CN108628329B - Anti-interference attitude control method for spacecraft for measuring and controlling replay attack of link - Google Patents

Anti-interference attitude control method for spacecraft for measuring and controlling replay attack of link Download PDF

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CN108628329B
CN108628329B CN201810225313.5A CN201810225313A CN108628329B CN 108628329 B CN108628329 B CN 108628329B CN 201810225313 A CN201810225313 A CN 201810225313A CN 108628329 B CN108628329 B CN 108628329B
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spacecraft
state
replay attack
attitude control
interference
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CN108628329A (en
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乔建忠
谷亚培
郭雷
李文硕
徐健伟
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Beihang University
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Abstract

The invention relates to an anti-interference attitude control method for a spacecraft, which measures and controls a link to be attacked by playback. The method aims at the problem that a measurement and control link between a spacecraft and a ground system is attacked by playback and the spacecraft is interfered by the environment; firstly, establishing a spacecraft attitude control system model for observing and controlling a playback attack on a link and a spacecraft interference by environment; secondly, designing a full-order observer to observe an augmented system state formed by the attitude control system state and the interference, and constructing a composite controller by utilizing observer information; thirdly, in order to provide a uniform framework for analyzing the replay attack, a virtual system and a virtual control input are constructed aiming at the augmentation system, and then whether the spacecraft attitude control system can detect the replay attack is checked; and finally, under the condition that the attitude control system cannot detect replay attack, designing a controller containing a watermark to construct an anti-interference attitude control method for the spacecraft for measuring and controlling the replay attack of the link. The invention is suitable for high-precision and high-reliability control of the attitude of the spacecraft.

Description

Anti-interference attitude control method for spacecraft for measuring and controlling replay attack of link
Technical Field
The invention relates to an anti-interference attitude control method for a spacecraft with a measurement and control link under replay attack, which can solve the problem of high-precision and high-reliability control of an attitude system with a spacecraft measurement and control link under replay attack in an interference environment.
Background
With the development of aerospace technology, more and more precise aerospace missions require a spacecraft attitude control system to have higher control precision. However, on one hand, due to the complex space environment, the spacecraft is interfered by external environments such as solar radiation torque, gravity gradient torque, magnetic interference torque and the like, and the interference torque can cause the attitude of the spacecraft to generate disturbance; on the other hand, as the outer space gradually becomes the highest strategic point of maintaining national security and vital interests of countries in the world, the space countermeasure has become an important strategic means of the country, the spacecraft is used as a main attack object in the space countermeasure, and a measurement and control link between the spacecraft and the ground system is easily attacked by replay of enemies, so that the ground system receives wrong measurement information, the ground system makes wrong control decisions, and the task of the spacecraft fails and even crashes. The attack process of the replay attack is mainly divided into three steps, wherein in the first step, the historical value of the past measurement information is recorded by using a network monitoring method; secondly, capturing and erasing the current measurement information; and thirdly, replacing the current value of the measurement information with the historical value of the measurement information. Therefore, the method for controlling the anti-interference attitude of the spacecraft under the replay attack has important significance.
The maximum error detection in the conventional false information detection technology is widely applied to a static model system. Both chinese patent application No. 201310237995.9 and chinese patent application No. 201410059572.7 employ a filter residual-chi-square detection method to detect the maximum error. However, when an attacker has some a priori knowledge of the structure of the system, the attacker can inject deviations in a specific direction into the system and does not cause a change in the error. Similarly, if the attacker plays back the historical value of the measurement information to my party, under certain conditions, the error does not change, and the system cannot detect the attack. The chinese patent application No. 201510652179.3 proposes a satellite navigation forwarding type spoofing attack defense method and apparatus, but the forwarding type spoofing attack is different from the replay attack, the forwarding type spoofing attack injects a history value of measurement information to our party, but does not erase a real signal, the patent selects a signal emitting a world maximum signal as a real signal, and in the replay attack, an enemy not only plays back the history value of the measurement information to our party, but also erases the real measurement information, so that the system cannot obtain the real measurement information; the Chinese patent application number 201010042089.X provides a replay attack prevention system for an industrial wireless network, but a third-party detection module is introduced into the system, so that the complexity of a control system is increased, and the rapidity of the control system is influenced. In summary, the existing method cannot solve the problem of control of a system under a replay attack in an interference environment, and high-precision and high-reliability control of the attitude of the spacecraft is achieved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problem that the existing control system is difficult to realize the high-precision control of an attitude system in which a spacecraft measurement and control link is attacked by playback in an interference environment, the anti-interference attitude control method of the spacecraft in which the measurement and control link is attacked by playback is designed, and the method has the advantages of strong anti-interference performance and high autonomy.
The technical scheme adopted by the invention for solving the technical problems is as follows: an anti-interference attitude control method of a spacecraft with a measurement and control link under replay attack aims at the attitude control problem of the spacecraft with the measurement and control link under replay attack and containing environmental interference between the spacecraft and a ground system; firstly, establishing a spacecraft attitude control system model for observing and controlling a link under playback attack and a platform under environmental interference; secondly, designing a full-order observer to observe an augmentation system consisting of the state and the interference of the spacecraft attitude control system, and constructing a composite controller by utilizing observer information; thirdly, in order to provide a uniform framework for analyzing replay attack, a virtual system and a virtual control input are constructed for the augmentation system, and whether the spacecraft attitude control system can detect the replay attack is further checked; and finally, under the condition that the spacecraft attitude control system cannot detect replay attack, designing a controller containing a watermark mark, and constructing the anti-interference attitude control method for the spacecraft, which is used for measuring and controlling the link to be attacked by the replay attack. The specific implementation steps are as follows:
firstly, establishing a spacecraft attitude control system model sigma for measuring and controlling playback attack of a link and environmental interference of a platform1：
Figure GDA0001767320500000021
Wherein x is [ x ]1x2]TIn order to be in the state of the system,
Figure GDA0001767320500000022
is the time derivative of the state of the system,
Figure GDA0001767320500000023
theta and psi are respectively the rolling angle, the pitch angle and the yaw angle of the spacecraft,
Figure GDA0001767320500000024
roll angular velocity, pitch angular velocity and yaw angular velocity, respectively, y is a measurement output, u ═ u [ u ]1u2... un]TFor control input, uiFor the ith control input, i is 1,2,3, y' is a replay attack signal, d is a modelable environmental disturbance, and the requirements are met
Figure GDA0001767320500000025
α is normal value, C0For a matrix of coefficients of appropriate dimensions, the matrix of coefficients
Figure GDA0001767320500000026
J is the moment of inertia of the spacecraft, J-1Is an inverse matrix of the moment of inertia matrix J, 03×3And I3×3Respectively representing a 3 < th > order zero matrix and a 3 < th > order identity matrix, a non-linear matrix
Figure GDA0001767320500000027
In the form of a known non-linear function,
Figure GDA0001767320500000028
is a non-linear matrix
Figure GDA0001767320500000029
With respect to the derivative of time t, ω is the absolute angular velocity of the attitude, ω ═ ωxωyωz]T，ωx、ωy、ωzThe absolute angular velocities of the roll channel, the pitch channel and the yaw channel are respectively,
Figure GDA0001767320500000031
external environmental disturbance d can be described by the following external model ∑2：
Figure GDA0001767320500000032
Where ω is the state of the external model,
Figure GDA0001767320500000033
for the time derivative of the external model state, a coefficient matrix
Figure GDA0001767320500000034
V is an adaptive constant known matrix, omega0Is a known constant.
And secondly, designing a full-order observer to observe an augmentation system consisting of the system state and the interference, and constructing a composite controller by using observer information, wherein the method is specifically realized as follows:
define the augmented state z ═ x ω]TThen system Σ1Can be converted into an augmentation system ∑ as follows3In the form of:
Figure GDA0001767320500000035
wherein,
Figure GDA0001767320500000036
for time derivatives of the augmented state z, a matrix of coefficients
Figure GDA0001767320500000037
Figure GDA0001767320500000038
E＝[I3×303×3]T；
Based on augmentation system sigma3Designed full-order observer sigma4Comprises the following steps:
Figure GDA0001767320500000039
wherein L is the gain of the full-order observer,
Figure GDA00017673205000000310
in order to estimate the augmented state z,
Figure GDA00017673205000000311
is an estimate of the state x of the system,
Figure GDA00017673205000000312
for external model ∑2An estimate of the state omega is obtained by,
Figure GDA00017673205000000313
is composed of
Figure GDA00017673205000000314
The time derivative of (a) of (b),
Figure GDA00017673205000000315
an estimate of y is output for the measurement.
According to a full-order observer sigma4Estimation of the augmented state z
Figure GDA00017673205000000316
Design spacecraft anti-interference attitude controller sigma5Comprises the following steps:
Figure GDA00017673205000000317
where K is the controller gain to be designed,
Figure GDA00017673205000000318
for the estimation of the externally modelable disturbance d,
Figure GDA00017673205000000319
K1＝[K03×2]，V1＝[03×6V]。
based on the linear system separation principle, the gain L of the full-order observer and the gain K of the controller are respectively solved through pole allocation:
|sI-(A-LC)|＝(s+ω1)n+2
|sI-(A0+B0K)|＝(s+ω2)n
where s is a complex variable, I is a unity matrix of appropriate dimensions, n > 0 is the order of the system, | denotes the determinant for solving the square matrix, ω1、ω2Given a constant, the bandwidth of the system is represented.
Anti-interference attitude controller sigma of spacecraft5Into a full-order observer ∑4In this way, an augmented state estimation value can be obtained
Figure GDA00017673205000000417
The dynamic equation of (a) is:
Figure GDA0001767320500000041
thirdly, in order to provide a unified framework for analyzing the replay attack, a virtual system and a virtual control input are constructed for the augmentation system, and whether the system can detect the replay attack is further checked, which is specifically realized as follows:
in order to provide a uniform framework for analyzing the playback disturbances y ', the playback disturbances y' are treated as a virtual system Σ6The output of (1):
Figure GDA0001767320500000042
wherein z' is a virtual system ∑4In the state of being enlarged, the light-emitting element,
Figure GDA0001767320500000043
is the time derivative of z ', u' is the virtual system ∑4To the control input of (2).
For constructed virtual system ∑6The design of the full-order observer is sigma7：
Figure GDA0001767320500000044
Wherein,
Figure GDA0001767320500000045
for the estimation of the virtual system augmented state z',
Figure GDA0001767320500000046
an estimate of y 'is output for the virtual system measurements, and u' is the control input for the virtual system.
According to a full-order observer sigma7Estimating virtual system states, designing virtual system control inputs u' Σ8Comprises the following steps:
Figure GDA0001767320500000047
wherein
Figure GDA0001767320500000048
Is an estimate of the virtual system state x',
Figure GDA0001767320500000049
is an estimate of the external environmental disturbance d' in the virtual system,
Figure GDA00017673205000000410
Figure GDA00017673205000000411
is an estimated value of the external environment interference model state omega' in the virtual system.
Inputting virtual system control into ∑8Into a full-order observer ∑7In this way, the estimated value of the virtual system expansion state can be obtained
Figure GDA00017673205000000412
The dynamic equation of (a) is:
Figure GDA00017673205000000413
combining augmented state estimates
Figure GDA00017673205000000414
And virtual system augmented state estimate
Figure GDA00017673205000000415
The dynamic equation of (c) can be found:
Figure GDA00017673205000000416
by formula ∑9It can be seen that when the matrix A is used1＝A+B(K1-V1) When the characteristic roots of + LC all have negative real parts, the system cannot detect replay attacks.
And fourthly, under the condition that the system can not detect the playback attack, designing a controller containing the watermark as follows:
Figure GDA0001767320500000051
wherein K is the gain of the controller,
Figure GDA0001767320500000052
is an estimate of the state x of the system,
Figure GDA0001767320500000053
ζ represents the watermark sign and is a constant value, which is an estimate of the external environmental disturbance d.
Defining residual signals
Figure GDA0001767320500000054
The residual evaluation function/is defined as follows:
Figure GDA0001767320500000055
when the system is not under the replay attack, then
Figure GDA0001767320500000056
γ represents a threshold value, which is a known constant.
Therefore, whether the system is under a replay attack can be judged by the following logic:
Figure GDA0001767320500000057
and once the observation and control link of the system is detected to be attacked by playback, the spacecraft is switched to the own attitude control system to adjust the attitude. Meanwhile, the replay attack is continuously detected, and the ground system is used for attitude control after the enemy stops the replay attack.
Compared with the prior art, the invention has the advantages that:
the invention relates to an anti-interference attitude control method of a spacecraft, aiming at the problems that the existing spacecraft attitude control system can not realize high-precision anti-interference and high-reliability control of the spacecraft attitude system under the condition that a measurement and control link between the spacecraft and a ground control system is subjected to playback attack, a full-order observer is designed to estimate and compensate the external environment interference, and a controller containing a watermark mark is designed to detect the playback attack under the condition that the spacecraft attitude control system can not detect the playback attack.
Drawings
Fig. 1 is an anti-interference attitude control method for a spacecraft, which measures and controls a link to be attacked by replay.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The invention relates to an anti-interference attitude control method for a spacecraft with a measurement and control link being attacked by replay, which comprises the following design steps: firstly, establishing a spacecraft attitude control system model for observing and controlling a link under playback attack and a platform under environmental interference; secondly, designing a full-order observer to observe an augmentation system consisting of the state and the interference of the spacecraft attitude control system, and constructing a composite controller by utilizing observer information; thirdly, in order to provide a uniform framework for analyzing replay attack, a virtual system and a virtual control input are constructed for the augmentation system, and whether the spacecraft attitude control system can detect the replay attack is further checked; and finally, under the condition that the spacecraft attitude control system cannot detect replay attack, designing a controller containing a watermark mark, and constructing the anti-interference attitude control method for the spacecraft, which is used for measuring and controlling the link to be attacked by the replay attack. The specific implementation steps are as follows:
firstly, establishing a spacecraft attitude control system model sigma for measuring and controlling playback attack of a link and environmental interference of a platform1：
Figure GDA0001767320500000061
Wherein x is [ x ]1x2]TIn order to be in the state of the system,
Figure GDA0001767320500000062
is the time derivative of the state of the system,
Figure GDA0001767320500000063
theta and psi are respectively the rolling angle, the pitch angle and the yaw angle of the spacecraft, the initial values are respectively 0.003rad, 0.01rad and 0.03rad,
Figure GDA0001767320500000064
roll angular velocity, pitch angular velocity and yaw angular velocity, respectively, the initial values are all 0rad/s, y is the measurement output, u ═ u [ [ u [ ]1u2... un]TFor control input, uiFor the ith control input, i is 1,2,3, y' is a replay attack signal, d is a modelable environmental disturbance and takes a value of
Figure GDA0001767320500000065
Coefficient matrix
Figure GDA0001767320500000066
Coefficient matrix
Figure GDA0001767320500000067
J isThe rotational inertia of the spacecraft is taken as
Figure GDA0001767320500000068
J-1Is an inverse matrix of the moment of inertia matrix J, 03×3And I3×3Respectively representing a 3 < th > order zero matrix and a 3 < th > order identity matrix, a non-linear matrix
Figure GDA0001767320500000069
For a known non-linear function, the specific expression is:
Figure GDA00017673205000000610
ω3constant angular velocity of the track, 0.0012rad/s, LboThe method comprises the following steps of representing a coordinate transformation matrix from a flexible spacecraft orbit coordinate system to a body coordinate system, wherein the specific expression is as follows:
Figure GDA0001767320500000071
Figure GDA0001767320500000072
is a non-linear matrix
Figure GDA0001767320500000073
With respect to the derivative of time t, ω is the absolute angular velocity of the attitude, ω ═ ωxωyωz]T，ωx、ωy、ωzThe absolute angular velocities of the roll channel, the pitch channel and the yaw channel are respectively,
Figure GDA0001767320500000074
external environmental disturbance d can be described by the following external model ∑2：
Figure GDA0001767320500000075
Wherein,ω is the state of the external model,
Figure GDA0001767320500000076
for the time derivative of the external model state, a coefficient matrix
Figure GDA0001767320500000077
And secondly, converting the control system model into an augmentation system and constructing a virtual system, so as to provide a uniform framework for analyzing replay attacks, and specifically realizing the following steps:
define the augmented state z ═ x ω]TThen system Σ1Can be converted into an augmentation system ∑ as follows3In the form of:
Figure GDA0001767320500000078
wherein,
Figure GDA0001767320500000079
for time derivatives of the augmented state z, a matrix of coefficients
Figure GDA00017673205000000710
Figure GDA00017673205000000711
E＝[I3×303×3]T；
Based on augmentation system sigma3Designed full-order observer sigma4Comprises the following steps:
Figure GDA00017673205000000712
wherein L is the gain of the full-order observer,
Figure GDA00017673205000000713
in order to estimate the augmented state z,
Figure GDA00017673205000000714
is an estimate of the state x of the system,
Figure GDA00017673205000000715
for external model ∑2An estimate of the state omega is obtained by,
Figure GDA00017673205000000716
is composed of
Figure GDA00017673205000000717
The time derivative of (a) of (b),
Figure GDA00017673205000000718
an estimate of y is output for the measurement.
According to a full-order observer sigma4Estimation of the augmented state z
Figure GDA0001767320500000081
Design spacecraft anti-interference attitude controller sigma5Comprises the following steps:
Figure GDA0001767320500000082
where K is the controller gain to be designed,
Figure GDA0001767320500000083
for the estimation of the externally modelable disturbance d,
Figure GDA0001767320500000084
K1＝[K03×2]，V1＝[03×6V]。
the gain L of the full-order observer and the gain K of the controller respectively take values as follows:
Figure GDA0001767320500000085
Figure GDA0001767320500000086
spacecraftAnti-interference attitude controller sigma5Into a full-order observer ∑4In this way, an augmented state estimation value can be obtained
Figure GDA0001767320500000087
The dynamic equation of (a) is:
Figure GDA0001767320500000088
thirdly, in order to provide a unified framework for analyzing the replay attack, a virtual system and a virtual control input are constructed for the augmentation system, and whether the system can detect the replay attack is further checked, which is specifically realized as follows:
in order to provide a uniform framework for analyzing the playback disturbances y ', the playback disturbances y' are treated as a virtual system Σ6The output of (1):
Figure GDA0001767320500000089
wherein z' is a virtual system ∑4In the state of being enlarged, the light-emitting element,
Figure GDA00017673205000000810
is the time derivative of z ', u' is the virtual system ∑4To the control input of (2).
For constructed virtual system ∑6The design of the full-order observer is sigma7：
Figure GDA00017673205000000811
Wherein,
Figure GDA00017673205000000812
for the estimation of the virtual system augmented state z',
Figure GDA00017673205000000813
an estimate of y 'is output for the virtual system measurements, and u' is the control input for the virtual system.
According to a full-order observer sigma7Estimating virtual system states, designing virtual system control inputs u' Σ8Comprises the following steps:
Figure GDA0001767320500000091
wherein
Figure GDA0001767320500000092
Is an estimate of the virtual system state x',
Figure GDA0001767320500000093
is an estimate of the external environmental disturbance d' in the virtual system,
Figure GDA0001767320500000094
Figure GDA0001767320500000095
is an estimated value of the external environment interference model state omega' in the virtual system.
Inputting virtual system control into ∑8Into a full-order observer ∑7In this way, the estimated value of the virtual system expansion state can be obtained
Figure GDA0001767320500000096
The dynamic equation of (a) is:
Figure GDA0001767320500000097
combining augmented state estimates
Figure GDA0001767320500000098
And virtual system augmented state estimate
Figure GDA0001767320500000099
The dynamic equation of (c) can be found:
Figure GDA00017673205000000910
by formula ∑9It can be seen that when the matrix A is used1＝A+B(K1-V1) When the characteristic roots of + LC all have negative real parts, the system cannot detect replay attacks.
And fourthly, under the condition that the system can not detect the playback attack, designing a controller containing the watermark as follows:
Figure GDA00017673205000000911
wherein K is the gain of the controller,
Figure GDA00017673205000000912
is an estimate of the state x of the system,
Figure GDA00017673205000000913
ζ represents a watermark marker for the estimated value of the external environmental disturbance d, and the simulated value according to this embodiment is ζ ═ 0.020.020.02]T。
Defining residual signals
Figure GDA00017673205000000914
The residual evaluation function/is defined as follows:
Figure GDA00017673205000000915
when the system is not under the replay attack, then
Figure GDA00017673205000000916
γ represents a threshold value, and the value of the present embodiment is γ is 6 × 10-6。
Therefore, whether the system is under a replay attack can be judged by the following logic:
Figure GDA00017673205000000917
and once the observation and control link of the system is detected to be attacked by playback, the spacecraft is switched to the own attitude control system to adjust the attitude. Meanwhile, the replay attack is continuously detected, and the ground system is used for attitude control after the enemy stops the replay attack.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (3)

1. An anti-interference attitude control method for a spacecraft for measuring and controlling a link under replay attack is characterized by comprising the following steps: the method comprises the following steps:
firstly, establishing a spacecraft attitude control system model for observing and controlling a link under playback attack and a platform under environmental interference;
secondly, designing a full-order observer to observe an augmentation system consisting of the state and the interference of the spacecraft attitude control system, and constructing a composite controller by utilizing observer information;
thirdly, in order to provide a uniform framework for analyzing replay attack, a virtual system and virtual control input are constructed aiming at the augmentation system, and whether the spacecraft attitude control system can detect the replay attack is further checked;
the third step is specifically realized as follows:
in order to provide a uniform framework for analyzing the playback disturbances y ', the playback disturbances y' are treated as a virtual system Σ6The output of (1):
Figure FDA0002444215820000011
wherein z' is a virtual system ∑4In the state of being enlarged, the light-emitting element,
Figure FDA00024442158200000115
is the time derivative of z ', u' is the virtual system ∑4A control input of (2);
for constructed virtual system ∑6The design of the full-order observer is sigma7：
Figure FDA0002444215820000012
Wherein,
Figure FDA0002444215820000013
for the estimation of the virtual system augmented state z',
Figure FDA0002444215820000014
outputting an estimated value of y 'for the virtual system measurement, and u' is a control input of the virtual system;
according to a full-order observer sigma7Estimating virtual system states, designing virtual system control inputs u' Σ8Comprises the following steps:
Figure FDA0002444215820000015
wherein,
Figure FDA0002444215820000016
is an estimate of the virtual system state x',
Figure FDA0002444215820000017
is an estimate of the external environmental disturbance d' in the virtual system,
Figure FDA0002444215820000018
Figure FDA0002444215820000019
an estimated value of an external environment interference model state omega' in the virtual system is obtained;
inputting virtual system control into ∑8Into a full-order observer ∑7In this way, the estimated value of the virtual system expansion state can be obtained
Figure FDA00024442158200000110
The dynamic equation of (a) is:
Figure FDA00024442158200000111
combining augmented state estimates
Figure FDA00024442158200000112
And virtual system augmented state estimate
Figure FDA00024442158200000113
The dynamic equation of (c) can be found:
Figure FDA00024442158200000114
by formula ∑9It can be seen that when the matrix A is used1＝A+B(K1-V1) When the characteristic roots of the + LC have negative real parts, the system cannot detect replay attack;
fourthly, under the condition that the spacecraft attitude control system cannot detect replay attack, designing a controller containing a watermark to construct an anti-interference attitude control method for the spacecraft, which measures and controls the link to be attacked by the replay attack;
and in the fourth step, under the condition that the system can not detect the playback attack, designing a controller containing the watermark as follows:
Figure FDA0002444215820000021
wherein K is the gain of the controller,
Figure FDA0002444215820000022
is an estimate of the state x of the system,
Figure FDA0002444215820000023
zeta represents watermark sign and is a constant value;
defining residual signals
Figure FDA0002444215820000024
The residual evaluation function/is defined as follows:
Figure FDA0002444215820000025
when the system is not under the replay attack, then
Figure FDA0002444215820000026
γ represents a threshold value, which is a known constant;
therefore, whether the system is under a replay attack can be judged by the following logic:
Figure FDA0002444215820000027
once the measurement and control link of the system is detected to be attacked by replay, the spacecraft is switched to the own attitude control system to adjust the attitude, meanwhile, the replay attack is continuously detected, and the ground system is used for attitude control after the enemy stops the replay attack.
2. The anti-interference attitude control method for the spacecraft for monitoring the replay attack of the link according to claim 1, wherein the attitude control method comprises the following steps: in the first step, a spacecraft attitude control system model sigma for measuring and controlling playback attack of a link and environmental interference of a platform is established1：
Figure FDA0002444215820000028
Wherein x is [ x ]1x2]TIn order to be in the state of the system,
Figure FDA0002444215820000029
Figure FDA00024442158200000210
is the time derivative of the state of the system,
Figure FDA00024442158200000211
theta and psi are respectively the rolling angle, the pitch angle and the yaw angle of the spacecraft,
Figure FDA00024442158200000212
roll angular velocity, pitch angular velocity and yaw angular velocity, respectively, y is a measurement output, u ═ u [ u ]1u2... un]TFor control input, uiFor the ith control input, i is 1,2,3, y' is a replay attack signal, d is a modelable environmental disturbance, and the requirements are met
Figure FDA00024442158200000213
α is normal value, C0For a matrix of coefficients of appropriate dimensions, the matrix of coefficients
Figure FDA00024442158200000214
J is the moment of inertia of the spacecraft, J-1Is an inverse matrix of the moment of inertia matrix J, 03×3And I3×3Respectively representing a 3 < th > order zero matrix and a 3 < th > order identity matrix, a non-linear matrix
Figure FDA0002444215820000031
In the form of a known non-linear function,
Figure FDA0002444215820000032
is a non-linear matrix
Figure FDA0002444215820000033
With respect to the derivative of time t, ω is the absolute angular velocity of the attitude, ω ═ ωxωyωz]T，ωx、ωy、ωzThe absolute angular velocities of the roll channel, the pitch channel and the yaw channel are respectively,
Figure FDA0002444215820000034
external environmental disturbance d can be described by the following external model ∑2：
Figure FDA0002444215820000035
Where ω is the state of the external model,
Figure FDA0002444215820000036
for the time derivative of the external model state, a coefficient matrix
Figure FDA0002444215820000037
V is an adaptive constant known matrix, omega0Is a known constant.
3. The anti-interference attitude control method for the spacecraft for monitoring the replay attack of the link according to claim 1, wherein the attitude control method comprises the following steps: the second step is specifically realized as follows:
define the augmented state z ═ x ω]TThen system Σ1Can be converted into an augmentation system ∑ as follows3In the form of:
Figure FDA0002444215820000038
wherein,
Figure FDA00024442158200000321
for time derivatives of the augmented state z, a matrix of coefficients
Figure FDA0002444215820000039
Figure FDA00024442158200000310
E＝[I3×303×3]T；
Based on augmentation system sigma3Designed full-order observer sigma4Comprises the following steps:
Figure FDA00024442158200000311
wherein L is the gain of the full-order observer,
Figure FDA00024442158200000312
in order to estimate the augmented state z,
Figure FDA00024442158200000313
Figure FDA00024442158200000314
is an estimate of the state x of the system,
Figure FDA00024442158200000315
for external model ∑2An estimate of the state omega is obtained by,
Figure FDA00024442158200000316
is composed of
Figure FDA00024442158200000317
The time derivative of (a) of (b),
Figure FDA00024442158200000318
outputting an estimate of y for the measurement;
according to a full-order observer sigma4Estimation of the augmented state z
Figure FDA00024442158200000319
Design spacecraft anti-interference attitude controller sigma5Comprises the following steps:
Figure FDA00024442158200000320
where K is the controller gain to be designed,
Figure FDA0002444215820000041
for the estimation of the externally modelable disturbance d,
Figure FDA0002444215820000042
K1＝[K03×2]，V1＝[03×6V]；
based on the linear system separation principle, the gain L of the full-order observer and the gain K of the controller are respectively solved through pole allocation:
|sI-(A-LC)|＝(s+ω1)n+2
|sI-(A0+B0K)|＝(s+ω2)n
where s is a complex variable, I is a unity matrix of appropriate dimensions, n > 0 is the order of the system, | denotes the determinant for solving the square matrix, ω1、ω2A given constant, representing the bandwidth of the system;
anti-interference attitude controller sigma of spacecraft5Into a full-order observer ∑4In this way, an augmented state estimation value can be obtained
Figure FDA0002444215820000043
The dynamic equation of (a) is:
Figure FDA0002444215820000044
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