CN116760574B - Distributed limited time observation method based on intelligent network linkage vehicle team - Google Patents

Distributed limited time observation method based on intelligent network linkage vehicle team Download PDF

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CN116760574B
CN116760574B CN202310599524.6A CN202310599524A CN116760574B CN 116760574 B CN116760574 B CN 116760574B CN 202310599524 A CN202310599524 A CN 202310599524A CN 116760574 B CN116760574 B CN 116760574B
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郭胜辉
陈丽
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Abstract

The invention discloses a distributed limited time observation method based on an intelligent network linkage vehicle team, which comprises the following steps: firstly, constructing a mathematical model of intelligent network connection and converting the mathematical model into a state space equation; then, designing a distributed finite time observer according to a state space equation, and obtaining a global estimation error system based on the distributed finite time observer; then, stability analysis is carried out on the overall estimation error through a global estimation error system, self-adaptive threshold attack detection method design is carried out on the attack signal of the vehicle, and FTB-H is judged through stability analysis ∞ Adequate conditions for performance; finally, carrying out numerical simulation instance detection on the intelligent network connection motorcade and obtaining the validity of simulation detection results; according to the invention, the intelligent network connected vehicle distributed limited time observer is designed, so that the condition constraint in the observer design process is reduced, and the accurate estimation of the vehicle attack signal in the limited time is flexibly realized.

Description

Distributed limited time observation method based on intelligent network linkage vehicle team
Technical Field
The invention relates to the field of automatic driving of vehicles, in particular to a distributed limited time observation method based on intelligent network linkage vehicle teams.
Background
The intelligent network coupling vehicle team is one of the main technologies used in the intelligent traffic system, and improves the traffic capacity and throughput of road traffic on the premise of ensuring safe and reliable running of vehicles; and the adjacent vehicles keep ideal interval running, so that the air resistance of the running vehicles is reduced, and the consumption of energy sources is reduced; but the intelligent network-connected vehicle is more prone to safety problems in the exposed network environment for a long time; the most important security problems are sensor attacks, actuator attacks, and communication network attacks.
As the data transmission amount of the system is continuously increased, the centralized estimation method is not applicable any more due to the problems of congestion, receiving delay and the like of a transmission line, and the problem of line congestion caused by huge data can be effectively avoided by using the distributed estimation method; aiming at informatization development, a limited time distribution fault estimation observer design method is utilized by using a Cyber-physical systems (CPSs), fault (or attack) detection and estimation methods of the information physical systems are applied to intelligent network buses, and detection and estimation are carried out within a limited time range, so that safe running of intelligent network buses is ensured.
However, since the unique power model and the attack model of the vehicle do not necessarily meet the conditions of the related art, not all CPS attack detection and estimation techniques are applicable to intelligent network coupling, so how to apply the existing CPS security detection techniques to intelligent network coupling is a concern of value.
Disclosure of Invention
The invention aims to provide a distributed limited time observation method based on an intelligent network linkage vehicle team, which solves the following technical problems:
how to design a distributed observer ensures accurate estimation of vehicle attack signals in a limited time and ensures safe running of intelligent network train.
The aim of the invention can be achieved by the following technical scheme:
a distributed limited time observation method based on intelligent network coupled fleets, the method comprising:
s1, constructing a mathematical model of intelligent network coupling and converting the mathematical model into a state space equation;
s2, designing a distributed finite time observer according to a state space equation, and obtaining a global estimation error system based on the distributed finite time observer;
s3, stability analysis is carried out on the overall estimation error through a global estimation error system, and self-adaptive threshold attack detection method is carried out on attack signals of the vehicleDesigning and judging FTB-H through stability analysis ∞ Adequate conditions for performance.
Preferably, the expression of the mathematical model of the intelligent network interconnection is:
wherein ρ is i Indicating the position, v, of the vehicle i Indicating the speed of the vehicle and,indicating the acceleration of the vehicle. σ represents a cranking time constant of the engine. d, d i Representing external disturbance->Is constant (I)>Representing disturbances in the velocity channel +.>Representing disturbances in the acceleration path, e.g. atmospheric disturbances, u i Representing actual control inputs of the vehicle;
considering the influence of wind resistance caused by vehicle distance on vehicle speed, the vehicle speed dynamic equation expression is:
wherein Γ is ij Describing the interconnection structure of a vehicle, if Γ ij =0 indicates that vehicle i is disconnected from vehicle j, Γ ij =1 denotes a connection between the vehicle i and the vehicle j, l denotes a windage coefficient between the vehicles, and k denotes a total number of following vehicles.
Preferably, the expression of the state space equation in the step S1 is:
wherein:
for the measurable output of the vehicle, +.>As a nonlinear function>Represents an attack signal of the vehicle, D x An attack distribution matrix for the vehicle;
is a constant matrix;obviously there is->
Preferably, the step S2 specifically includes: introducing an intermediate variable to design a distributed intermediate variable observer of an ith vehicle as an expression:
wherein,is a gain matrix of the system;
order the
Preferably, the distributed intermediate variable observer design method comprises the following steps:
(1) The global expression for vehicle state and intermediate variables is:
(2) The vehicle global observer expression is:
wherein, define Respectively representing the overall estimation error of the state of the motorcade, the overall estimation error of the intermediate variable, the overall estimation error of the attack signal and the overall estimation error of the output; performing a first transformation expression in combination with (1) and (2) calculations:
definition of the definitionRepresenting the overall estimation error of the nonlinear term; then:
where K represents an orthogonal matrix of eigenvectors of matrix Γ, Λ=diag { λ 1 ,λ 2 ,…,λ k }，λ i (i=1, 2, …, k) is the eigenvalue of matrix Γ,
I n representing the n-dimensional identity matrix,
preferably, the global estimation error system expression:
further transforming by transforming the first transformation expression:
wherein,orthogonal matrix properties, K T K＝I k 。
Preferably, the stability analysis in step S3 includes setting theorem:
given a scalar gamma > 0, delta > 0, zeta 1 ＞0,ξ 2 ＞0,β 1 ＞0,β 2 > 0, ε > 0, T > 0, positive definite matrices are presentSum matrix->The following three conditions are satisfied:
R 1 ＜P 1 ,R 2 ＜P 2
wherein,
λ min (N)＝min{λ min (N 1 ),λ min (N 2 )},λ max (N)＝max{λ max (N 1 ),λ max (N 2 )}；
then the global estimation error system is related to (beta) 1 ,β 2 ,[0T],R 1 ,R 2 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ And the gain matrix of the vehicle distributed observer is l=p 1 -1 W。
Preferably, the theorem further includes setting an axiom and defining:
the quotation: for any matrixAnd->The method meets the following conditions:
wherein ε > 0.
The definition includes a definition one and a definition two, the definition one: given constant beta 1 ＞0,β 2 > 0 and beta 1 ＜β 2 A matrixSatisfy hypothesis 3 and time interval [0, T ]]If there is a matrix ψ 1 ＞0,Ψ 2 > 0, satisfy:
the error system is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ) Is of the limited time limit (FTB);
the definition II: if the attack estimation error system meets the following conditions:
error system is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ) Is FTB;
in a non-zero initial state, the following is satisfied:
wherein kappa > 0, xi 1 ＞0,ξ 2 > 0, g (·) is a non-negative function;
the error system is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ 。
Preferably, the adaptive threshold attack detection method design includes:
the expression combining the state space equation is obtained:
wherein,
the vehicle acceleration estimated using the finite time observer can be expressed as:
further derivation:
finally designed attack detector:
wherein,is a positive scalar;
definition of the definitionThen when the vehicle i is not under attack, the error dynamic expression is:
when estimating errorsExceeds the designed adaptive attack detection threshold +.>At this point, the detector begins to sound an alarm.
Preferably, the method further comprises:
and S4, carrying out numerical simulation instance detection on the intelligent network connection motorcade and obtaining the effectiveness of simulation detection results.
The invention has the beneficial effects that: according to the invention, the intelligent network vehicle is mathematically modeled, the attack signals of the vehicles and other external disturbance are considered, and the wind resistance coefficient between each vehicle distance is more practical, so that the vehicle model is more close to reality, and meanwhile, the design accuracy of the distributed observer is improved; the invention provides a self-adaptive threshold attack detection method design of an intelligent network connection distribution type limited time observer, which realizes the estimation of vehicle attack signals in limited time; the observer can not only improve the estimation precision of attack signals through adjusting specified parameters, but also get rid of constraint conditions required to be met by other observers such as a gradual convergence observer and the like; the invention also designs a self-adaptive threshold attack detection method of the vehicle in the network layer based on the distributed observer, which is more flexible than fixed value detection attack, improves the accuracy of intelligent network train detection and ensures the safe running of intelligent network train teams.
Of course, it is not necessary for any one product to practice the invention to achieve all of the advantages set forth above at the same time.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a distributed finite time observation method based on intelligent network linkage vehicle teams;
FIG. 2 is a diagram showing the layout of an intelligent network coupled vehicle team according to the present invention;
FIG. 3 is a frame diagram of an intelligent network coupling attack detection module according to the present invention;
FIG. 4 is a Vehicle 1 state estimation value estimated by the observer according to the present invention;
FIG. 5 is a Vehicle 2 state estimation value estimated by the observer according to the present invention;
FIG. 6 is a Vehicle 3 state estimation value estimated by the observer according to the present invention;
FIG. 7 is a Vehicle 4 state estimation value estimated by the observer according to the present invention;
FIG. 8 is a Vehicle 1 attack estimate estimated by the observer of the present invention;
FIG. 9 is a view of an observer estimating Vehicle 2 attack estimate in accordance with the present invention;
FIG. 10 is a graph of the observer estimated Vehicle 3 attack estimate in accordance with the present invention;
FIG. 11 is a graph of the observer estimated Vehicle 4 attack estimate of the present invention;
FIG. 12 is a graph showing the estimated Vehicle 2 attack detection result by the observer according to the present invention;
FIG. 13 is a graph showing the state estimation of the analysis and subsystem 1 of the method of the present invention compared to the prior art;
FIG. 14 is a graph showing the state estimation of the analysis and subsystem 2 of the method of the present invention compared to the prior art;
fig. 15 shows attack (fault) estimates of the methods of the subsystems 1,2 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, the invention provides a distributed finite time observation method based on intelligent network linkage vehicle teams, which comprises the following steps:
s1, constructing a mathematical model of intelligent network coupling and converting the mathematical model into a state space equation;
s2, designing a distributed finite time observer according to a state space equation, and obtaining a global estimation error system based on the distributed finite time observer;
s3, performing stability analysis on the overall estimation error through a global estimation error system, designing an adaptive threshold attack detection method on an attack signal of the vehicle, and judging FTB-H through stability analysis ∞ Adequate conditions for performance.
Through the technical scheme: as the data transmission amount of the system is continuously increased, the problems of congestion, receiving delay and the like of a transmission line cause that the existing centralized estimation method is not applicable any more, and the problem of line congestion caused by huge data can be effectively avoided by using the distributed estimation method; the invention provides a design method of a distributed limited time observer for solving the problems of attack signals and disturbance contained in vehicles in a following driving scene of a plurality of intelligent network vehicles and an attack detection method based on the observer by utilizing an information physical system (CPSs) and providing a design method of the limited time distribution fault estimation observer, which is used for applying a fault (or attack) detection and estimation method of the information physical system to the intelligent network vehicles and solving the problems of detection and estimation in a limited time range so as to ensure that intelligent network vehicles can safely drive.
As an embodiment of the present invention, please refer to fig. 2 specifically, to perform mathematical modeling on an intelligent network connection. Each intelligent network vehicle can acquire its own position and speed values through a sensor similar to a GPS, and acquire the relative position and speed values of the front vehicle by using an on-board radar or a camera. Meanwhile, in an intelligent network connected vehicle team, adjacent vehicles can cooperate with each other through a communication network, so that the safety distance between the vehicles is ensured;
the expression of the mathematical model of the intelligent network connection is as follows:
wherein ρ is i Indicating the position, v, of the vehicle i Indicating the speed of the vehicle and,indicating the acceleration of the vehicle. ρ represents a cranking time constant of the engine. d, d i Representing external disturbance->Is constant (I)>Representing disturbances in the velocity channel +.>Representing disturbances in the acceleration path, e.g. atmospheric disturbances, u i Representing actual control inputs of the vehicle;
the vehicle-to-vehicle (V2V) keeps a desired distance, so that the influence of air resistance on the vehicle can be effectively relieved, and the influence of wind resistance caused by the distance of the vehicle on the vehicle speed is considered, wherein the expression of the dynamic equation of the vehicle speed is as follows:
wherein Γ is ij Describing the interconnection structure of a vehicle, if Γ ij =0 indicates that vehicle i is disconnected from vehicle j, Γ ij =1 denotes a connection between the vehicle i and the vehicle j, l denotes a windage coefficient between the vehicles, and k denotes a total number of following vehicles.
As an embodiment of the present invention, specifically, the expression of the state space equation is:
wherein:
for the measurable output of the vehicle, +.>As a nonlinear function>Represents an attack signal of the vehicle, D x An attack distribution matrix for the vehicle;
is a constant matrix;obviously there is->
Through the technical scheme: since intelligent network connection needs to be communicated and controlled by a control system in moving, the following two aspects are considered:
first, risk of network attack: because the intelligent network connected vehicle is more dependent on the communication network and the sensor than the traditional automobile, the characteristic causes the consideration of the safety problem of the intelligent network connected vehicle communication network. Communication networks are very vulnerable to malicious attacks, such as common replay attacks, false data injection attacks, denial of service attacks, and the like, during the process of transmitting data. The control signals are therefore at risk of being attacked by the network during transmission over the communication network. When the vehicle i is not attacked, the control signal u is designed i (t) will be the actual control input to the vehicle; when the control signal is inThe actual control input of the vehicle when the moment is influenced by the attack signal +.>Will be the design signal and the attack signal w i (t) the actual control input of the vehicle i is in other words the value of the designed control input after being influenced by the attack signal. The expression of the actual control input is therefore:
further analysis of the impact of network attacks on the actual control signal. The dummy data injection attack transmits dummy data to the control system or falsifies the value of the control signal (refer to fig. 3), so the control signal actually transmitted to the vehicle has the following values:
denial of service attacks can cause the communication network between vehicles to be busy, causing delays or congestion of the communication channel, and thus the impact of a denial of service attack on the actual control signal of a vehicle can be expressed as:
wherein t is d Representing an unknown delay time. According to the taylor theorem, and ignoring higher order terms, equation (5) may be approximated as:
definition of the definitionThen formula (6) can be expressed as +.>
The impact of a network attack on the vehicle control signal can be expressed as:
wherein w is i (t) may be not only w fi (t) may also be w di (t)。
Second, nonlinear dynamic behavior: the nonlinear dynamic behavior of the vehicle is generated by considering errors existing in vehicle modeling, friction between the vehicle and the ground, wind direction influence and the like.
In summary of the above analysis, definitionThe state space equation expression of the final ith vehicle is:
wherein:
for the measurable output of the vehicle, +.>As a nonlinear function>Represents an attack signal of the vehicle, D x Is an attack distribution matrix of the vehicle.
Is a constant matrix.Obviously there is->
It should be noted that: when b=d x It is apparent that the system formula (8) does not satisfy the observer constraint, and in order to solve the problem, consideration is given to the useThe inter-variable observer solves the problem of intelligent network connection distribution attack estimation.
The following assumptions are given before the next study is performed:
suppose 1: nonlinear function phi i (t,x i (t)) is known and satisfies the Lipschitz condition
||Φ i (t,x 1 (t))-Φ i (t,x 2 (t))||≤γ||x 1 (t)-x 2 (t)||
Wherein γ is Lipschitz constant.
Suppose 2: the intelligent network coupling vehicle team communication is an undirected topology, please refer to fig. 2.
Suppose 3: the external disturbance of the velocity channel is unknown but is bounded Attack Signal derivative is unknown but meets->Wherein->For a given scalar.
It should be noted that assuming 1 is a general processing method for processing nonlinear terms, and similar processing is performed as assuming 2 that the communication between vehicles is performed in the form of an undirected topology, the asymmetry of the laplacian matrix of the directed graph in the distributed attack estimator design makes the design more challenging, and for this reason, the present invention proposes this assumption. Suppose 3 is a common processing way for processing external disturbance of the system and attack signals, meanwhile, the assumed condition of the external disturbance is ubiquitous in the actual system, and if the external disturbance is unbounded, the external disturbance has no practical meaning.
Designing an observer for the system formula (8); first, an intermediate variable is introduced:
wherein the method comprises the steps of To vary the scalar, the convergence speed of the error system can be adjusted by varying this value when estimating the attack signal.
The dynamic equation of equation (9) can be further deduced in combination with system equation (8) as:
as an embodiment of the present invention, specifically, step S2 includes: introducing an intermediate variable to design a distributed intermediate variable observer of an ith vehicle as an expression:
wherein the method comprises the steps ofIs a gain matrix of the system;
order the
Γ＝[Γ ij ] k×k (i,j＝1,2,…,k)。
As an embodiment of the present invention, in particular, a distributed intermediate variable observer design is based on:
the global expression for vehicle state and intermediate variables is:
the vehicle global observer expression is:
/>
definition of the definition Respectively representing the overall estimation error of the state of the motorcade, the overall estimation error of the intermediate variable and the overall estimation of the attack signalAnd calculating errors and outputting overall estimation errors. Calculated by combining the formulas (15), (16), (17) and (18):
from the assumption 2, it is known that the matrix Γ is a symmetric matrix, so that a spectral decomposition of the matrix can be performed, Γ being expressed as:
Γ＝KΛK Τ
definition of the definitionRepresenting the overall estimation error of the nonlinear term; thus there is
Where K represents an orthogonal matrix of eigenvectors of matrix Γ, Λ=diag { λ 1 ,λ 2 ,…,λ k }，λ i (i=1, 2, …, k) is the eigenvalue of matrix Γ,
I n representing the n-dimensional identity matrix,
as an embodiment of the present invention, specifically, the global estimation error system expression:
further transformed from the formulas (20) (21):
/>
it should be noted that the invention researches the distributed limited time observer based on the existing distributed intermediate observer, and realizes the estimation of the vehicle attack signal in the limited time. Compared with other limited-time observers, the constraint conditions required to be met when the observer is designed are eliminated, and the application range is wider; secondly: the computational characteristics of the matrix Kronecker product are used in the derivation of equations (22) (23),orthogonal matrix properties, K T K＝I k 。
As an embodiment of the present invention, the stability analysis in step S3 includes setting theorem: given a scalar gamma > 0, delta > 0, zeta 1 ＞0,ξ 2 ＞0,β 1 ＞0,β 2 > 0, ε > 0, T > 0, positive definite matrices are presentSum matrixThe following three conditions are satisfied:
R 1 ＜P 1 ,R 2 ＜P 2
wherein the method comprises the steps of，
λ min (N)＝min{λ min (N 1 ),λ min (N 2 )},λ max (N)＝max{λ max (N 1 ),λ max (N 2 )}；
Then the global estimation error system is related to (beta) 1 ,β 2 ,[0T],R 1 ,R 2 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ And the gain matrix of the vehicle distributed observer is l=p 1 -1 W。
Theorem also includes setting an axiom and definition:
and (5) lemma: for any matrixAnd->Satisfy->
Wherein ε > 0.
The definition includes definition one and definition two, definition one: given constant beta 1 ＞0,β 2 > 0 and beta 1 ＜β 2 A matrixSatisfy hypothesis 3 and time interval [0, T ]]If there is a matrix ψ 1 ＞0,Ψ 2 > 0, satisfy
The error system is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ) Is of the limited time limit (FTB);
definition two: if the attack estimation error system meets the following conditions:
error system is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ) Is FTB;
in a non-zero initial state, the following is satisfied:
wherein, kappa > 0, xi 1 ＞0,ξ 2 > 0, g (·) is a non-negative function; the error system is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ 。
Through the technical scheme: important quotations and definitions required in the calibration are given before the stability analysis of the error system (22) (23).
Lemma 1: for any matrixAnd->The method meets the following conditions:
wherein ε > 0.
Definition 1: given constant beta 1 ＞0,β 2 > 0 and beta 1 ＜β 2 A matrixSatisfy hypothesis 3 and time interval [0, T ]]If there is a matrix ψ 1 ＞0,Ψ 2 > 0, satisfyThe system (22) is then set to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ) Is of the limited time limit (FTB).
Definition 2: if the attack estimation error system meets the following conditions:
error system (22) is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ) Is FTB;
in a non-zero initial state, the following is satisfied:
wherein kappa > 0, xi 1 ＞0,ξ 2 > 0, g (·) is a non-negative function.
The error system is related to (beta) 1 ,β 2 ,[0T],Ψ 0 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ 。
Theorem 1: given a scalar gamma > 0, delta > 0, zeta 1 ＞0,ξ 2 ＞0,β 1 ＞0,β 2 > 0, ε > 0, T > 0, positive definite matrices are presentSum matrix->The following 3 conditions are satisfied:
R 1 ＜P 1 ,R 2 ＜P 2 (25)
/>
wherein:
λ min (N)＝min{λ min (N 1 ),λ min (N 2 )},λ max (N)＝max{λ max (N 1 ),λ max (N 2 )}。
the error system (22) (23) is then set to (beta) 1 ,β 2 ,[0 T],R 1 ,R 2 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ And the gain matrix of the vehicle distributed observer is l=p 1 -1 W。
The Lyapunov function was demonstrated to be constructed as:
deriving (28) and combining (22) and (23) to obtain:
the following inequality can be obtained according to the quotation 1:
with the combination of hypothesis 1, equations (30) (31) may be converted to:
substitution of formulas (32) (33) into formula (29) can be achieved:
based on (34) it is possible to:
wherein:
definition of the definitionW＝P 1 L, in combination with schur complement, pushes the equation (27):
Ξ 1 -Λ 1 ＜0 (37)
it can then be deduced that:
the combination formula (35) can be further deduced that:
multiplying the left and right sides of (38) by e -δt And performing calculation to obtain:
next, equation (39) is integrated from 0 to t, where t ε [0, T ], one can get:
known from hypothesis 3Satisfying the condition, further deduce-> Wherein d is a ，w a For a given scalar. Since delta > 0, 0 < e -δt And < 1. The equation (40) is converted into:
according to definition 1, a given scalarAnd->The following inequality can be deduced:
now, the formula (42) and the formula (43) are added, and calculated to obtain:
wherein the method comprises the steps of
According to (44) and positive definite matrix R 1 ,R 2 Is obtainable in combination with formula (28):
because of the fact that,
then, there are:
next, substituting (41), (45), (46) into (40) can obtain:
further calculation results in:
based on equations (26) and (47), then it is possible to:
from definition 1, the error system (22) (23) of the observer is FTB.
Next, it was demonstrated that the error system (22) was H ∞ . From the formulae (24), (27), (38):
e is multiplied simultaneously on the left side and the right side of the pair (49) -δt And (3) carrying out integral calculation to obtain:
according to formula (28), (50), we obtain:
wherein the method comprises the steps ofThus proving that the error system (22) is FTB-H ∞ 。
As an embodiment of the present invention, specifically, the adaptive threshold attack detection method design includes:
the expression of the combined state space equation is obtained:
wherein (1)>
The vehicle acceleration estimated using the finite time observer can be expressed as:
further derivation:
finally designed attack detector:
wherein,is a positive scalar;
definition of the definitionThen when the vehicle i is not under attack, the error dynamic expression is: />
When estimating errorsExceeds the designed adaptive attack detection threshold +.>At this point, the detector begins to sound an alarm.
Through the technical scheme: from the system (8) can be derived:
wherein the method comprises the steps ofVehicle acceleration estimated by means of a limited time observer (11)The degree can be expressed as:
from equation (52), it can be further deduced that:
an attack detector of the form:
wherein the method comprises the steps ofIs a positive scalar.
Definition of the definitionThen when the vehicle i is not under attack, the error dynamic expression is:
theorem 2 when the assumption 3 is true, the estimation errorExceeds the designed adaptive attack detection threshold +.>When the vehicle i is attacked and an attack signal is detected, wherein
And (3) proving: will beBoth sides of (56) are simultaneously takenThe method comprises the following steps:
simultaneous integration of both sides of equation (58) can be obtained:
from (59) can be deduced that:
the design threshold expression is:
wherein the method comprises the steps ofIt is further possible to obtain:
/>
when the vehicle contains an attack, equation (56) will be rewritten as:
it can then be deduced that:
it is obvious that when the vehicle is under attack,the value will exceed the designed detection threshold (61). Once the threshold is exceeded, the detector will start to sound an alarm.
It should be noted that: compared with a fixed threshold detection method, the self-adaptive threshold designed by the invention is more flexible, and the threshold initial value can be adjustedAnd +.>The false alarm rate of the attack detector is reduced. In the intelligent network coupled vehicle team, if each vehicle shares acceleration, the attack signal detection may be performed directly using the value of the shared acceleration, instead of using the acceleration estimated by the observer.
As an embodiment of the present invention, finally, taking 5 intelligent network connected vehicle teams following running as examples to perform numerical simulation verification, and simulation results show that the effectiveness of the method of the present invention in this embodiment verifies the feasibility of the method of the present invention by selecting 2 simulation cases, and example 1 is that the intelligent network connected vehicle teams are used to perform example analysis:
let it be assumed that the intelligent network fleet consists of one reference vehicle, 4 following vehicles (k=4). The reference vehicle (Vehice 0) is assumed to be in an ideal state of running without external interference, each vehicle follows the previous vehicle, and the engine index is selected to be 0.1s according to lean-related research. The initial values of position, speed, acceleration and corresponding disturbance for each vehicle are shown in the table:
the topology of the vehicle adjacencies is shown in fig. 2, and the matrix Γ can be derived from fig. 2.α is selected to be 1, the windage coefficient between adjacent vehicles is assumed to be l=0.005, given γ=0.9, δ=3.6.
The distribution coefficients of the speed and acceleration disturbance of the vehicle are respectivelyThe control input of the vehicle is [ u ] 1 ,u 2 ,u 3 ,u 4 ]＝[sin(5t),sin(5t),sin(5t),0.3*heaviside(t)]Wherein u is i (i=1, 2,3, 4) denotes a control input of the i-th vehicle, and weaveside () denotes a step function. The attack signal for each vehicle is set as follows:
/>
from FIG. 2, it is found that the inter-vehicle neighbor matrix is Γ, the vehicle nonlinear term distribution matrix is F, and the attack distribution matrix is D x The specific values are as follows:
selectingCalculating the gain matrix for each vehicle as according to equations (25) (26) (27)
The estimation effect of the observer is shown in fig. 4-7, and the detection effect of the attack detector is shown in fig. 12. Legend x in FIG. 4 ij (i=1, 2,3,4; j=1, 2, 3) represents the j-th state of the i-th vehicle, j=1,2,3 represent the position, speed and acceleration of the vehicle, respectively. It is apparent from fig. 4-7 that when the vehicle has an attack and external disturbance, the distributed observer can accurately estimate the state of the vehicle in a limited time range, which shows that the observer designed by the invention has better estimation performance. Fig. 8-11 show the estimation effect of the vehicle attack signal, and it can be seen that when the transformation amplitude of the attack signal is large, the observer can also quickly converge, and the validity of the observer designed by the invention is verified. Fig. 12 shows the attack detection result of the 2 nd vehicle, and the given attack detection threshold is 3, (0) =1.2, and from the figure, it can be seen that the 2 nd vehicle is attacked at 0.25 s.ltoreq.t.ltoreq.6s, and the adjustment is performedThe value can effectively adjust the convergence speed of the detector, and the validity and the flexibility of the self-adaptive threshold attack detection method are verified.
To further demonstrate the superiority of the distributed finite time observer designed by the invention, the distributed finite time observer is compared with the existing gradual convergence observer; using a system consisting of two identically structured subsystems; the finite time observer of the present invention is compared with a progressively converging observer, irrespective of the nonlinear behaviour of the system and other external disturbances. FIGS. 13-14 and 15 show the state estimation, attack (fault) estimation effects of the two methods, respectively; wherein, in fig. 13-14, a: an actual value representing a state of the subsystem; b: representing an estimated value obtained using the method of the present invention; c: representing an estimated value obtained using the existing method; compared with the existing method C, the estimated value obtained by the method B has higher coincidence with the actual value state and higher convergence speed; fig. 15 a: representing the actual value of the subsystem attack signal; b: representing an estimated value obtained using the method of the present invention; c: representing an estimated value obtained using the existing method; compared with the existing method C, the method B has higher coincidence between the estimated value obtained by the method B and the actual value of the subsystem attack signal; illustrating more accurate convergence.
Summary of proposed finite time observationsBoth the observer and the gradual convergence observer have the performance of accurately estimating the system state, but the observer provided by the invention has higher convergence speed in the aspect of convergence speed. Meanwhile, it is noted that the gradual convergence observer can realize accurate estimation of the system state and faults under the constraint of meeting the assumption 1, while the coefficient matrixes C and D of the vehicle in the embodiment 1 of the invention x Failing to satisfy hypothesis 1, it indicates that the observer is no longer applicable to the scene. From this, it can be derived that the distributed finite time observer proposed by the present invention not only has a faster convergence speed but also gets rid of the constraint of hypothesis 1.
The foregoing is merely illustrative and explanatory of the principles of the invention, as various modifications and additions may be made to the specific embodiments described, or similar thereto, by those skilled in the art, without departing from the principles of the invention or beyond the scope of the appended claims.

Claims (5)

1. A distributed limited time observation method based on intelligent network coupled fleets, the method comprising:
s1, constructing a mathematical model of intelligent network coupling and converting the mathematical model into a state space equation;
the expression of the mathematical model of the intelligent network connection is as follows:
wherein ρ is i Indicating the position, v, of the vehicle i Indicating the speed of the vehicle and,representing acceleration of the vehicle; σ represents a cranking time constant of the engine; d, d i Represents external disturbance, θ 1 ，θ 2 Is constant, θ 1 d i Representing disturbances, θ, in the velocity channel 2 d i Representing disturbances in the acceleration channel, u i Representing actual control inputs of the vehicle;
considering the influence of wind resistance caused by vehicle distance on vehicle speed, the vehicle speed dynamic equation expression is:
wherein Γ is ij Describing the interconnection structure of a vehicle, if Γ ij =0 indicates that vehicle i is disconnected from vehicle j, Γ ij =1 denotes a connection between the vehicle i and the vehicle j, l denotes a windage coefficient between the vehicles, and k denotes a total number of following vehicles;
the expression of the state space equation in the step S1 is:
wherein:
for the measurable output of the vehicle, +.>As a nonlinear function>Represents an attack signal of the vehicle, D x An attack distribution matrix for the vehicle;
is a constant matrix; vehicle state->Vehicle actual control input +.>Vehicle external disturbance->Obviously have
S2, designing a distributed finite time observer according to a state space equation, and obtaining a global estimation error system based on the distributed finite time observer;
s3, performing stability analysis on the overall estimation error through a global estimation error system, designing an adaptive threshold attack detection method on an attack signal of the vehicle, and judging FTB-H through stability analysis ∞ Adequate conditions for performance;
the stability analysis in step S3 includes setting theorem:
given a scalar gamma > 0, delta > 0, zeta 1 ＞0,ξ 2 ＞0,β 1 ＞0,β 2 > 0, ε > 0, T > 0, positive definite matrices are presentSum matrix->The following three conditions are satisfied:
R 1 ＜P 1 ,R 2 ＜P 2
wherein,
λ min (N)＝min{λ min (N 1 ),λ min (N 2 )},λ max (N)＝max{λ max (N 1 ),λ max (N 2 )}；
then the global estimation error system is related to (beta) 1 ,β 2 ,[0T],R 1 ,R 2 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ And the gain matrix of the vehicle distributed observer is l=p 1 -1 W；
The theorem also includes setting an axiom and defining:
the quotation: for any matrixAnd->The method meets the following conditions:
a constant wherein ε > 0;
the definition includes a definition one and a definition two, the definition one: given constant beta 1 ＞0,β 2 > 0 and beta 1 ＜β 2 A matrixSatisfy hypothesis 3: the external disturbance of the velocity channel is unknown but is bounded to meet +.>Attack Signal derivative is unknown but meets->Wherein->d a ,w a For a given scalar; time interval [0, T]If there is a matrix ψ 1 ＞0,Ψ 2 > 0, satisfy:
the error system is related to (beta) 1 ,β 2 ,[0 T],Ψ 0 ,d a ,w a ) Is of the limited time limit (FTB);
the definition II: if the attack estimation error system meets the following conditions:
error system is related to (beta) 1 ,β 2 ,[0 T],Ψ 0 ,d a ,w a ) Is FTB;
in a non-zero initial state, the following is satisfied:
wherein kappa > 0, xi 1 ＞0,ξ 2 > 0, g (·) is a non-negative function;
the error system is related to (beta) 1 ,β 2 ,[0 T],Ψ 0 ,d a ,w a ,κ,ξ 1 ,ξ 2 ) Is FTB-H ∞ ；
The self-adaptive threshold attack detection method comprises the following steps:
the expression combining the state space equation is obtained:
wherein (1)>
The vehicle acceleration estimated using the finite time observer can be expressed as:
wherein,a 3 rd state value representing the i-th vehicle estimated by the observer;
further derivation:
finally designed attack detector:
wherein,is a positive scalar;
definition of the definitionThen when the vehicle i is not under attack, the error dynamic expression is:
when estimating errorsExceeds the designed adaptive attack detection threshold +.>At this point, the detector begins to sound an alarm.
2. The method for distributed limited time observation based on intelligent network coupled fleets according to claim 1, wherein the step S2 specifically comprises: the expression of the distributed intermediate variable observer of the ith vehicle is designed by introducing the intermediate variable as follows:
wherein,for the introduced intermediate variables, matrix-> Is a change scalar; />Is a gain matrix of the system;
order the
Γ＝[Γ ij ] k×k (i,j＝1,2,…,k)。
3. A distributed limited time observation method based on intelligent network coupled fleets according to claim 2, wherein the distributed intermediate variable observer design method is as follows:
(1) The global expression for vehicle state and intermediate variables is:
(2) The vehicle global observer expression is:
wherein, define Respectively representing the overall estimation error of the state of the motorcade, the overall estimation error of the intermediate variable, the overall estimation error of the attack signal and the overall estimation error of the output; the first transformation expression is performed in combination with observer design Fang Fashi (1), equation (2) calculations:
definition of the definitionRepresenting the overall estimation error of the nonlinear term; then:
where K represents an orthogonal matrix of eigenvectors of matrix Γ, Λ=diag { λ 1 ,λ 2 ,…,λ k }，λ i (i=1, 2, …, k) is the eigenvalue of matrix Γ,
I n representing the n-dimensional identity matrix,
4. a distributed limited time observation method based on intelligent network fleets according to claim 3, wherein the global estimation error system expression:
further transforming by transforming the first transformation expression:
；
wherein,orthogonal matrix properties, K T K＝I k 。
5. The intelligent network-coupled fleet-based distributed limited time observation method as set forth in claim 1, further comprising:
and S4, carrying out numerical simulation instance detection on the intelligent network connection motorcade and obtaining the effectiveness of simulation detection results.
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