness of the yaw direction of the missile trajectory in three-dimensional space.

[0148] According to the simulation results Figure 2(a)-2(f) As shown, for the speed-constrained collaborative guidance of fixed targets, the space-time synchronization scheme can achieve the simultaneity of guidance under the preset attack angle, and the multi-missile collaborative guidance task is successfully completed.

Claims

1. A missile space-time synchronous coordinated guidance method based on axial velocity uncontrollable constraint, characterized in that: The steps include: Step 1: Design a two-dimensional reference motion trajectory that meets the characteristics of time-space synchronization and has a segmented form: an adjustment segment and a straight segment. The adjustment segment realizes the spatial predetermined attack angle adjustment, and the straight segment maintains the predetermined attack angle until the guidance task is completed. Step 2: Design a collaborative strategy that satisfies the consistency of arrival time in the two-dimensional reference motion trajectory, that is, to make the remaining flight distance S dg,i At the same time, they converge to 0; to make the remaining distance S dg,i At the same time, it converges to 0, and the remaining range is dynamically expressed as: Therefore, the following collaborative strategy is designed: in, represents the control amount for the coordinated regulation of the remaining distance, represents the control amount for tracking error compensation feedback, Indicates the component of the reference speed affected by the control input. Indicates the component of the reference speed affected by the feedback compensation amount; Select the adjustment amount Strategy to achieve coordinated consistency convergence of the remaining distance and meet the reference speed Approaching the true speed V m,i : Among them, λ d1 and λ d2 In the collaborative network, the consistency adjustment parameters are all constant values ​​greater than 0. V d,max,i =V m,i , the function f(·) satisfies: (i) Step 3: Establish an error model between the two-dimensional reference motion trajectory and the longitudinal plane guidance system to ensure that the longitudinal plane guidance motion trajectory conforms to the two-dimensional reference motion trajectory; define the distance tracking error R e,i =R i -R d,i , the line of sight tracking error q e,i =q θ,i -q d,i , define a new state variable x 1e,i =[R e,i q e,i ] T , μ i (x 2,i )=[μ R,i μ q,i ] T ,in μ q,i = sinθ m,i , and define the input variables Under the constraint of fixed missile speed, the kinematic virtual command Subject to the constraints of the triangular relationship, that is, Defining Error and Among them, sat is a saturation function, which is defined as sat(·,b)=sign(·)min(|·|,b). According to the composition of the reference trajectory in the coordination strategy, Define the function: in, and Represent the components of the total force in the control input and feedback compensation respectively, and the relative kinematic and dynamic models of a single missile: B 1,i (x 1,i )=-diag{V m,i ,V m,i / R i } Although the speed-limited space-time synchronous cooperative guidance loses the freedom of missile speed adjustment, the speed limit of the reference trajectory is used as an additional adjustment method to compensate for the control effect; Step 4: Design a kinematic tracking control strategy to achieve convergence of kinematic tracking error and velocity compensation to a preset distance; achieve x 1e,i and At the preset distance R 0,i -R d,i =R 0,i -R p1,i Before convergence, define the state variable z i =[z 1,i z 2,i ] T , where z 1,i =x 1e,i , Define the time-varying T c1,i Scaling function: Select the shape The Lyapunov candidate function of x is designed 2,i and Preset distance control law: Based on the above state of z, the Lyapunov function V z,i The derivative with respect to distance becomes: when No saturation occurs And the dynamic tracking converges Then V z,i At a distance R d,i Reduce to R p1,i Previously converged; Step 5: Design a dynamic tracking control strategy to achieve convergence of the dynamic tracking error to a preset distance; 2,i At the preset distance R 0,i -R d,i =R 0,i -R p2,i , R p2,i >R p1,i Preconvergence, definition Select the shape of V e2,i =||e 2,i ||'s Lyapunov candidate function and calculate the desired control law: Derivation of the Lyapunov function V e2,i The derivative of is expressed as: Step 6: Design a switching strategy for control force distribution to obtain an ideal control force distribution; b 3,i = cosθ m,i / V m,i , and get the ideal control force distribution: For and The tracking control takes both into account and As the first priority, choose the control law: Among them, ε is a sufficiently small quantity to avoid singularity in calculation; V d,i Gradually converges to V m,i and remain unchanged, so μ R,i The command signal will converge to 1, which requires Gradually converges to 0, through R c,i The selection of adjusts the smoothness of the yaw direction of the missile trajectory in three-dimensional space; Step 7: Combining the reference trajectory and coordination strategy in step 2, the control strategy in step 4, the control strategy in step 5, and the switching strategy in step 6, if there is a suitable reference speed V d,i Assign so that μ i (x 2,i ) and u i No saturation occurs Then the synchronization of space and time can be achieved, completing the simultaneous attack of multiple missiles from different viewing angles.

2. The missile space-time synchronous coordinated guidance method based on the axial velocity uncontrollable constraint as claimed in claim 1 is characterized in that: In step 1, the missile kinematic model in the three-dimensional guidance mode is established: Among them, for missile M i , R i Indicates the distance between the projectile and the target, q θ,i Indicates the elevation angle of the missile's sight. V represents the azimuth of the missile-target line of sight. m,i represents the missile speed, θ m,i and a mθ,i Indicates the missile's current elevation angle and its control acceleration. and Indicates the current position angle of the missile and its control acceleration.

3. The missile space-time synchronous coordinated guidance method based on the axial velocity uncontrollable constraint as claimed in claim 1 is characterized in that: In step 1, define the two-dimensional reference trajectory motion model of the i-th missile Among them, R d,i Indicates the reference distance, V d,i represents the reference speed, q d,i represents the reference sight angle, η d,i represents the reference lead angle, and R d,i (0) = R 0,i ,q d,i (0) = q θ0,i , subscript 0 represents the initial time, and subscript d represents the reference trajectory; Define a new distance-related variable r d,i =f r,i (R d,i ) and two specified quantities r c,i and r f,i , f r,i (R d,i ) is the distance scale function, the subscript c represents the dividing point between the adjustment segment and the straight segment state, and the subscript f represents the final state, which satisfies the following conditions: When f r ' ,i (R d,i ) = df r,i (R d,i ) / dR d,i and f r ' , ' i (R d,i ) = df r ' ,i (R d,i ) / dR d,i When r d,i Relationship with time t:

4. The missile space-time synchronous coordinated guidance method based on the axial velocity uncontrollable constraint as claimed in claim 3 is characterized in that: When in the straight line segment R d,i ∈[0,R c,i ], the reference trajectory maintains linear motion, that is, maintains q d,i =q f,i ; When in adjustment section R d,i ∈[R c,i ,R 0,i ], we get: Consider the reference trajectory obeying the following segmentation form: when R d,i ∈(R c,i ,R 0,i ], so that: Among them, k d1,i =N 1,i N 2,i , k d2,i =N 1,i +N 2,i -1, N 1,i and N 2,i is the reference trajectory adjustment coefficient, N 1,i <N 2,i , and N 1,i , N 2,i is a positive integer, so we get:

5. The missile space-time synchronous coordinated guidance method based on the axial velocity uncontrollable constraint as claimed in claim 4 is characterized in that: The maximum lead angle in the reference trajectory motion is obtained The final total distance of the reference trajectory S df,i From the following we get: Proof S df,i and V d,i are not related, which provides the possibility for spatial and temporal synchronization control; Based on the principle of straight path and shortest distance difference, the design parameter R is optimized. c,i ,N 1,i ,N 2,i s.t.η dM,i (R c,i ,N 1,i ,N 2,i )≤η M,i 0<R c,i <R 0,i ,

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