CN116401752A - Self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on super-twist observer - Google Patents

Self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on super-twist observer Download PDF

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CN116401752A
CN116401752A CN202310055120.0A CN202310055120A CN116401752A CN 116401752 A CN116401752 A CN 116401752A CN 202310055120 A CN202310055120 A CN 202310055120A CN 116401752 A CN116401752 A CN 116401752A
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程昊宇
闫天
黄汉桥
周欢
张勃
宋睿佳
贾吾山
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Northwestern Polytechnical University
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Abstract

Aiming at the problem of multi-aircraft collaborative guidance law design with time and attack angle constraint, the invention provides a self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on a super-twist observer. On the basis of establishing a bullet mesh relative motion model, dividing the design of a guidance law into a sight line direction and a sight line normal direction, designing a guidance instruction of the sight line direction based on a multi-agent consistency principle, and ensuring that the rest time of each aircraft can be converged so as to realize sight line cooperative attack; based on the self-adaptive sliding mode method, a guidance instruction of the normal direction of the sight line is designed, and the aircraft is ensured to attack the target at a given angle, so that the angle constraint is satisfied.

Description

Self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on super-twist observer
Technical Field
The invention relates to the field of multiple aircrafts, in particular to a self-adaptive sliding mode multiple aircrafts collaborative terminal guidance law design method based on a super-twist observer.
Background
Modern combat environments are increasingly complex, combat tasks are increasingly diverse, task targets are more intelligent, maneuverability is greatly improved, partial targets can even launch bait bullets to interfere with interception of incoming missiles, and under the condition, the missiles can complete identification of the targets and high-precision attack (interception) and detection tasks. In this trend, the mode of multi-aircraft cooperative combat has become a research hotspot in recent years, and cooperative guidance is a key technology in this mode. The multi-aircraft cooperative guidance is that a plurality of missiles are mutually matched under the support of a communication network, the plurality of missiles are fused into an information sharing, functional complementation and tactical cooperative battle group, and the whole cooperative missile group realizes a certain attack or defending task according to a certain cooperative control strategy. In the collaborative guidance process, more accurate and efficient striking can be realized by researching the multi-constraint condition under terminal guidance. The multi-constraint condition mainly comprises attack time constraint, attack angle constraint and the like. The time constraint under the multi-constraint condition is to hit the target by the missile at the same time so as to achieve the effect of saturation attack, and the sudden prevention capability is enhanced; the attack angle constraint under the multi-constraint condition is to obtain a better striking effect, and the missile is required to strike the target at a certain angle, so that the damage performance of the missile is fully exerted.
The sliding mode variable structure control can overcome the uncertainty of the system, has strong robustness to external interference and unmodeled dynamics, has a simple structure and high response speed, and is very suitable for the design of guidance laws. However, in the design of sliding mode variable structure control, singular and buffeting phenomena often occur, which is unfavorable for system control; meanwhile, the sliding mode variable structure control design is designed aiming at a fixed interference upper bound, and the interference upper bound is generally far greater than actual interference, so that the conservation of the system is high.
Disclosure of Invention
Technical problem to be solved
Aiming at the problem of multi-aircraft collaborative guidance law design with time and attack angle constraint, the invention provides a self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on a super-torsion observer.
Technical proposal
A self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on a super-torsion observer is characterized by comprising the following steps:
step 1: dividing the design of the guidance law into a sight line direction and a sight line normal line direction;
step 2: during the terminal guidance phase of the aircraft, the remaining time t is defined go Is that
Figure BDA0004060282090000021
Wherein R, (-) ->
Figure BDA0004060282090000022
The sight distance and its derivative;
step 3: converting the collaborative guidance law design problem into a design problem of a sight direction and a sight normal acceleration instruction, and converting the sight direction guidance law into a design problem of a sight normal acceleration instruction
Figure BDA0004060282090000023
Ensure the remaining time t go To achieve a synergistic attack; line-of-sight normal guidance law u i Ensuring that the target is hit at a given angle;
step 4: first, a cooperative guidance law is designed under nominal conditions, i.e. without taking into account target maneuvers
Let t be the current time, t goi Intercepting the target for the i-th aircraft for the remaining time, i=1, 2, …, n; then the predicted time of the interception target of the ith aircraft is t at the time t fi ＝t+t goi And due to t goj -t goi ＝t fj -t fi So ensure t fi Tend to be consistent and can ensure t goi Achieving consistency; for t fi The derivation can be obtained:
Figure BDA0004060282090000024
wherein d is ri Is the upper bound of unknown bounded disturbance and +.>
Figure BDA0004060282090000025
The next design objective is by design +.>
Figure BDA0004060282090000026
Thereby ensuring t fi Tend to be consistent; selecting integration sliding mode surface as +.>
Figure BDA0004060282090000027
t fi (0) At t fi Is used for the initial value of (a), c ij Is a coefficient;
the guidance law cooperative guidance law in the sight line direction is designed based on an integral sliding mode control method and is as follows:
Figure BDA0004060282090000028
wherein l i ＞0，0＜δ i < 1, adaptive parameter omega i The update law is as follows:
Figure BDA0004060282090000031
Figure BDA0004060282090000032
in the formula, 0 < k 1i ＜1,k 2i ＞0,k 3i ＞0,γ 0i ＞0，γ i ＞0，T 0 For the time constant, the value can be chosen as a sufficiently small positive constant, sign () is a sign function, then there is +.>
Figure BDA0004060282090000033
Can ensure the system state t fi Can be consistent in a limited time; to weakenBuffeting caused by symbol function in sliding mode guidance, introducing Sigmoid function instead of symbol function, sigmoid function can be expressed as +.>
Figure BDA0004060282090000034
Wherein a > 0, is a constant;
the collaborative guidance algorithm for designing the normal direction of the sight line based on the rapid nonsingular sliding mode control method is as follows:
Figure BDA0004060282090000035
Figure BDA0004060282090000036
k 4 ＝(k 41 ,k 42 ) And has k 1 ＞0，k 2 ＞0，k 3 ＞0k 41 ＞0，k 42 ＞0，ε＞0，μ＞0，/>
Figure BDA0004060282090000037
For the estimation of k, M i System matrix for ith aircraft, B i Input matrix for ith aircraft, x 1i ，x 2i Lambda is the angle error of sight 1 ，λ 2 Is constant and has lambda 1 ＞λ 2 ，1＜λ 2 ＜2，α＝diag(α 1 ,α 2 ) And β=diag (β 1 ,β 2 ) Is a parameter to be designed;
step 5: further, consider the uncertainty term caused by the maneuver of the target as interference, estimate it based on the hyper-distortion observer; for the purpose of
Figure BDA0004060282090000038
Unknown upper bound d of bounded disturbance in (2) ri Let the actual disturbance be D ri Design auxiliary variable y ri The method comprises the following steps:
Figure BDA0004060282090000039
wherein->
Figure BDA00040602820900000310
Definition t fi And y ri The error between is e ri ＝t fi -y ri The disturbance observer is designed to be +.>
Figure BDA00040602820900000311
Wherein->
Figure BDA00040602820900000312
Figure BDA00040602820900000313
p ri Are positive constants and satisfy the following conditions:
p ri ≥2，
Figure BDA00040602820900000314
wherein the method comprises the steps of
Figure BDA0004060282090000041
Figure BDA0004060282090000042
The designed observer can guarantee error e ri And->
Figure BDA0004060282090000043
Convergence to 0 within a finite time to estimate the actual disturbance, i.e., y i →t fi ，/>
Figure BDA0004060282090000044
A computer system, comprising: one or more processors, a computer-readable storage medium storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the methods described above.
A computer readable storage medium, characterized by storing computer executable instructions that when executed are configured to implement the method described above.
Advantageous effects
The invention is based on a self-adaptive sliding mode method and a super-twist observer, and completes the design of the cooperative guidance law aiming at the condition of simultaneous time and attack angle constraint. On the basis of a given bullet relative motion model, the design of a guidance law is divided into a sight line direction and a sight line normal direction, and the guidance instruction of the sight line direction is designed based on the multi-agent consistency principle, so that the remaining time of each aircraft can be converged, and the cooperative attack is realized; based on the self-adaptive sliding mode method, a guidance instruction of the normal direction of the sight line is designed, and the aircraft is ensured to attack the target at a given angle, so that the angle constraint is satisfied. Further, the target maneuver is regarded as interference, and the target maneuver is estimated and compensated based on the super-twist observer, so that the attack on the maneuver target is realized.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
Fig. 1 is a schematic ballistic diagram.
Fig. 2 is a schematic diagram of the remaining time.
FIG. 3 is a view angle rate
Figure BDA0004060282090000051
Response curves.
FIG. 4 is a view angle rate
Figure BDA0004060282090000052
Response curves.
FIG. 5 is a view angle θ L Response curves.
FIG. 6 is a view angle phi L Response curves.
Fig. 7 is a view direction acceleration command a LM Response curves.
FIG. 8 is a line of sight normal acceleration command a YM 。
FIG. 9 is a line of sight normal acceleration command a ZM 。
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
Aiming at singular and buffeting phenomena in sliding mode variable structure control, the invention designs a self-adaptive law with better performance, can improve the convergence speed of the sliding mode, and weakens the buffeting phenomena caused by a symbol function in sliding mode guidance; aiming at the problem that the sliding mode variable structure control is high in conservation of a large maneuvering target, the system conservation is reduced by combining the advantage of the super-twist observer that interference can be compensated in a limited time. For multi-aircraft collaborative attack problems with time constraints and angle constraints. According to the invention, the movement of the aircraft is divided into a sight line direction and a sight line normal direction, a guidance law in the sight line direction is designed based on an integral sliding mode method, the aircraft is guaranteed to hit a target, and further, a super-twist observer is designed under the condition of considering the large maneuvering movement of the target, so that generalized interference is compensated, and the effective tracking of a high maneuvering target is realized; and based on the rapid nonsingular sliding mode, the upward guidance instruction of the line-of-sight method is designed, so that the aircraft can finish cooperative attack at a specified angle.
According to the self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on the super-torsion observer, on the basis of establishing a bullet mesh relative motion model, the guidance law design is divided into a sight line direction and a sight line normal direction, and the sight line direction guidance instruction is designed based on a multi-agent consistency principle, so that the remaining time of each aircraft can be converged, and the sight line collaborative attack is guaranteed; based on the self-adaptive sliding mode method, a guidance instruction of the normal direction of the sight line is designed, and the aircraft is ensured to attack the target at a given angle, so that the angle constraint is satisfied. Finally, the effectiveness of the method is verified through simulation. The method comprises the following steps:
step 1, dividing the design of the guidance law into a sight line direction and a sight line normal line direction.
Step 2, defining the remaining time t in the terminal guidance stage of the aircraft go Is that
Figure BDA0004060282090000061
R、/>
Figure BDA0004060282090000062
The sight distance and its derivative;
step 3, converting the collaborative guidance law design problem into a design problem of a sight line direction and a sight line normal acceleration instruction, wherein the sight line direction is the same as the sight line direction
Figure BDA0004060282090000063
Ensure the remaining time t go To achieve a synergistic attack; normal u of line of sight i Ensuring that the target is hit at a given angle.
Step 4: first, a collaborative guidance law under nominal conditions (without taking into account target maneuvers) is designed. Let t be the current time, t goi (i=1, 2, …, n) is the remaining time of the i-th missile interception target, and the predicted time of the i-th missile interception target is t at time t fi ＝t+t goi And due to t goj -t goi ＝t fj -t fi So ensure t fi Tend to be consistent and can ensure t goi And achieving consistency. For t fi The derivation can be obtained:
Figure BDA0004060282090000064
wherein d is ri Is the upper bound of unknown bounded disturbance and +.>
Figure BDA0004060282090000065
The next design objective is by design +.>
Figure BDA0004060282090000066
Thereby ensuring t fi And tend to be consistent. Selecting an integral sliding die surface as
Figure BDA0004060282090000067
t fi (0) At t fi Initial value of c ij Is a coefficient. The guidance law cooperative guidance law in the sight line direction is designed based on an integral sliding mode control method and is as follows:
Figure BDA0004060282090000068
wherein l i ＞0，0＜δ i < 1, adaptive parameter omega i The update law is as follows:
Figure BDA0004060282090000069
Figure BDA0004060282090000071
in the formula, 0 < k 1i ＜1,k 2i ＞0,k 3i ＞0,γ 0i ＞0，γ i ＞0，T 0 For the time constant, the value can be chosen as a sufficiently small positive constant, sign () is a sign function, then there is +.>
Figure BDA0004060282090000072
Can ensure the system state t fi May tend to agree over a limited period of time. To attenuate buffeting phenomena caused by symbol functions in sliding mode guidance, a Sigmoid function is introduced instead of the symbol functions, which can be expressed as +.>
Figure BDA0004060282090000073
Wherein a > 0, is a constant;
the collaborative guidance algorithm for designing the normal direction of the sight line based on the rapid nonsingular sliding mode control method is as follows:
Figure BDA0004060282090000074
Figure BDA0004060282090000075
k 4 ＝(k 41 ,k 42 ) And has k 1 ＞0，k 2 ＞0，k 3 ＞0k 41 ＞0，k 42 ＞0，ε＞0，μ＞0，/>
Figure BDA0004060282090000076
For the estimation of k, M i System matrix for ith missile, B i Input matrix for ith missile, x 1i ，x 2i Lambda is the angle error of sight 1 ，λ 2 Is constant and has lambda 1 ＞λ 2 ，1＜λ 2 ＜2，α＝diag(α 1 ,α 2 ) And β=diag (β 1 ,β 2 ) Is a parameter to be designed.
Step 5: further, the uncertainty term caused by the maneuver of the target is considered as an interference, which is estimated based on the hyper-distortion observer. For the purpose of
Figure BDA0004060282090000077
Unknown upper bound d of bounded disturbance in (2) ri Let the actual disturbance be D ri Design auxiliary variable y ri The method comprises the following steps:
Figure BDA0004060282090000078
wherein->
Figure BDA0004060282090000079
Definition t fi And y ri The error between is e ri ＝t fi -y ri The disturbance observer is designed to be +.>
Figure BDA00040602820900000710
Wherein->
Figure BDA00040602820900000711
Figure BDA00040602820900000712
p ri Are positive constants and satisfy the following conditions:
p ri ≥2，
Figure BDA00040602820900000713
wherein the method comprises the steps of
Figure BDA0004060282090000081
Figure BDA0004060282090000082
The designed observer can guarantee error e ri And->
Figure BDA0004060282090000083
Convergence to 0 within a finite time to estimate the actual disturbance, i.e., y i →t fi ，/>
Figure BDA0004060282090000084
The guidance law in the line of sight direction shown in step 4 can ensure that the sliding mode surface converges within a limited time, i.e. the residual time of multiple aircrafts tends to be consistent within a limited time, for systems with interference and limited first derivative of interference, i.e. a constant d exists ri And m ri So that |D ri |≤d ri ，
Figure BDA0004060282090000085
Wherein D is ri For interference define
Figure BDA0004060282090000086
Figure BDA0004060282090000087
Defining Lyapunov function as
Figure BDA0004060282090000088
For V 1 Can obtain the derivation
Figure BDA0004060282090000089
As can be seen from the above description,
Figure BDA00040602820900000811
and delta are bounded, and thus omega can be obtained i And gamma i Is bounded; according to the Lassel invariant principle, it is possible to obtain a signal which can be used for a finite time t 0 Inner part (S)>
Figure BDA00040602820900000810
For t > t 0 Can obtain
Figure BDA0004060282090000091
Definition of Lyapunov function V 2 Is that
Figure BDA0004060282090000092
For V 2 Can obtain the derivation
Figure BDA0004060282090000093
In summary, the slip-form surface can converge within a limited time.
Aiming at a kinematic equation of a line-of-sight normal of a multi-aircraft attack, if the guidance law in the direction of the line-of-sight normal meets the step 4, the sliding mode surface converges to the following area in a limited time:
|s j |≤ε j ＝min{ε 1j ,ε 2j } (2)
Figure BDA0004060282090000094
wherein s is j The j-th component of the slide plane is represented, and ζ is a normal number; x is x 1i And x 2i Converging to the following areas:
Figure BDA0004060282090000095
wherein x is 1i(j) And x 2i(j) Represents x 1i And x 2i Is the j-th component of (c).
Consider the case where 3 aircraft are simultaneously attacking a maneuver target, with the aircraft initial parameters shown in Table 1.
Table 1 aircraft initial parameters
Figure BDA0004060282090000101
The initial target position is (0, 0) m, and the component of the initial target speed under the first elastic visual line coordinate system is (75,279.9,77.65) m/s.
Guidance law in line of sight
Figure BDA0004060282090000102
The parameters of (a) are selected as follows: l (L) i ＝15,δ i =0.5 and, k 1i ＝0.9,k 2i ＝0.01,k 3i ＝1.2,γ 0i ＝0.3,T 0 ＝0.05。
Guidance law u in the normal direction of line of sight 1i The parameters in (i=1, 2, 3) are selected as follows: k (k) i ＝1,α i ＝2,c i ＝0.7，p i ＝5，η i ＝1，r i ＝0.5，β 1 ＝0.08,β 1 ＝0.03,β 1 ＝0.05，
Figure BDA0004060282090000103
a i ＝0.8，γ 0i ＝3.5，γ 00i ＝4.2,γ 1i =0.1 and γ 2i ＝0.99。
Fig. 1 shows the trajectory of the bullet, fig. 2 shows the remaining time of three aircraft, from which it can be seen that the remaining time of three aircraft eventually reaches unity, and fig. 3 and 4 are graphs of the line of sight angle over time, from which it can be seen that the line of sight angle rate of three aircraft converges to zero in a limited time. Fig. 5 and 6 show a plot of line of sight over time, from which it can be seen that three aircraft each converge to a desired line of sight. Fig. 7, 8 and 9 show the acceleration command of the aircraft, which is the acceleration command in the line-of-sight direction, and it can be seen that the acceleration command in the line-of-sight direction has saturation in the first five seconds from the start of terminal guidance, because attack needs to be performed at a specified angle, guidance law in the line-of-sight direction needs to ensure that the line-of-sight angle converges to a desired value, but that the saturation value is within a reasonable range, and that the saturation phenomenon converges quickly.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made without departing from the spirit and scope of the invention.

Claims (3)

1. A self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on a super-torsion observer is characterized by comprising the following steps:
step 1: dividing the design of the guidance law into a sight line direction and a sight line normal line direction;
step 2: during the terminal guidance phase of the aircraft, the remaining time t is defined go Is that
Figure FDA0004060282080000011
Wherein R, (-) ->
Figure FDA0004060282080000012
The sight distance and its derivative;
step 3: converting the collaborative guidance law design problem into a design problem of a sight direction and a sight normal acceleration instruction, and converting the sight direction guidance law into a design problem of a sight normal acceleration instruction
Figure FDA0004060282080000013
Ensure the remaining time t go To achieve a synergistic attack; line-of-sight normal guidance law u i Ensuring that the target is hit at a given angle;
step 4: first, a cooperative guidance law is designed under nominal conditions, i.e. without taking into account target maneuvers
Let t be the current time, t goi Intercepting the target for the i-th aircraft for the remaining time, i=1, 2, …, n; then the predicted time of the interception target of the ith aircraft is t at the time t fi ＝t+t goi And due to t goj -t goi ＝t fj -t fi So ensure t fi Tend to be consistent and can ensure t goi Achieving consistency; for t fi The derivation can be obtained:
Figure FDA0004060282080000014
wherein d is ri Is the upper bound of unknown bounded disturbance, and
Figure FDA0004060282080000015
the next design objective is by design +.>
Figure FDA0004060282080000016
Thereby ensuring t fi Tend to be consistent; selecting an integral sliding die surface as
Figure FDA0004060282080000017
t fi (0) At t fi Initial value of c ij Is a coefficient;
the guidance law cooperative guidance law in the sight line direction is designed based on an integral sliding mode control method and is as follows:
Figure FDA0004060282080000018
wherein l i ＞0，0＜δ i < 1, adaptive parameter omega i The update law is as follows:
Figure FDA0004060282080000019
Figure FDA00040602820800000110
in the formula, 0 < k 1i ＜1,k 2i ＞0,k 3i ＞0,γ 0i ＞0，γ i ＞0，T 0 For the time constant, the value can be chosen as a sufficiently small positive constant, sign () is a sign function, then there is +.>
Figure FDA0004060282080000021
Can ensure the system state t fi Can be consistent in a limited time; to attenuate buffeting phenomena caused by symbol functions in sliding mode guidance, a Sigmoid function is introduced instead of the symbol functions, which can be expressed as +.>
Figure FDA0004060282080000022
Wherein a > 0, is a constant;
the cooperative guidance law of the normal direction of the sight line is designed based on a rapid nonsingular sliding mode control method and is as follows:
Figure FDA0004060282080000023
Figure FDA0004060282080000024
k 4 ＝(k 41 ,k 42 ) And has k 1 ＞0，k 2 ＞0，k 3 ＞0k 41 ＞0，k 42 ＞0，ε＞0，μ＞0，/>
Figure FDA0004060282080000025
For the estimation of k, M i System matrix for ith aircraft, B i Input matrix for ith aircraft, x 1i ，x 2i Lambda is the angle error of sight 1 ，λ 2 Is constant and has lambda 1 ＞λ 2 ，1＜λ 2 ＜2，α＝diag(α 1 ,α 2 ) And β=diag (β 1 ,β 2 ) Is a parameter to be designed;
step 5: further, consider the uncertainty term caused by the maneuver of the target as interference, estimate it based on the hyper-distortion observer; for the purpose of
Figure FDA0004060282080000026
Unknown upper bound d of bounded disturbance in (2) ri Let the actual disturbance be D ri Design auxiliary variable y ri The method comprises the following steps:
Figure FDA0004060282080000027
wherein->
Figure FDA0004060282080000028
Definition t fi And y ri The error between is e ri ＝t fi -y ri The disturbance observer is designed to be +.>
Figure FDA0004060282080000029
Wherein->
Figure FDA00040602820800000210
Figure FDA00040602820800000211
p ri Are positive constants and satisfy the following conditions:
p ri ≥2，
Figure FDA00040602820800000212
wherein the method comprises the steps of
Figure FDA00040602820800000213
Figure FDA0004060282080000031
The designed observer can guarantee error e ri And->
Figure FDA0004060282080000032
Convergence to 0 within a finite time to estimate the actual disturbance, i.e., y i →t fi ，
Figure FDA0004060282080000033
2. A computer system, comprising: one or more processors, a computer-readable storage medium storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of claim 1.
3. A computer readable storage medium, characterized by storing computer executable instructions that, when executed, are adapted to implement the method of claim 1.
CN202310055120.0A 2023-02-03 2023-02-03 Self-adaptive sliding mode multi-aircraft collaborative terminal guidance law design method based on super-twist observer Pending CN116401752A (en)

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CN117193336A (en) * 2023-09-12 2023-12-08 中国船舶集团有限公司第七一九研究所 Underwater vehicle cooperative guidance method based on time and angle constraint
CN117193336B (en) * 2023-09-12 2024-03-22 中国船舶集团有限公司第七一九研究所 Underwater vehicle cooperative guidance method based on time and angle constraint

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