CN113162804B - Binary synchronization method of symbol network under joint influence of spoofing attack and pulse interference - Google Patents

Binary synchronization method of symbol network under joint influence of spoofing attack and pulse interference Download PDF

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CN113162804B
CN113162804B CN202110429942.1A CN202110429942A CN113162804B CN 113162804 B CN113162804 B CN 113162804B CN 202110429942 A CN202110429942 A CN 202110429942A CN 113162804 B CN113162804 B CN 113162804B
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symbol
pulse
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spoofing attack
symbol network
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CN113162804A (en
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张小美
陆国平
盛苏英
刘焰森
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Nantong University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention discloses a dichotomous synchronization method of a symbol network under the joint influence of deception attack and impulse interference, which comprises the following steps: consider having antagonismEstablishing a symbol network model in a coupled complex network under the joint influence of deception attack and pulse interference of interaction and random pulse intensity; then, obtaining a modified symbol network model by utilizing a Laplacian matrix and standard transformation; defining an error signal to obtain a symbol network error system in a form of a kronecker product; obtaining the dichotomy synchronization theorem of the symbol network, and adjusting the average pulse interval when the dichotomy synchronization theorem is not less than T a The error system can be stabilized and the symbol network can be synchronized in two halves. Aiming at the fact that malicious information/physical attacks, deterministic pulses or random pulse interference possibly exist in an actual information/physical network at the same time, the invention researches and provides a binary synchronization method of a symbol network under the common influence of pulse interference and deception attack.

Description

Binary synchronization method of symbol network under joint influence of spoofing attack and pulse interference
Technical Field
The invention relates to the technical field of complex network synchronization, in particular to a dichotomous synchronization method of a symbol network under the joint influence of deception attack and impulse interference.
Background
In the last two decades, due to the rise of fields such as multi-vehicle coordination control, networking mobile manipulators, network physical micro-grid and the like, the synchronization of complex networks and the consistency problem of multi-agent systems are widely researched. Most of the existing coordination control problem research of the complex network and the multi-agent system is carried out on the basis of the assumption that all adjacent nodes are in cooperative relationship, but in reality, the coordination control problem research is carried out on the basis of the network in which some cooperative and competitive relationships coexist, so that the binary synchronization research of the symbol network is carried out at the same time.
In general, pulses in the real world fall into two categories: deterministic pulses and stochastic pulses, wherein the research on the problem of symbol network binary synchronization (e.g., cooperative control of multi-agent networks) under the influence of deterministic pulses has achieved a great deal of research effort, while the research effort on the problem of symbol network binary synchronization under the influence of stochastic pulses is very small. The multi-agent network is easy to be attacked by adversarial attack because the communication between agents is carried out based on locally exchanged information, and in recent years, the problem of safety synchronization control of the multi-agent network has attracted great research interest. The existing research only aims at the dichotomous synchronization/consistency problem under the influence of a single factor such as a resistance attack or a deterministic pulse, however, malicious information/physical attacks, deterministic pulses or random pulse interference may exist in an actual information/physical network at the same time.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problem that malicious information/physical attacks and deterministic pulse or random pulse interference possibly exist in an actual information/physical network at the same time, and the existing research only aims at the current situation of dichotomy synchronization/consistency under the influence of a single factor, the invention provides a dichotomy synchronization method of a symbol network under the joint influence of pulse interference with random pulse intensity and deception attack.
The technical scheme is as follows: a binary synchronization method of a symbol network under the joint influence of spoofing attack and impulse interference comprises the following steps:
(1) Considering a coupling network with antagonistic interactions and spoof attack interference at the pulse time, a nonlinear symbol network model is established,
Figure BDA0003031064740000011
wherein,
Figure BDA0003031064740000012
for the status variable of the i-th node, <' >>
Figure BDA0003031064740000013
Figure BDA0003031064740000014
Is a non-linear odd function. />
Figure BDA0003031064740000015
Is a constant matrix. τ (t) is time-varying time lag and satisfies->
Figure BDA0003031064740000016
Wherein->
Figure BDA0003031064740000021
Is a constant. c. C 1 >0 and c 1 >0 is the coupling strength; />
Figure BDA0003031064740000022
Symbol map implied by the symbol network (1)>
Figure BDA0003031064740000023
Of the adjacent matrix. />
Figure BDA0003031064740000024
For a pulse sequence, satisfy 0= t 0 <t 1 <t 2 <…<t k <…,lim k→∞ t k = ∞; presence constant T>1 so that->
Figure BDA0003031064740000025
Figure BDA0003031064740000026
Figure BDA0003031064740000027
Are random pulse intensities. Non-linear odd function->
Figure BDA0003031064740000028
For deceiving the attack signal, the attack signal randomly occurs at each pulse time; beta (t) k ) E {0,1}, and determines whether an impulse interference or a spoofing attack occurs at the impulse time when beta (t) is greater than k ) Pulse interference occurs when =0, i.e. x i (t) at t k Jumping of time; when beta (t) k ) Spoofing attacks occur when = 1;
then make the symbol diagram
Figure BDA0003031064740000029
Middle Laplacian matrix L s Is->
Figure BDA00030310647400000210
Is expressed as->
Figure BDA00030310647400000211
The symbol network (1) can be expressed as follows,
Figure BDA00030310647400000212
wherein,
Figure BDA00030310647400000213
and->
Figure BDA00030310647400000214
Finally order
Figure BDA00030310647400000215
Satisfies b i E {1, -1}, then ∈ +>
Figure BDA00030310647400000216
The symbol network (2) can be represented as follows,
Figure BDA00030310647400000217
wherein
Figure BDA00030310647400000218
(2) Defining an error signal
Figure BDA00030310647400000219
Has->
Figure BDA00030310647400000220
And let W = (W) ij ) (N-1)×(N-1) In which>
Figure BDA00030310647400000221
A symbol network error system in the form of the kronecker product is obtained, expressed as follows,
Figure BDA00030310647400000222
wherein,
Figure BDA00030310647400000223
Figure BDA00030310647400000224
is kronecker product;
(3) Adjusting average pulse interval
If for constants λ > ε >0 and γ >1, a positive definite matrix P >0 exists, constants δ >0 and r >0, such that the following inequality holds,
Figure BDA0003031064740000031
Figure BDA0003031064740000032
wherein,
Figure BDA0003031064740000033
Figure BDA0003031064740000034
wherein,
Figure BDA0003031064740000035
Figure BDA0003031064740000036
wherein alpha is satisfied
Figure BDA0003031064740000037
When the adjusted average pulse interval is not less than T a The error system (4) is stable, i.e. the symbol network (1) is dichotomously synchronized.
Further, the method for dichotomous synchronization of symbol network under the joint influence of spoofing attack and impulse interference is described in the step (1)
Figure BDA0003031064740000038
Is a non-linear odd function, and means for any m e {1,2, \8230;, n x }, non-linear odd function f m (x im (t)) satisfy
Figure BDA0003031064740000039
Wherein v m >0 is a known constant.
Further, the method for binary synchronization of the symbol network under the joint influence of the spoofing attack and the impulse interference is described in the step (1)
Figure BDA00030310647400000310
Symbol map implied by the symbol network (1)>
Figure BDA00030310647400000311
In which the symbol map +>
Figure BDA00030310647400000312
Is structurally balanced and contains a directed spanning tree.
Further, the method for binary synchronization of the symbol network under the joint influence of the spoofing attack and the impulse interference is described in the step (1)
Figure BDA00030310647400000313
Is a random pulse intensity, meaning that there are S possible pulse intensities @>
Figure BDA00030310647400000314
Wherein
Figure BDA00030310647400000315
Are mutually independent random variable sequences, and Prob { sigma (t) k )＝q}＝π q ∈(0,1)，/>
Figure BDA00030310647400000316
Satisfy->
Figure BDA00030310647400000317
Further, the nonlinear odd function in the step (1) in the binary synchronization method of the symbol network under the joint influence of the spoofing attack and the impulse interference
Figure BDA00030310647400000318
For spoofing attack signals, satisfy
Figure BDA00030310647400000319
Where θ >0 is a known constant.
Further, the nonlinear odd function in the step (1) in the binary synchronization method of the symbol network under the joint influence of the spoofing attack and the impulse interference
Figure BDA00030310647400000320
The random occurrence of the attack signals at each pulse time refers to the spoofing attack h (x) i (t)) the probability of occurrence at a pulse instant is random, and the sequence->
Figure BDA0003031064740000041
Indicate, i.e. ->
Figure BDA0003031064740000042
And &>
Figure BDA0003031064740000043
Wherein->
Figure BDA0003031064740000044
Is a known constant.
Has the advantages that: the invention researches a binary synchronization method of a Lipschitz network with antagonistic and time-lag interaction, and considers the common influence of pulse interference with random pulse intensity and deception attack; secondly, by utilizing the standard transformation, the Lyapunov function method and the linear matrix inequality technology, the sufficient condition of the binary synchronization of the symbol network is established, the binary synchronization of the symbol network can be realized only by properly adjusting the average pulse interval, and the realization is convenient.
Drawings
FIG. 1 is a schematic diagram of a binary synchronization method of a symbol network under the joint influence of spoofing attack and impulse interference according to the present invention;
FIG. 2 is a symbolic diagram consisting of 9 nodes in the numerical simulation example 1 of the present invention;
FIG. 3 is a diagram of a pulse instant self-hopping or spoofing attack in the numerical simulation example 1 of the present invention;
FIG. 4 is a state trace diagram in numerical simulation example 1 of the present invention;
FIG. 5 is a symbolic diagram consisting of 7 nodes in numerical simulation example 2 of the present invention;
FIG. 6 is a diagram of a pulse instant self-hopping or spoofing attack in the numerical simulation example 2 of the present invention;
FIG. 7 is a state diagram of the numerical simulation example 2 of the present invention.
Detailed Description
Considering a coupling network with antagonistic interaction and spoof attack interference at the pulse time, a nonlinear symbol network model is established,
Figure BDA0003031064740000045
wherein,
Figure BDA0003031064740000046
is the ith sectionThe state variable of the point is changed to,
Figure BDA0003031064740000047
Figure BDA0003031064740000048
is a non-linear odd function. />
Figure BDA0003031064740000049
Is a constant matrix. τ (t) is a time-varying time lag and satisfies >>
Figure BDA00030310647400000410
Wherein->
Figure BDA00030310647400000411
Is a constant. c. C 1 >0 and c 1 >0 is the coupling strength. />
Figure BDA00030310647400000412
Symbol map implied by the symbol network (1)>
Figure BDA00030310647400000419
Of the adjacent matrix. />
Figure BDA00030310647400000413
For a pulse sequence, satisfy 0= t 0 <t 1 <t 2 <…<t k <…,lim k→∞ t k = ∞. Existence constant T>1 so that->
Figure BDA00030310647400000414
Figure BDA00030310647400000415
Figure BDA00030310647400000416
For random pulse intensities, there are S possible pulse intensities->
Figure BDA00030310647400000417
Wherein->
Figure BDA00030310647400000418
Are mutually independent random variable sequences, and Prob { sigma (t) k )＝q}＝π q ∈(0,1)，/>
Figure BDA0003031064740000051
Satisfy the requirements of
Figure BDA0003031064740000052
Non-linear odd function->
Figure BDA0003031064740000053
For spoofing attack signals, which occur randomly at each pulse instant, a Bernoulli distribution sequence is used>
Figure BDA0003031064740000054
Is represented by beta (t) k )∈{0，1}，/>
Figure BDA0003031064740000055
And
Figure BDA0003031064740000056
wherein->
Figure BDA0003031064740000057
Determining whether impulse interference or spoofing attack occurs at the impulse time, when beta (t) is a known constant k ) A pulse disturbance occurs when =0, i.e. x i (t) at t k Jumping of time; when beta (t) k ) A spoofing attack occurs when = 1.
Then make the symbol diagram
Figure BDA0003031064740000058
Middle Laplacian matrix L s Is->
Figure BDA0003031064740000059
Is expressed as->
Figure BDA00030310647400000510
The symbol network (1) can be expressed as follows,
Figure BDA00030310647400000511
wherein,
Figure BDA00030310647400000512
and->
Figure BDA00030310647400000513
Suppose 1 for any m e {1,2, \8230;, n x }, non-linear odd function f m (x im (t)) satisfy
Figure BDA00030310647400000514
Wherein v m >0 is a known constant.
Assumption 2. Spoofing attack signal
Figure BDA00030310647400000515
Is a non-linear odd function, satisfies
Figure BDA00030310647400000516
Where θ >0 is a known constant.
Hypothesis 3. Symbolic diagram
Figure BDA00030310647400000517
Is structurally balanced and contains directed spanning trees.
Definition 1 if for any i eN(i ≠ 1) there are
Figure BDA00030310647400000518
Wherein,
Figure BDA00030310647400000519
representing mathematical expectations, the symbol network is said to be dichotomously synchronous.
Order to
Figure BDA00030310647400000520
Satisfies b i E {1, -1}, then ∈ +>
Figure BDA00030310647400000521
Can be obtained from hypothesis 1>
Figure BDA00030310647400000522
Also by assuming that 2 is available>
Figure BDA00030310647400000523
The above-described symbolic network model can be expressed as follows,
Figure BDA00030310647400000524
wherein
Figure BDA0003031064740000061
Order to
Figure BDA0003031064740000062
Figure BDA0003031064740000063
Figure BDA0003031064740000064
W＝(w ij ) (N-1)×(N-1) Wherein
Figure BDA0003031064740000065
/>
Then there is
Figure BDA0003031064740000066
Wherein,
Figure BDA0003031064740000067
initial value->
Figure BDA0003031064740000068
Definition 2 (average pulse interval) if there is a positive integer N 0 And a positive number T a So that the following holds:
Figure BDA0003031064740000069
wherein, N (t) 0 And t) indicates that the pulse sequence is in the interval (t) 0 T) is called a pulse sequence
Figure BDA00030310647400000610
Average pulse interval of not less than T a 。
Lesion 1. Under assumption 3, the matrix
Figure BDA00030310647400000611
Has one zero eigenvalue and the remaining N-1 eigenvalues have real positive parts.
Theorem 2 under assumption 3, matrix W = (W) ij ) (N-1)×(N-1) There are no zero eigenvalues and all of their eigenvalues have a real positive part.
Theorem 3. Suppose that the nonnegative function V (t), t ∈ [ - τ, ∞) satisfies
Figure BDA00030310647400000612
Wherein 0 is not less than beta<α，
Figure BDA00030310647400000613
Then
Figure BDA00030310647400000614
Wherein γ >0 is an equation
γ-α+βe γτ ＝0
Is determined.
Based on the above description, the final goal is to adjust the average pulse interval such that the average pulse interval satisfies the following theorem to achieve binary synchronization of the symbol network:
theorem 1. If for constants λ > ε >0 and γ >1, there is a positive definite matrix P >0, constants δ >0 and r >0, such that the following inequality holds,
Figure BDA0003031064740000071
Figure BDA0003031064740000072
wherein,
Figure BDA0003031064740000073
Figure BDA0003031064740000074
wherein,
Figure BDA0003031064740000075
Figure BDA0003031064740000076
wherein alpha is satisfied
Figure BDA0003031064740000077
When the adjusted average pulse interval is not less than T a The error system (15) is stable, i.e. the symbol network (12) is dichotomously synchronized.
And (3) proving that: from hypothesis 1
Figure BDA0003031064740000078
Wherein
Figure BDA0003031064740000079
The Lyapunov function is constructed as follows
V(t)＝e T (t)Pe(t) (22)
When t ∈ [ t ] k-1 ,t k ) When V (t) is derived along the trajectory of the system (15), and the positive numbers delta and lambda can be arbitrarily determined by the formula (21)>Epsilon, has
Figure BDA00030310647400000710
Wherein
Figure BDA00030310647400000711
Figure BDA00030310647400000712
Wherein->
Figure BDA00030310647400000713
From the formula (17), Ω <0. And further obtained from the formula (23)
Figure BDA0003031064740000081
Derived from introduction 3
Figure BDA0003031064740000082
Wherein alpha is>0 satisfies
Figure BDA0003031064740000083
When t = t k Then, from (15)
Figure BDA0003031064740000084
From hypothesis 2
Figure BDA0003031064740000085
Figure BDA0003031064740000086
Wherein λ is max (P) represents the maximum eigenvalue of matrix P. And due to
Figure BDA0003031064740000087
Figure BDA0003031064740000088
So that there are
Figure BDA0003031064740000089
Obtainable from the formulae (16) and (18)
Figure BDA0003031064740000091
Then the compounds represented by the formulae (29) and (30) can be obtained
Figure BDA0003031064740000092
Thus, when t ∈ [ t ] k-1 ,t k ) When the temperature of the water is higher than the set temperature,
Figure BDA0003031064740000093
using definition 2, we can obtain the time t ∈ [ t ] k-1 ,t k ) When the temperature of the water is higher than the set temperature,
Figure BDA0003031064740000094
this means that
Figure BDA0003031064740000095
Wherein
Figure BDA0003031064740000096
Is represented by the formula (19)
Figure BDA0003031064740000097
As can be seen from definitions 1 and 2, the symbol network (12) is binary synchronized.
Example 1 was numerically simulated.
Consider a network (12) of 9 Chua's circuits, in which the parameter matrices A, B and the non-linear function f (x) i (t)) are shown below, respectively,
Figure BDA0003031064740000098
B＝diag(1,1,1)，/>
Figure BDA0003031064740000099
it is easy to verify that the following relation holds: />
Figure BDA00030310647400000912
Wherein v 1 ＝0.884.
The topology of the network (12) is shown in FIG. 2, the adjacency matrix
Figure BDA00030310647400000911
Is represented as follows, with the additional symbol diagram structure being balanced, whereinN 1 ＝{1,2,3,8,9}，N 2 = 4,5,6,7, and contains a directed spanning tree,
Figure BDA0003031064740000101
let λ =1, ∈ =0.5,
Figure BDA00030310647400001014
then α =0.3424 is the equation £ r>
Figure BDA0003031064740000102
The root of (2). Let h (x) i (t))＝[0.3x i1 (t),-0.3sin(x i2 (t)),tanh(0.3x i3 (t))] T Then>
Figure BDA00030310647400001015
Where θ =0.3. Let c 1 ＝8，c 2 ＝1，/>
Figure BDA0003031064740000104
σ(t k )∈{1,2}，Prob{σ(t k )＝1}＝0.4，Prob{σ(t k ) =1} =0.6. And assume a random variable ρ 1 Obey a uniform distribution U (0.1, 0.3), random variable ρ 2 The probability distribution for e {0.2,0.15,0.1} is as follows: prob { ρ 2 ＝0.2}＝0.3，Prob{ρ 2 ＝0.15}＝0.2，Prob{ρ 2 =0.1} =0.5. Let gamma = e 0.9α ＝1.3610，T a =1, then have->
Figure BDA0003031064740000105
Solving the linear matrix inequalities (16) - (18) in theorem 1 can obtain feasible solutions thereof, and as can be seen from theorem 1, when the adjusted average pulse interval is not less than T a The symbol network is dichotomously synchronized. Taking t in the simulation k -t k-1 And =1s (the strength of the pulse time when the self-hopping or the spoofing attack occurs is shown in fig. 3), fig. 4 shows that the symbol network can achieve binary synchronization.
Numerical simulation example 2.
Consider a network (12) of 7 Chua's circuits, where the parameter matrices A, B and the non-linear function f (x) i (t)) are shown below, respectively,
A＝diag{-1.2,-1.2,-1.2}，
Figure BDA0003031064740000106
it is easy to verify that the following relation holds:
Figure BDA0003031064740000107
the topology of the network (12) is shown in FIG. 5, the adjacency matrix
Figure BDA0003031064740000108
Is represented as follows, with the additional symbol diagram structure being balanced, whereinN 1 ＝{1,2,3}，N 2 = 4,5,6,7, and contains a directed spanning tree,
Figure BDA0003031064740000109
let λ =2, ε =1,
Figure BDA00030310647400001016
then α =0.7483 is the equation £ r>
Figure BDA00030310647400001010
The root of (2). h (x) i (t))，/>
Figure BDA00030310647400001011
And &>
Figure BDA00030310647400001012
The same as in example 1. Let c 1 ＝7，c 2 ＝0.8，γ＝1.35，T a =0.45 satisfies =>
Figure BDA00030310647400001013
Solving the linear matrix inequalities (16) - (18) in theorem 1 can obtain feasible solutions thereof, and as can be seen from theorem 1, when the adjusted average pulse interval is not less than T a The symbol network is dichotomously synchronized. Taking t in the simulation k -t k-1 =0.45s (the strength of the pulse instant at which the self-hopping or spoofing attack occurs is shown in fig. 6), and fig. 7 shows that the symbol network can achieve binary synchronization. />

Claims (6)

1. A dichotomous synchronization method of a symbol network under the joint influence of spoofing attack and impulse interference is characterized by comprising the following steps:
1) Considering a coupled complex network under the joint influence of spoofing attack and pulse interference with antagonistic interaction and random pulse intensity, a nonlinear symbol network model is established,
Figure FDA0003922918970000011
wherein,
Figure FDA0003922918970000012
is a state variable of the ith node,
Figure FDA0003922918970000013
Figure FDA0003922918970000014
is a non-linear odd function>
Figure FDA0003922918970000015
Is a constant matrix, τ (t) is a time-varying time lag, and satisfies->
Figure FDA0003922918970000016
Wherein +>
Figure FDA0003922918970000017
Is a constant number c 1 >0 and c 1 >0 is the coupling strength, is greater than or equal to>
Figure FDA0003922918970000018
For a symbol diagram implied by a symbol network (1)>
Figure FDA0003922918970000019
Is adjacent to the matrix, < >>
Figure FDA00039229189700000110
For a pulse sequence, satisfy 0= t 0 <t 1 <t 2 <…<t k <…,lim k→∞ t k = ∞ existence of constant T>1 is such that device for selecting or keeping>
Figure FDA00039229189700000111
Figure FDA00039229189700000112
Figure FDA00039229189700000113
For random pulse intensity, a non-linear odd function->
Figure FDA00039229189700000114
For spoofing attack signals, randomly occurring at each pulse instant, beta (t) k ) E.g. 0,1, determining the pulseWhether impulse interference or spoofing attack occurs at the moment when beta (t) k ) Pulse interference occurs when =0, x i (t) at t k Time of day is changed when beta (t) k ) A spoofing attack occurs when the value is =1,
then make the symbol diagram
Figure FDA00039229189700000115
Middle Laplacian matrix L s Is->
Figure FDA00039229189700000116
Is expressed as->
Figure FDA00039229189700000117
The symbol network (1) can be expressed as follows,
Figure FDA00039229189700000118
wherein,
Figure FDA00039229189700000119
and->
Figure FDA00039229189700000120
Finally, standard conversion is carried out to ensure that
Figure FDA00039229189700000121
Satisfies b i E {1, -1}, then ∈ +>
Figure FDA00039229189700000122
The symbol network (2) can be represented as follows,
Figure FDA00039229189700000123
/>
wherein
Figure FDA0003922918970000021
2) Defining an error signal
Figure FDA0003922918970000022
Is provided with
Figure FDA0003922918970000023
Let W = (W) ij ) (N-1)×(N-1) Wherein->
Figure FDA0003922918970000024
A sign network error system in the form of a kronecker product is obtained, expressed as follows,
Figure FDA0003922918970000025
wherein,
Figure FDA0003922918970000026
Figure FDA0003922918970000027
is kronecker product;
3) Adjusting average pulse interval
If a positive definite matrix P >0, constants delta >0 and r >0 exist for constants lambda > epsilon >0 and gamma >1, such that the following inequality holds,
Figure FDA0003922918970000028
Figure FDA0003922918970000029
wherein,
Figure FDA00039229189700000210
Figure FDA00039229189700000211
wherein,
Figure FDA00039229189700000212
Figure FDA00039229189700000213
wherein alpha is satisfied
Figure FDA00039229189700000214
When the adjusted average pulse interval is not less than T a The error system (4) is stable and the symbol network (1) is dichotomously synchronized.
2. The binary synchronization method for the symbol network under the joint influence of the spoofing attack and the impulse interference as claimed in claim 1, wherein: the method described in step (1)
Figure FDA00039229189700000215
Is a non-linear odd function, and refers to the function for any m e {1,2, \8230;, n x }, non-linear odd function f m (x im (t)) satisfy
Figure FDA00039229189700000216
Wherein v m >0 is a known constant.
3. A spoofing attack and pulse stem as recited in claim 1The binary synchronization method of the symbol network under the influence of interference is characterized in that: described in step (1)
Figure FDA00039229189700000217
Symbol map implied by the symbol network (1)>
Figure FDA00039229189700000218
In which the symbol map->
Figure FDA00039229189700000219
Is structurally balanced and contains directed spanning trees.
4. The binary synchronization method for symbol networks under the joint influence of spoofing attack and impulse interference according to claim 1, characterized in that: the method described in step (1)
Figure FDA0003922918970000031
To be random pulse intensity means that there are S possible pulse intensities
Figure FDA0003922918970000032
Wherein->
Figure FDA0003922918970000033
Are mutually independent random variable sequences, and Prob { sigma (t) k )＝q}＝π q ∈(0,1)，/>
Figure FDA0003922918970000034
Satisfy->
Figure FDA0003922918970000035
5. The binary synchronization method for symbol networks under the joint influence of spoofing attack and impulse interference according to claim 1, characterized in that: non-linear as described in step (1)Sexual odd function
Figure FDA0003922918970000036
For spoofing attack signals, satisfy
Figure FDA0003922918970000037
Where θ >0 is a known constant.
6. The binary synchronization method for the symbol network under the joint influence of the spoofing attack and the impulse interference as claimed in claim 1, wherein: the non-linear odd function in the step (1)
Figure FDA0003922918970000038
The random occurrence of the attack signals at each pulse time refers to the spoofing attack h (x) i (t)) the probability of occurrence at a pulse instant is random, and the sequence->
Figure FDA0003922918970000039
Means for>
Figure FDA00039229189700000310
And &>
Figure FDA00039229189700000311
Wherein->
Figure FDA00039229189700000312
Is a known constant. />
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