CN112379600B - Distributed cooperative guidance law construction method based on communication time-varying delay - Google Patents

Distributed cooperative guidance law construction method based on communication time-varying delay Download PDF

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CN112379600B
CN112379600B CN202011314928.9A CN202011314928A CN112379600B CN 112379600 B CN112379600 B CN 112379600B CN 202011314928 A CN202011314928 A CN 202011314928A CN 112379600 B CN112379600 B CN 112379600B
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方洋旺
王志凯
吴自豪
马文卉
邓天博
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Northwestern Polytechnical University
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Abstract

The invention discloses a distributed cooperative guidance law construction method based on communication time-varying delay. On the basis of an improved multi-agent consistency theory, arrival time is selected as a state variable in the sight direction, and under the condition that time-varying delay exists in inter-missile communication, the arrival time of multiple missiles is ensured to be consistent through the action of a consistency protocol, and finally the attack target of the multiple missiles at the same time is achieved. And selecting the line-of-sight angle error and the line-of-sight angle rate as state variables on the basis of a sliding mode control theory in a line-of-sight method, and enabling the line-of-sight angle error and the line-of-sight angle rate to approach 0 by constructing a sliding mode controller, so that the missile attacks the target according to a preset angle. The method does not need to consider maximum delay constraint, and can dynamically change parameters in a consistency convergence protocol according to the delay size, so that the multi-missile cooperative attack target under communication time-varying delay is realized.

Description

Distributed cooperative guidance law construction method based on communication time-varying delay
Technical Field
The invention belongs to the technical field of guidance, and particularly relates to a guidance law construction method.
Background
With the increasing enhancement of air defense and anti-missile technology, especially at the tail end of missile attack, the air defense and anti-missile technology is easily intercepted by enemy counterweapons, and various active/passive deception jamming devices cause difficulty in identifying targets. The traditional single missile fighting mode is difficult to realize accurate and stable hitting on the target. When the operation mode of cooperative attack of a plurality of missiles is adopted, the missiles attack the target from different angles, and the interception and interference difficulty of an enemy counterguidance system is greatly increased. Therefore, in recent years, the cooperative guidance of multiple missiles is receiving more and more attention from domestic and foreign scholars and industries.
Cooperative guidance is further divided into centralized cooperative guidance and distributed cooperative guidance according to a communication topological structure. The centralized cooperation is to select a missile as a communication central node, and the other nodes receive the information of the central node to realize the arrival at the same time. The method has the advantages that the convergence speed of the cooperative instruction is high; the disadvantage is that once the central node fails, the battle mission for the entire group of projectiles fails. A decentralized communication structure is adopted in distributed cooperation, each node only needs to communicate with other nodes in the communication range of the node, and the distributed cooperation method has the advantages that the network communication structure is strong in robustness and more suitable for engineering application; the disadvantage is that the speed of convergence of the cooperative instruction is slow, especially in the case of communication delay, the effect is more obvious.
Due to the strong robustness of distributed network architectures, more and more learners in current collaborative guidance adopt distributed network architectures. At present, some scholars research distributed cooperative guidance of multiple missiles under the condition of communication delay, but most of the scholars assume that the communication delay among the missiles is fixed and constant. (see [1] HE S, KIM, SONG T, et al, three-dimensional salvo attack guidance communication delay [ J ]. Aerospace Science and Technology,2018,73:1-9 [2] Penpenc, Seaman winter, Zhang flood, etc.. Multi-missile cooperative guidance in non-continuous connectivity communication topology [ J ]. Industrial Science). Some scholars consider time-varying communication delay, but the design of the consistency protocol is designed based on the maximum delay tolerable by the system, and the design parameters in the cooperative guidance law fail to reflect the time variation of the communication delay. (see: SUN X, ZHOU R, HOU D, et al. Consenssus of leader-followers system of multi-missing with time-delays and switching topologies [ J ]. Optik,2014,125(3): 1202-.
However, in the actual battlefield environment, the form of electromagnetic countermeasure is complicated, especially in the terminal guidance phase, the communication network is easily interfered by enemy, and the delay between the communication nodes is inevitable. Usually, the distance between a plurality of missiles changes from large to small when the missiles cooperate. The communication delay is related to the distance, and when the distance between the missile eyes is long, the communication delay between missiles is large; as the eyes of the projectiles approach each other, the latency of communication between the projectiles decreases. The distributed cooperative guidance law design research under the communication time-varying delay condition is not reported at present.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a distributed cooperative guidance law construction method based on communication time-varying delay. On the basis of an improved multi-agent consistency theory, arrival time is selected as a state variable in the sight direction, and under the condition that time-varying delay exists in inter-missile communication, the arrival time of multiple missiles is ensured to be consistent through the action of a consistency protocol, and finally the attack target of the multiple missiles at the same time is achieved. And selecting a line-of-sight angle error and a line-of-sight angle rate as state variables on the basis of a sliding mode control theory in a line-of-sight method, and enabling the line-of-sight angle error and the line-of-sight angle rate to approach 0 by constructing a sliding mode controller, so that the missile attacks a target according to a preset angle. The method does not need to consider maximum delay constraint, and can dynamically change parameters in a consistency convergence protocol according to the delay size, so that the multi-missile cooperative attack target under communication time-varying delay is realized.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: establishing multi-missile cooperative guidance mathematical model
The motion relation model between the missile and the target in the two-dimensional plane is as follows:
Figure GDA0003543811970000021
wherein R is the distance between the missile and the target, q is the sum
Figure GDA0003543811970000022
Respectively, the angle of the line of sight of the bullet eye and the rate of the angle of sight of the bullet eye, VmAnd VtThe velocity of the missile and the target, thetamAnd thetatRespectively missile and meshA target ballistic dip angle;
the left side and the right side of the expression (1) are simultaneously derived from time to obtain an expression form of the bullet eye movement relation model under a sight line coordinate system:
Figure GDA0003543811970000023
wherein, arFor control input of the missile in the direction of the line of sight, aqInputting control of the missile in the normal direction of the sight line;
respectively constructing a multi-missile cooperative guidance model in the sight line direction and the sight line normal direction, wherein the multi-missile cooperative guidance model is represented by the formula (3) and the formula (4):
three state variables of a multi-missile cooperative guidance model are respectively selected to be x1i、x2i、x3i，x1i＝tgofi＝tgoi+t，x2i＝qi-qfi，
Figure GDA0003543811970000031
Wherein, tgoiRepresenting the remaining time of the ith missile end-guidance phase,
Figure GDA0003543811970000032
i represents the ith missile, i belongs to {1,2, …, n }, n is the number of missiles, RiRepresents the distance between the ith missile and the target, and t represents time; q. q.siShowing the eye line of sight angle of the ith missile,
Figure GDA0003543811970000033
representing the projectile eye angular rate of the ith missile; t is tgofiIs the total flight time of the ith missile; qfiThe desired terminal line-of-sight angle for the ith missile;
for the state variable x1iObtaining a cooperative guidance model in the sight direction after derivation:
Figure GDA0003543811970000034
will state variable x2i、x3iAnd (3) obtaining a cooperative guidance model in the sight line normal direction by substituting formula (2):
Figure GDA0003543811970000035
wherein, ariIs the control input of the ith missile in the direction of sight, aqiIs the control input of the ith missile in the normal direction of the sight line;
step 2: constructing a sight direction cooperative guidance law;
and (4) constructing a sight direction cooperative guidance law according to the cooperative guidance model in the sight direction given by the formula (3) and by combining communication delay among missiles, wherein the sight direction cooperative guidance law is as shown in a formula (5):
Figure GDA0003543811970000036
wherein N isiIs the set of all missiles communicating with the ith missile; t isiIs the self time delay, T, of the ith missileijIs the communication delay time between the jth and ith missiles,
Figure GDA0003543811970000037
diis the penetration of the ith missile; a isijIs the connection weight between the jth missile and the ith missile, and when information flows from the missile j to the missile i, aijGet 1, otherwise aij Taking 0; k is a radical ofiIs the adaptive parameter, ki>0 and satisfy
Figure GDA0003543811970000038
And 3, step 3: constructing a sight normal cooperative guidance law;
writing the cooperative guidance model in the line-of-sight normal direction of equation (4) into the form:
Figure GDA0003543811970000041
wherein the content of the first and second substances,
Figure GDA0003543811970000042
ui＝aqi；
defining a nonsingular terminal sliding mode surface:
Figure GDA0003543811970000043
wherein the content of the first and second substances,
Figure GDA0003543811970000044
sign is a sign function; beta is ai＝Pi/Qi，PiAnd QiIs a positive odd number greater than zero and satisfies 1 < Pi/Qi＜2；k1iIs a normal number;
in order to realize the rapid convergence of the nonsingular terminal sliding mode surface, a rapid exponential approximation law is constructed as shown in the formula (8):
Figure GDA0003543811970000045
wherein k is2iAnd k3iIs a normal number greater than zero, 0 < rhoi＜1；
The guided missiles obtained by combining the formulas (6), (7) and (8) are guided in a cooperative mode in the normal direction of the sight line as follows:
Figure GDA0003543811970000046
the invention provides a distributed cooperative guidance law construction method based on communication time-varying delay, which has the following beneficial effects that:
1. compared with the prior method, the method does not need to consider the maximum delay constraint, can dynamically change the parameters in the consistency convergence protocol according to the delay size, and realizes the multi-missile cooperative attack target under the communication time-varying delay.
2. The method adopts a two-direction guidance model, independently constructs guidance laws in the sight line direction and the sight line normal direction, ensures that a plurality of missiles strike the target simultaneously in the sight line direction, and ensures that the missiles strike the target according to an expected angle in the sight line direction.
3. The distributed cooperative guidance algorithm provided by the invention can realize that multiple missiles simultaneously carry out saturation attack from different angles, can allow time-varying communication delay among the missiles in distributed communication, and greatly improves the communication anti-interference capability of the missiles.
Drawings
FIG. 1 is a diagram of the communication topology between three missiles in accordance with an embodiment of the present invention;
fig. 2 is a graph of communication delay time between missile 1 and missile 2, and missile 2 and missile 3 according to the embodiment of the invention.
FIG. 3 is a ballistic diagram of multiple missiles in a two-dimensional plane to attack a single uniform velocity target cooperatively according to an embodiment of the invention.
FIG. 4 is a graph of the residual attack time for multiple missiles in accordance with an embodiment of the present invention.
FIG. 5 is a graph of relative distances between multiple missiles and a target in accordance with an embodiment of the present invention.
FIG. 6 is a graph showing the change of the line-of-sight angle of multiple missiles according to the embodiment of the invention.
FIG. 7 is a diagram of control inputs to multiple missiles in the direction of the line of sight according to an embodiment of the invention.
FIG. 8 is a diagram of control inputs for multiple missiles in a line-of-sight normal in accordance with an embodiment of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
A distributed cooperative guidance law construction method based on communication time-varying delay comprises the following steps:
step 1: establishing multi-missile cooperative guidance mathematical model
The motion relation model between the missile and the target in the two-dimensional plane is as follows:
Figure GDA0003543811970000051
wherein R is the distance between the missile and the target, q is the sum
Figure GDA0003543811970000052
Respectively, the angle of the line of sight of the bullet eye and the rate of the angle of sight of the bullet eye, VmAnd VtThe velocity of the missile and the target, thetamAnd thetatTrajectory inclination angles of the missile and the target, respectively;
the left side and the right side of the expression (1) are simultaneously derived from time to obtain an expression form of the bullet eye movement relation model under a sight line coordinate system:
Figure GDA0003543811970000053
wherein, arFor control input of the missile in the direction of the line of sight, aqInputting control of the missile in the normal direction of the sight line;
respectively constructing a multi-missile cooperative guidance model in the sight line direction and the sight line normal direction, wherein the multi-missile cooperative guidance model is represented by the formula (3) and the formula (4):
three state variables of a selected multi-missile cooperative guidance model are x respectively1i、x2i、x3i，x1i＝tgofi＝tgoi+t，x2i＝qi-qfi，
Figure GDA0003543811970000054
Wherein, tgoiRepresenting the remaining time of the ith missile end-guidance phase,
Figure GDA0003543811970000055
i represents the ith missile, i belongs to {1,2, …, n }, n is the number of missiles, RiRepresents the distance between the ith missile and the target, and t represents time; q. q.siShowing the eye line of sight angle of the ith missile,
Figure GDA0003543811970000056
representing the projectile eye angular rate of the ith missile; t is tgofiIs the total flight time of the ith missile; qfiThe desired terminal line-of-sight angle for the ith missile;
for the state variable x1iObtaining a cooperative guidance model in the sight direction after derivation:
Figure GDA0003543811970000061
will state variable x2i、x3iAnd (3) obtaining a cooperative guidance model in the sight line normal direction by substituting formula (2):
Figure GDA0003543811970000062
wherein, ariIs the control input of the ith missile in the direction of sight, aqiIs the control input of the ith missile in the normal direction of the sight line;
step 2: constructing a sight direction cooperative guidance law;
according to the cooperative guidance model in the sight direction given by the formula (3), the cooperative guidance law in the sight direction is constructed by combining the communication delay among the missiles, wherein the formula is as follows (5):
Figure GDA0003543811970000063
wherein N isiIs the set of all missiles communicating with the ith missile; t isiIs the self time delay, T, of the ith missileijIs the communication delay time between the jth and ith missiles,
Figure GDA0003543811970000064
diis the penetration of the ith missile; a isijIs the connection weight between the jth missile and the ith missile when having confidenceWhen information flows from missile j to missile i, aij Get 1, otherwise aij Taking 0; k is a radical ofiIs the adaptive parameter, ki>0 and satisfy
Figure GDA0003543811970000065
And step 3: constructing a sight normal cooperative guidance law;
writing the cooperative guidance model in the line-of-sight normal direction of equation (4) into the form:
Figure GDA0003543811970000066
wherein the content of the first and second substances,
Figure GDA0003543811970000067
ui＝aqi；
defining a nonsingular terminal sliding mode surface:
Figure GDA0003543811970000068
wherein the content of the first and second substances,
Figure GDA0003543811970000071
sign is a sign function; beta is ai＝Pi/Qi，PiAnd QiIs a positive odd number greater than zero and satisfies 1 < Pi/Qi＜2；k1iIs a normal number;
in order to realize the rapid convergence of the nonsingular terminal sliding mode surface, a rapid exponential approximation law is constructed as shown in the formula (8):
Figure GDA0003543811970000072
wherein k is2iAnd k3iIs a normal number greater than zero, 0 < rhoi＜1；
The guided missiles obtained by combining the formulas (6), (7) and (8) are guided in a cooperative mode in the normal direction of the sight line as follows:
Figure GDA0003543811970000073
the specific embodiment is as follows:
in the embodiment, three missiles launched from different positions and angles are considered to attack the uniform-speed linear motion aerial target. Under the action of the constructed control law, three missiles attack the target from different angles at the same time, so that the effectiveness of the constructed method is verified. In the simulation, the communication among the three missiles adopts the communication topology shown in fig. 1, the delay of the communication among the missiles is considered, and the communication delay is assumed to be larger as the distance between the missiles is farther, so that the communication among the missiles has the minimum delay.
1. Establishing three-missile cooperative guidance mathematical model
The formula (1) is derived and converted to a sight line coordinate system, and the following equation of state can be obtained by considering the assumed uniform velocity target of cooperative attack of three missiles in the embodiment
Figure GDA0003543811970000074
I is belonged to {1,2,3} in the expression. The control law constructed by the invention aims to control three missiles to hit a target from different directions simultaneously. By making x3iApproaching to zero, and ensuring that each missile hits the target; by making x2iApproaching to zero, so that each missile can attack the target according to a specific angle; by making x1iThe approaches are consistent, so that three missiles can hit the target at the same time.
The simulation initial conditions of three missiles and the target in this embodiment are given below:
missile 1: initial position (4000,0), initial velocity 580m/s, initial ballistic dip-6 °, maximum available overload ± 30g, g-9.8 m/s, desired end-line-of-sight angle 15 °.
Missile 2: initial position (4908, -800), initial velocity 600m/s, initial ballistic dip 5 °, maximum available overload ± 30g, g-9.8 m/s, desired terminal line of sight angle 0 °.
Missile 3: initial position (5900, -1041), initial velocity 620m/s, initial ballistic inclination 5 °, maximum available overload ± 30g, g-9.8 m/s, desired terminal line of sight angle-20 °.
The target is as follows: initial position (0, -0), initial velocity 200m/s, initial ballistic inclination 30 °.
2. Constructing cooperative guidance law of three missiles in sight direction
The invention aims to construct a guidance law in the sight direction so as to enable state variables x of three missiles1iTo achieve consistency, a multi-agent consistency protocol based on time-varying communication delays is used.
Dynamic equation considering first-order multi-agent system
Figure GDA0003543811970000081
Wherein λiFor each agent's motion state, uiFor each agent's control input. Consistent convergence of multi-agent states may be achieved when the control inputs of the agents satisfy equation (12).
Figure GDA0003543811970000082
In this example to
Figure GDA0003543811970000083
In this embodiment, state x is selected1i＝tgofiAs state variables, applying a consistency protocol may result in:
Figure GDA0003543811970000084
this can be substituted into equation (10) to obtain:
Figure GDA0003543811970000085
the cooperative guidance law of the three missiles obtained after simplification in the sight line direction is as follows:
Figure GDA0003543811970000086
3. constructing cooperative guidance law of three missiles in the normal direction of sight line
Considering the guidance model in the direction of the line of sight as equation (6),
and (4) constructing a sliding mode control law aiming at the second-order nonlinear system shown in the formula (6). In order to realize the rapid finite time convergence of the system state, a nonsingular terminal sliding mode face is selected as formula (7), and P is selectedi＝11、Qi＝9、k1i3. In order to realize the rapid convergence of the sliding mode surface, a rapid exponential approximation law is constructed as a formula (8), and k is selected2i＝10、k3i＝10、ρi＝0.6。
The cooperative guidance law of the finally obtained missile in the normal direction of the sight line is as follows:
Figure GDA0003543811970000091
4. simulation analysis
The cooperative guidance law of the three missiles in the sight line direction and the sight line normal direction is obtained through the construction of the steps, the effectiveness of the cooperative guidance law construction algorithm based on communication time-varying delay, which is provided by the patent, is verified through algorithm simulation, and the simulation analysis is as follows:
first, fig. 1 shows the communication topology of three missiles in this embodiment. The variation curve of the inter-missile time-varying communication delay involved in the present embodiment is given in fig. 2. Since the communications of the missiles are assumed to be undirected, the communications between any two missiles are considered to be bidirectional and have the same transmission characteristics. In fig. 2, M1 to M2 represents the communication delay curve of missile 1 and missile 2, and M2 to M3 represents the communication delay curve of missile 2 and missile 3. As can be seen from fig. 3, the larger the distance between the missiles is, the longer the communication delay time is, and vice versa, and the communication delay is not reduced when the distance between the missiles is less than a certain value, and it is assumed that the communication delay between the missiles is 100ms at minimum in this embodiment.
Fig. 3 is a diagram of the motion relationship between three missiles and a target in a two-dimensional plane, and it can be seen from fig. 3 that the three missiles are launched from different initial positions and angles and hit the target simultaneously under respective guidance laws. It can be seen from fig. 4 and 5 that the initial remaining time and the initial remaining distance of the three missiles are different, and the simultaneous target hitting is finally realized under the action of respective guidance laws. Fig. 7 shows the cooperative guidance law control input curves in the line-of-sight direction, the maximum values of the control amounts are each smaller than the assumed maximum overload, and the control amounts gradually converge. This demonstrates the effectiveness of the constructed cooperative guidance law in the direction of the line of sight.
Fig. 6 shows the change curves of the sight angles of three missiles, and the initial sight angles of the three missiles are different and finally gradually converge to the respective expected terminal sight angles. FIG. 8 shows the cooperative guidance law control input curve in the line-of-sight normal, with the maximum controlled variable not greater than the assumed maximum overload, and the controlled variable converging to zero. This indicates the effectiveness of the cooperative guidance law constructed in the line-of-sight normal.

Claims (1)

1. A distributed cooperative guidance law construction method based on communication time-varying delay is characterized by comprising the following steps:
step 1: establishing multi-missile cooperative guidance mathematical model
The motion relation model between the missile and the target in the two-dimensional plane is as follows:
Figure FDA0003543811960000011
wherein R is the distance between the missile and the target, q is the sum
Figure FDA0003543811960000016
Are lines of sight of eyesAngular and bullet eye line of sight angular rate, VmAnd VtThe velocity of the missile and the target, thetamAnd thetatTrajectory inclination angles of the missile and the target, respectively;
the left side and the right side of the expression (1) are simultaneously derived from time to obtain an expression form of the bullet eye movement relation model under a sight line coordinate system:
Figure FDA0003543811960000012
wherein, arFor control input of the missile in the direction of the line of sight, aqInputting control of the missile in the normal direction of the sight line;
respectively constructing a multi-missile cooperative guidance model in the sight line direction and the sight line normal direction, wherein the multi-missile cooperative guidance model is represented by the formula (3) and the formula (4):
three state variables of a selected multi-missile cooperative guidance model are x respectively1i、x2i、x3i，x1i＝tgofi＝tgoi+t，x2i＝qi-qfi，
Figure FDA0003543811960000017
Wherein, tgoiRepresenting the remaining time of the ith missile end-guidance phase,
Figure FDA0003543811960000013
representing the ith missile, i belongs to {1,2, …, n }, n is the number of missiles, RiRepresents the distance between the ith missile and the target, and t represents time; q. q.siShowing the eye line of sight angle of the ith missile,
Figure FDA0003543811960000018
representing the projectile eye angular rate of the ith missile; t is tgofiIs the total flight time of the ith missile; qfiThe desired terminal line-of-sight angle for the ith missile;
for the state variable x1iObtaining a cooperative guidance model in the sight direction after derivation：
Figure FDA0003543811960000014
Will state variable x2i、x3iAnd (3) obtaining a cooperative guidance model in the sight line normal direction by substituting formula (2):
Figure FDA0003543811960000015
wherein, ariIs the control input of the ith missile in the direction of sight, aqiIs the control input of the ith missile in the normal direction of the sight line;
step 2: constructing a sight direction cooperative guidance law;
according to the cooperative guidance model in the sight direction given by the formula (3), the cooperative guidance law in the sight direction is constructed by combining the communication delay among the missiles, wherein the formula is as follows (5):
Figure FDA0003543811960000021
wherein N isiIs the set of all missiles communicating with the ith missile; t isiIs the self time delay, T, of the ith missileijIs the communication delay time between the jth and ith missiles,
Figure FDA0003543811960000022
diis the penetration of the ith missile; a isijIs the connection weight between the jth missile and the ith missile, and when information flows from the missile j to the missile i, aijGet 1, otherwise aijTaking 0; k is a radical of formulaiIs the adaptive parameter, ki>0 and satisfy
Figure FDA0003543811960000023
And step 3: constructing a sight normal cooperative guidance law;
writing the cooperative guidance model in the line-of-sight normal direction of equation (4) into the form:
Figure FDA0003543811960000024
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003543811960000025
defining a nonsingular terminal sliding mode surface:
Si＝x3i+k1isig(x2i)βi (7)
wherein the content of the first and second substances,
Figure FDA0003543811960000027
sign is a sign function; beta is ai＝Pi/Qi，PiAnd QiIs a positive odd number greater than zero and satisfies 1 < Pi/Qi＜2；k1iIs a normal number;
in order to realize the rapid convergence of the nonsingular terminal sliding mode surface, a rapid exponential approximation law is constructed as shown in the formula (8):
Figure FDA0003543811960000026
wherein k is2iAnd k3iIs a normal number greater than zero, 0 < rhoi＜1；
The guided missiles obtained by combining the formulas (6), (7) and (8) are guided in a cooperative mode in the normal direction of the sight line as follows:
Figure FDA0003543811960000031
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