CN109795277B - Reliability control method for DoS attack on active suspension system - Google Patents

Reliability control method for DoS attack on active suspension system Download PDF

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CN109795277B
CN109795277B CN201811209604.1A CN201811209604A CN109795277B CN 109795277 B CN109795277 B CN 109795277B CN 201811209604 A CN201811209604 A CN 201811209604A CN 109795277 B CN109795277 B CN 109795277B
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dos attack
suspension system
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active suspension
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CN109795277A (en
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储尧
孙翔
顾洲
阚宇超
李元哲
钱孝龙
林榆森
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Nanjing Forestry University
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Abstract

The invention discloses a reliability control method for an active suspension system under DoS attack, which considers the situation that the DoS attack occurs in a network between a controller and an execution unit, adopts a random switching method to process the attack, and enables the active suspension system to be switched back and forth between an attacked subsystem and an attacked subsystem. After the method is adopted, the reliability of the control of the attacked suspension system is ensured.

Description

Reliability control method for DoS attack on active suspension system
Technical Field
The invention relates to an active suspension control method, in particular to an active suspension reliability control method for an in-vehicle network under DoS (noise-of-service) attack.
Background
With the development of network control, a large system network for wireless communication and information exchange between vehicles and X (X: vehicles, roads, the Internet and the like) is formed in the Internet of vehicles, and the network is an integrated network capable of realizing intelligent traffic management, intelligent dynamic information service and intelligent vehicle control. The suspension system is one of main components influencing the riding comfort and the comfort of the vehicle, and is naturally connected with an integrated network for intelligent control of the vehicle through an in-vehicle network, so that the superiority of the network is utilized to carry out better control.
Compared with the traditional suspension system which transmits information through an in-vehicle bus, the suspension control system information based on network communication is obtained through network remote filtering and sensing, and the robust and reliable control problem of the network control system comes with the following problems: network attack, network skew, data packet loss, misordering, etc. Network attacks are a major concern as the most common network security issue. In many practical control systems, network attacks can be injected into the system through the network part in a stealthy and unpredictable manner. The DoS is a short term for Denial of Service, that is, Denial of Service, and the attack behavior of DoS is called DoS attack, which aims to make a computer or a network unable to provide normal services. Among the various malicious attacks, DoS attacks can cause actuator and sensor data to be blocked rather than reaching their respective destinations and causing data loss for the relevant components, further affecting the stability of the control system.
Disclosure of Invention
The invention aims to provide a reliability control method for an active suspension system under DoS attack, aiming at the problem that the actuator and sensor data are blocked by the DoS attack to cause data loss of related components.
The technical scheme of the invention is as follows:
the invention provides a method for controlling the reliability of an active suspension system under DoS attack, which is designed to comprise the following steps
Firstly, establishing a quarter active suspension system model;
Figure GDA0003192735170000021
wherein: t represents the time of day and,
Figure GDA0003192735170000022
is the state equation of the system, x (t) is the state variable, a, B, C and D are the coefficient matrices of the state equation, u (t) is the active control force, ω (t) is the road surface input, z (t) is the control output variable;
in the second step, when the network between the controller and the actuator is attacked by DoS (noise-of-service), the following active suspension switching system model is used for description:
Figure GDA0003192735170000023
wherein:
Figure GDA0003192735170000024
is the equation of state of the system, x (t) is the state variable, αi(t) is a random variable which is,
Figure GDA0003192735170000025
Figure GDA0003192735170000026
and DiIs a coefficient matrix of a state equation, i is the number of the automobile suspension subsystems, N represents the total number of the automobile suspension subsystems, ω (t) is the road surface input, h is the sampling period, lkIs the number of the data packet,/k(k-1, 2,3 …) is a positive real number and
Figure GDA0003192735170000027
τkis the firstkTransmission time of a data packet, etamIs the lower bound of η (t), ηMIs { (l)k+1-lk)h+τk+1K is the upper bound of 1,2, …, z (t) is the control output variable, t0Represents an initial time, and t represents a current time; Φ (t) represents the initial time of the state variable;
thirdly, establishing a state feedback controller: u (t) ═ Kix(t-η(t))
Wherein: η (t) is the network delay;
the fourth step, use H∞Method for determining feedback gain K of controlleriAnd updating the active suspension switching system model in the second step to control the reliability of the active suspension.
Further, in the second step, the random variable αi(t) the following formula is used:
Figure GDA0003192735170000031
wherein: σ (t) represents a switching signal in DoS attack, i is 1 when the DoS attack is not received, and i is 2 when the DoS attack is received; in this case, the automotive suspension system is divided into two subsystems.
Further, the probability of each subsystem staying is obtained through probability statistics
Figure GDA0003192735170000032
The following conditions are satisfied:
Figure GDA0003192735170000033
Figure GDA0003192735170000034
wherein E { α [ ]i(t) } denotes αi(t) mathematical expectation.
Further, ηmIs taken to be 0, etaMIs 0.39, H∞Norm bound gamma is 3.
Further, in the second step,
Figure GDA0003192735170000035
wherein A isiAnd BiIs the state parameter matrix, Δ A, of the ith subsystemi(t) and. DELTA.Bi(t) is an uncertainty in the system, and the following condition is satisfied: [ Delta A ]i(t) ΔBi(t)]＝GiFi(t)[E1i E2i]Wherein G isi，E1iAnd E2iIs a real matrix of appropriate dimensions, function Fi(t) is an uncertainty matrix and satisfies
Figure GDA0003192735170000036
Further, η (t) is network delay, and includes data packet loss and delay information.
Further, in the first step, road surface input ω (t) is a disturbance parameter, and road surface displacement data acquired by a sensor is adopted.
The invention has the beneficial effects that:
the invention considers the situation that the DoS attack occurs in the network between the controller and the execution, and adopts a random switching method to process the attack, so that the active suspension system is switched back and forth between an attacked subsystem and an un-attacked subsystem. After the method is adopted, the reliability of the control of the attacked suspension system is ensured.
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The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts throughout.
Fig. 1 shows a flow chart of the present invention.
FIG. 2 shows a vehicle suspension system control flow diagram.
Fig. 3 shows a schematic diagram of a handover sequence in an embodiment.
Fig. 4 shows a state response curve in an embodiment.
Detailed Description
Preferred embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein.
The invention provides a method for controlling the reliability of an active suspension system under DoS attack, which is designed to comprise the following steps
Firstly, establishing a quarter active suspension system model;
Figure GDA0003192735170000041
wherein: t represents the time of day and,
Figure GDA0003192735170000042
is the state equation of the system, x (t) is the state variable, a, B, C and D are the coefficient matrices of the state equation, u (t) is the active control force, ω (t) is the road surface input, z (t) is the control output variable;
in the second step, when the network between the controller and the actuator is attacked by DoS (noise-of-service), the following active suspension switching system model is used for description:
Figure GDA0003192735170000051
wherein:
Figure GDA0003192735170000052
is the equation of state of the system, x (t) is the state variable, αi(t) is a random variable which is,
Figure GDA0003192735170000053
Figure GDA0003192735170000054
and DiIs a coefficient matrix of a state equation, i is the number of the automobile suspension subsystems, N represents the total number of the automobile suspension subsystems, ω (t) is the road surface input, h is the sampling period, lkIs the number of the data packet,/k(k-1, 2,3 …) is a positive real number and
Figure GDA0003192735170000055
τkis the firstkTransmission time of a data packet, etamIs the lower bound of η (t), ηMIs { (l)k+1-lk)h+τk+1K is an upper bound of 1, 2. }, z (t) is a control output variable, t0Represents an initial time, and t represents a current time; Φ (t) represents the initial time of the state variable;
thirdly, establishing a state feedback controller: u (t) ═ Kix(t-η(t))
Wherein: η (t) is the network delay;
the fourth step, use H∞Method for determining feedback gain K of controlleriAnd updating the active suspension switching system model in the second step to control the reliability of the active suspension.
In specific implementation, the design principle of the invention is as follows:
the related data of the quarter active suspension system can be obtained through a sensor, a sampler transmits the data to a controller in the form of data packets through a network, the controller determines that a controllable acting force device outputs corresponding acting force through the sampled data, then signals are transmitted to an actuating mechanism through the network, and finally the actuating mechanism executes instructions of the controller. We now consider the case where the network between the controller and the actuator is subject to a DoS attack. The invention adopts a random switching method to process the attack based on the situation, so that the active suspension system is switched back and forth between the attacked subsystem and the non-attacked subsystem. And then designing a controller, solving the feedback gain, and finally performing simulation in MATLAB, wherein the simulation result shows that the reliability of the active suspension system can be ensured under the condition of DOS network attack by the proposed method.
1. System modeling
In the present study, a two-degree-of-freedom quarter automotive suspension model was considered for controller design. This model has been widely used in research because it can capture many important features of many complex suspension models. For a quarter-vehicle suspension model, the equations for motion control of sprung and unsprung masses can be expressed as
Figure GDA0003192735170000061
Wherein m issIs a sprung mass, representing the chassis of the vehicle; m isuUnsprung mass, representing a wheel assembly; c. CsAnd ksDamping and stiffness of the passive suspension, respectively; k is a radical oftAnd ctRespectively, the compressibility and the damping of the pneumatic tire; z is a radical ofs(t) and zu(t) displacement of unsprung and unsprung masses, respectively; z is a radical ofr(t) is a road displacement input; u (t) represents the active control force, which is typically provided by a hydraulic actuator placed between the sprung mass and the unsprung mass of the vehicle suspension.
Defining the state variables according to
x(t)＝[x1(t) x2(t) x3(t) x4(t)]T
Here, the
x1(t)＝zs(t)-zu(t), suspension displacement;
x2(t)＝zu(t)-zr(t), tire displacement;
Figure GDA0003192735170000062
sprung mass velocity;
Figure GDA0003192735170000063
unsprung mass velocity;
thus, equation (1) is written in the form of a state space equation
Figure GDA0003192735170000064
Where x (t) ε R4，w(t)∈R，u(t)∈R，A∈R4×4，B∈R4×1，D∈R4×1。
Furthermore, it is possible to provide a liquid crystal display device,
Figure GDA0003192735170000071
Figure GDA0003192735170000072
Figure GDA0003192735170000073
the invention considers the situation that the DoS attack occurs in the network between the controller and the execution, and adopts a random switching method to process the attack, so the system can be divided into two subsystems: one is the suspension subsystem under DoS attack, and the other is the active suspension subsystem which is not under attack and normal, so that the active suspension system can switch between the two subsystems under attack and not under attack. Since the data packet may have transmission time lag, data packet loss and other problems during transmission, the system (equation 2) may be expressed as:
Figure GDA0003192735170000074
where h is the sampling period, lk( k 1,2, 3.) is a positive real number and
Figure GDA0003192735170000076
τkdenotes the lkTransmission time of a data packet, etaMDenotes { (l)k+1-lk)h+τk+1K is the upper bound of 1, 2. Phi (t) the initial function of the system. The state feedback controller shown below is used for the system:
u(t+)＝Kσ(t)x(lkh)，t∈{lkh+τk，k＝1，2，...}
for t e [ l ∈ [ ]kh+τk，lk+1h+τk+1]Definition of η (t) ═ t-ikh, from the above analysis, η (t) includes the comprehensive information such as the packet loss and the delay, and ηm≤ηMThus, the state feedback controller may be denoted as u (t) ═ Kσ(t)x (t- η (t)). Substituting the above formula for u (t) in (3), the following system equation can be obtained:
Figure GDA0003192735170000075
where η (t) is unknown and time-varying, σ (t) is the switching signal, σ (t) ═ i (i ∈ Ω · {1, 2.., N }) denotes switching to the ith subsystem, and N denotes the number of subsystems, where N is obviously 2. A. thei，Bi，Ci，DiRepresenting a constant matrix of appropriate dimensions, K, in the ith subsystemiIs the state table feedback controller gain for the ith subsystem.
In this example, for the convenience of study and explanation, we make the following assumptions:
suppose 1.1 in the present invention, we assume that the suspension system dwell probability under Dos attack is known, i.e., Pr { σ (t) ═ i | t ∈ Z+，
Figure GDA0003192735170000081
Wherein
Figure GDA0003192735170000082
Indicating the probability of the system switching to stay in the ith subsystem.
Note 1.1
Figure GDA0003192735170000083
It can be obtained by statistical methods:
Figure GDA0003192735170000084
wherein k isiIs that σ (a) ═ i in the interval [1, a ]]，a∈Z+The number of times.
Assume a class 1.2 random variable αi(t) is defined as
Figure GDA0003192735170000085
Then alphaiThe mathematical expectation of (t) is
Figure GDA0003192735170000086
And alpha isi(t) and alphaiSatisfy the requirement of
Figure GDA0003192735170000087
Note that 1.2 assumes α in 1.2i(t) satisfies Bernoulli distribution, αiThe variance of (t) can be expressed as
Figure GDA0003192735170000088
Therefore, the suspension system model in the present invention can be expressed as:
Figure GDA0003192735170000089
in order to obtain the results of the stability analysis, several arguments are given below which play a significant role in the analysis of the main results:
introduction 1.1 pairsGiven a positive integer n, m and a scalar α ∈ (0, 1), a given n × n matrix R > 0, W1，W2∈
Figure GDA00031927351700000810
Definitions for all variables ξ ∈ E
Figure GDA00031927351700000811
The function Θ (α, R), defined as:
Figure GDA00031927351700000812
then if there is a matrix H e
Figure GDA00031927351700000813
So that
Figure GDA00031927351700000814
Then inequality
Figure GDA00031927351700000815
This is true.
Lemma 1.2 for a given n × n matrix R > 0 and all continuous differentiable functions
Figure GDA00031927351700000816
Inequality
Figure GDA0003192735170000091
It is true that, among other things,
Figure GDA0003192735170000092
theorem 1.3 given a matrix W, M, N of appropriate dimensions, where W is symmetric, the following inequality W + MF (t) N + NTFT(t)MT< 0 for arbitrarily satisfying FT(t) F (t) ≧ I F (t) holds, if and only if there is a scalar ε > 0 such that W + ε MMT+ε-1NTN < 0 or equivalent to:
Figure GDA0003192735170000093
theorem 1.4(Schur complement) gives a constant matrix A, P, Q, where Q ═ QT，P＝PTIf greater than 0, then ATPA + Q < 0 holds, if and only if
Figure GDA0003192735170000094
Or
Figure GDA0003192735170000095
2. Demonstration of stability
Mean square stability and H of the principal analysis System (5) of this subsection∞Performance, to simplify the analysis, defines:
Figure GDA0003192735170000099
Figure GDA0003192735170000096
thus, the system (5) can be represented as:
Figure GDA0003192735170000097
note 3.3 in the following demonstration of the main results, the integral [ t-eta ] will be integratedM，t]Is divided into [ t- η ]M，t-η(t)]And [ t- η (t), t)]Two intervals were analyzed.
Definition 1.1 for a suspension system under DoS attack, the following two conditions are assumed to hold:
(1) when w (t) is 0, the system (6) is stable in mean square;
(2) for scalar γ > 0, under zero initial conditions, the control outputs z (t) satisfying:
Figure GDA0003192735170000098
then, we say that the system (6) is mean square stable and fullFoot H∞Norm bound gamma.
Theorem 1.1 given handover probability information
Figure GDA00031927351700001013
And positive real numbers gamma and matrix Ki(i ∈ Ω ═ {1, 2.., N }), if there is a matrix of appropriate dimensions P > 0, Q > 0, R > 0, and H such that the following linear matrix inequality is in η (t) ∈ { η }, where Q > 0m，ηMIs true
Figure GDA0003192735170000101
Figure GDA0003192735170000102
Figure GDA0003192735170000103
Wherein the content of the first and second substances,
Figure GDA0003192735170000104
Figure GDA0003192735170000105
Figure GDA0003192735170000106
Figure GDA0003192735170000107
Figure GDA0003192735170000108
Figure GDA0003192735170000109
Figure GDA00031927351700001010
Figure GDA00031927351700001011
Figure GDA00031927351700001012
then the system (6) is mean square stable and satisfies H∞Norm bound gamma.
And (3) proving that: constructing a Lyapunov function of the form:
Figure GDA0003192735170000111
since P > 0, Q > 0, and R > 0, the Lyapunov function is positive, and mathematically expecting this function yields:
Figure GDA0003192735170000112
attention is paid to
Figure GDA0003192735170000113
Equation (8) may become
Figure GDA0003192735170000114
Then, the integral term in the above formula (9) is added
Figure GDA0003192735170000115
The upper and lower bounds in (1) are divided into two intervals for analysis, namely:
Figure GDA0003192735170000116
applying the theorem 1.2 to the above formula (9) then yields:
Figure GDA0003192735170000117
wherein the content of the first and second substances,
Figure GDA0003192735170000118
applying the theorem 1.1, if there is a matrix H e
Figure GDA0003192735170000119
So that
Figure GDA00031927351700001110
Then
Figure GDA00031927351700001111
By combining formula (9) and formula (10), we can obtain,
Figure GDA0003192735170000121
then using the theorem 1.4 to the right of equation (11) yields:
Figure GDA0003192735170000122
wherein the content of the first and second substances,
Figure GDA0003192735170000123
then, the left and right sides of the matrix on the left side of the inequality (11) are simultaneously multiplied by a diagonal matrix diag { I, I, I, I, I, R }, etaMAnd
Figure GDA0003192735170000127
then we can get the following inequality:
Figure GDA0003192735170000128
thus, when the presence matrix H satisfies
Figure GDA0003192735170000124
And Ψ1When < 0, E { ζT(t)Ψ1Zeta (t) } is less than or equal to 0, let t → ∞, under the zero initial condition and in combination with the definition of 3.1, we can obtain that the system (6) is stable in mean square and satisfies H∞Norm bound gamma.
When the system (6) contains an uncertain item, the system equation is expressed as:
Figure GDA0003192735170000125
wherein the content of the first and second substances,
Figure GDA0003192735170000129
[ΔAi(t) ΔBi(t)]＝GiFi(t)[E1i E2i]wherein G isiE1iAnd E2iIs a real matrix of appropriate dimensions, function Fi(t) is an indeterminate array and satisfies
Figure GDA0003192735170000126
Based on theorem 3.1, the following results can be obtained:
theorem 3.2 given handover probability information
Figure GDA00031927351700001210
And positive real numbers gamma and matrix Ki(i ∈ Ω · {1, 2.. N }), if a matrix inequality exists at η (t) ∈ { η ·m，ηMThe interval is established
Figure GDA0003192735170000131
Figure GDA0003192735170000132
Wherein the content of the first and second substances,
Figure GDA0003192735170000133
N＝[E1i E2iKi 0 0 0 0 0]
then, the suspension system (12) of the uncertain DoS attack is robust, mean square stable and satisfies H∞Norm bound gamma
And (3) proving that: similar to the proof method of theorem 3.1, provided that A is usedi+GiFi(t)E1iAnd Bi+GiFi(t)E2iInstead of A in inequality (5)iAnd BiThe following can be obtained:
Figure GDA0003192735170000134
using the lemma 3.3, then, if and only if there is a constant $ \ varespsilon _1 > 0$, the following inequality always holds:
Ψ1+ε1MMT+ε1NNT＜0
finally, by using the theorem of 3.4, the inequality (13) can be obtained from the inequality (7), and the certificate is complete.
3. Robust H∞Controller design
Theorem 3.3 for given handover probability information
Figure GDA0003192735170000137
And positive real numbers gamma and matrix epsilon0If a matrix of appropriate dimensions P > 0, Q > 0, R > 0 and H and a scalar ε are present1> 0 such that the underlying LMIs are ∈ η (t) { η ∈m，ηMIs true
Figure GDA0003192735170000135
Figure GDA0003192735170000136
Figure GDA0003192735170000141
Wherein the content of the first and second substances,
Figure GDA0003192735170000142
Figure GDA0003192735170000143
Figure GDA0003192735170000144
Figure GDA0003192735170000145
Figure GDA0003192735170000146
Figure GDA0003192735170000147
Figure GDA0003192735170000148
Figure GDA0003192735170000149
Figure GDA00031927351700001410
Figure GDA00031927351700001411
Figure GDA00031927351700001412
Figure GDA00031927351700001413
Θ31＝[E1iX E2iYi 0 0 0 0 0]
Figure GDA00031927351700001414
then, the suspension system (12) of the uncertain DoS attack is robust, mean square stable and satisfies H∞Norm bound gamma feedback gain of Ki＝YiX-1。
And (3) proving that: first, the left side of the left matrix of the inequality (13) is multiplied by the diagonal matrix diag { I, P }, and the right side is multiplied by its transpose, so as to obtain the following inequality:
Figure GDA0003192735170000151
wherein the content of the first and second substances,
Figure GDA0003192735170000152
then define
Figure GDA0003192735170000153
Because of the fact that
Figure GDA0003192735170000154
Wherein epsiloniGiven positive real numbers, the following inequality must be givenThe following holds true:
Figure GDA0003192735170000155
then, the left and right sides of the matrix on the left side of equation (17) are multiplied by the diagonal matrix diag { X, X, X, X, X, I, X, I, I }, and finally, using theorem 3.4, inequalities (15) and (16) can be obtained from inequalities (17) and (18).
4. And (3) simulation results:
a quarter of the vehicle suspension system parameters are given as follows:
Figure GDA0003192735170000156
the coefficient matrix can be obtained from the parameters
Figure GDA0003192735170000157
Figure GDA0003192735170000158
C1＝C2＝[-0.0563 0 -0.0031 0.0031]
Figure GDA0003192735170000161
Figure GDA0003192735170000162
Figure GDA0003192735170000163
Figure GDA0003192735170000164
The feedback gain K1 determined using the LMI toolbox in matllab based on the above parameters,
Figure GDA0003192735170000165
and the DoS attack period K2 is 0.
Here we take ε0＝1，
Figure GDA0003192735170000166
For a given ηm＝0，ηM0.39, the initial state of the system is takent＝[0.04 0.003 3 4]TExternal disturbance w (t) ═ 2 × e-0.5tsin(0.5t)
The switching sequence is as in fig. 3, so the state response graph 4 of the system (12) can be simulated.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims (7)

1. A reliability control method for DoS attack on an active suspension system is characterized in that the method comprises the following steps
Firstly, establishing a quarter active suspension system model;
Figure FDA0003214106370000011
wherein: t represents the time of day and,
Figure FDA0003214106370000012
is the state equation of the system, x (t) is the state variable, a, B, C and D are coefficient matrices, u (t) is the active control force, ω (t) is the road surface input, z (t) is the control output variable;
in the second step, when the network between the controller and the actuator is attacked by DoS (noise-of-service), the following active suspension switching system model is used for description:
Figure FDA0003214106370000013
wherein:
Figure FDA0003214106370000014
is the equation of state of the system, x (t) is the state variable, αi(t) is a random variable which is,
Figure FDA0003214106370000015
Figure FDA0003214106370000016
Ciand DiIs a coefficient matrix, i is the number of the automotive suspension subsystems, N represents the total number of the automotive suspension subsystems, ω (t) is the road surface input, h is the sampling period, l is the total number of the automotive suspension subsystemskIs the number of the data packet,/k(k-1, 2,3 …) is a positive real number and
Figure FDA0003214106370000017
τkis the firstkTransmission time of a data packet, etamIs the lower bound of η (t), ηMIs { (l)k+1-lk)h+τk+1K is the upper bound of 1,2, …, z (t) is the control output variable, t0Represents an initial time, and t represents a current time; Φ (t) represents the initial time of the state variable;
thirdly, establishing a state feedback controller: u (t) ═ Kix(t-η(t))
Wherein: η (t) is the network delay;
the fourth step, use H∞Method for determining feedback gain K of controlleriAnd updating the active suspension switching system model in the second step to control the reliability of the active suspension.
2. A method for addressing active as claimed in claim 1The reliability control method of DoS attack on suspension system is characterized by that in the second step, random variable alphai(t) the following formula is used:
Figure FDA0003214106370000021
wherein: σ (t) represents a switching signal in DoS attack, i is 1 when the DoS attack is not received, and i is 2 when the DoS attack is received; in this case, the automotive suspension system is divided into two subsystems.
3. The method for controlling the reliability of DoS attack on an active suspension system according to claim 1 or 2, wherein the probability of each subsystem staying is obtained through probability statistics
Figure FDA0003214106370000022
Figure FDA0003214106370000023
Satisfying the following conditions
Figure FDA0003214106370000024
Figure FDA0003214106370000025
Wherein E { α [ ]i(t) } denotes αi(t) mathematical expectation.
4. The method of claim 1, wherein η is greater than or equal to η |, where η is greater than or equal to ηmIs taken to be 0, etaMIs 0.39, H∞Norm bound gamma is 3.
5. A method for addressing active as claimed in claim 1The reliability control method for the DoS attack on the suspension system is characterized in that in the second step,
Figure FDA0003214106370000026
wherein A isiAnd BiIs the state parameter matrix, Δ A, of the ith subsystemi(t) and. DELTA.Bi(t) is an uncertainty in the system, and the following condition is satisfied: [ Delta A ]i(t) ΔBi(t)]＝GiFi(t)[E1i E2i]Wherein G isi，E1iAnd E2iIs a real matrix of appropriate dimensions, function Fi(t) is an uncertainty matrix and satisfies Fi T(t)Fi(t)≤I。
6. The method as claimed in claim 1, wherein η (t) is network delay and includes information about packet loss and delay.
7. The method as claimed in claim 1, wherein in the first step, the road input ω (t) is a disturbance parameter, and the road displacement data obtained by the sensor is used.
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