CN113625684A - Tracking controller and method based on event trigger mechanism under hybrid network attack - Google Patents

Tracking controller and method based on event trigger mechanism under hybrid network attack Download PDF

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CN113625684A
CN113625684A CN202110843029.6A CN202110843029A CN113625684A CN 113625684 A CN113625684 A CN 113625684A CN 202110843029 A CN202110843029 A CN 202110843029A CN 113625684 A CN113625684 A CN 113625684A
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曹杰
刘金良
杨泽宇
赵慕阶
张洋
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Yunjing Business Intelligence Research Institute Nanjing Co ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a tracking controller and a method based on an event trigger mechanism under hybrid network attack. According to the current sampling data and the latest transmission data, establishing a trigger condition based on an event trigger mechanism; and respectively considering the influence of the deception attack and the DoS attack on the transmission data, and establishing a hybrid network attack model. And establishing an error system of the tracking controller and giving a tracking performance index. Sufficient conditions and controller gains to ensure tracking performance of the tracking system are obtained. The invention can effectively save network bandwidth resources and ensure the effectiveness of the system.

Description

Tracking controller and method based on event trigger mechanism under hybrid network attack
Technical Field
The invention belongs to the field of network control, and particularly relates to a design method of a tracking controller with an event trigger mechanism and hybrid network attacks (including spoofing attacks and denial of service attacks).
Background
The goal of output tracking control is to ensure that the system output tracks the known reference model as closely as possible through a suitable controller. With the development of industry, the actual demand is gradually increased, the structure of a control system is increasingly complex, the position of a networked control system in the control system is more and more important, and tracking control is used as a basic problem in the research of control theory and application research and is widely applied in modern industry. Therefore, the research on the tracking control problem of the networked control system has certain theoretical and practical significance.
With the gradual expansion of the scale of the networked control system, the structure of the system is increasingly complex, and important problems such as network delay, data packet loss, transmission limitation and the like are inevitably brought, and the problems not only reduce the control performance of the system, but also influence the stability of the system. In addition, because the bandwidth of the communication channel in the networked control system is limited, the network load is increased, the network is blocked, and the like. The present invention therefore introduces an event triggering mechanism in order to reduce unnecessary waste of bandwidth resources in the network.
The wide introduction of the network system improves the performance of the control system in more aspects, such as resource sharing, convenient maintenance and the like. But at the same time, the system also generates a plurality of potential safety hazards, and the network system is easy to be attacked by the network. Generally, the cyber attack includes a replay attack, a spoofing attack, a denial of service (DoS attack), and the like. The basic principle of replay attacks is to transmit the previously intercepted data intact to the recipient. Spoofing attacks typically replace the actual data of the system with fake data to achieve the specific goals of the attacker. The DoS attack is to send a large number of requests to a server, occupy server resources, and make a user unable to respond in time, thereby losing normal network service.
However, it is understood that most of the existing research results only study one kind of network attack, but actually, these systems may suffer from various network attacks at the same time. To be closer to reality, two common cyber attacks are considered herein, including spoofing attacks and DoS attacks. To our knowledge, there is currently no relevant research effort to study the tracking control problem of networked control systems with event-triggered mechanisms and hybrid network attacks.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides the tracking controller and the method based on the event trigger mechanism under the hybrid network attack, and the event trigger scheme is introduced while the influence of the DoS attack and the deception attack on the network security is considered, so that the network bandwidth resource can be effectively saved, and the effectiveness of the system is ensured.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a tracking controller based on an event trigger mechanism under hybrid network attack is disclosed, wherein an error system of the tracking controller is as follows:
Figure BDA0003179753370000021
wherein,
Figure BDA0003179753370000022
denotes the derivative of e (t), t denotes the time, e (t) denotes the tracking error, e (t) x (t) -xr(t), x (t) denotes a systematic vector, xr(t) represents a reference model system vector, alpha (t) is a Bernoulli variable used for describing whether the spoofing attack occurs or not, wherein when the value is 1, the value does not occur, and when the value is 0, the value occurs; A. b, C, D, E, K is the required controller gain,
Figure BDA0003179753370000023
representing the actual input to the controller; h (e (t)k,nh) A non-linear function representing a spoofing attack; eta of 0 ≦k,n(t)≤ηmRepresenting a time delay, ηk,n(t) represents the time delay, ηmAn upper bound of the time lag is indicated,
definition of We(t)＝(A-D)xr(t) + Cω (t) -Er (t), ω (t) representing the system external disturbance, r (t) representing the bounded reference input vector, εk,n(t) represents the error threshold between the last transmitted signal and the current sampled signal, V1,n-1Indicating DoS attack not launchTime of birth, V2,n-1Indicating the moment at which the DoS attack occurred.
The tracking performance indexes to be met are set as follows:
Figure BDA0003179753370000024
where U is a positive definite matrix. Gamma > 0 is a tracking performance indicator. t is tfIndicating the termination time and U represents a matrix of appropriate dimensions.
Preferably: the sufficient conditions of the tracking performance of the tracking controller are as follows:
Ξ1＜0
Ξ2＜0
the constraint conditions are as follows:
Figure BDA0003179753370000025
Figure BDA0003179753370000031
wherein: i is 1, 2; xi1Denotes an intermediate parameter one, xi2Representing the intermediate parameter two, P1、P2、Qi、Q3-i、Ri、R3-i、Zi、Z3-iAll represent positive definite matrices; tau is2、τ1、β1、β2、τ3-i、
Figure BDA0003179753370000036
zmin、ιDRepresents a given positive parameter; h denotes a sampling period.
Preferably: xi1The following were used:
Figure BDA0003179753370000032
Figure BDA0003179753370000033
Σ11＝2β1P1+P1A+ATP1+Q1-g1R1-g1Z1n+U
Σ32＝g1(R1+S1+Z1+M1)
Σ21＝αKTBTP1+g1R1+g1S1+g1Z1+g1M1
Σ22＝-2g1R1-g1S1-g1S1 T-2g1Z1-g1M1n-g1M1 T+cΩ
Σ31＝-g1S1-g1M1
Σ32＝g1(R1+S1+Z1+M1)
Σ33＝-g1Q1-g1R1-g1Z1
Figure BDA0003179753370000034
Figure BDA0003179753370000035
Δ22＝diag{-Ω,-γ2I,-I}
Figure BDA0003179753370000041
Figure BDA0003179753370000042
Figure BDA0003179753370000043
Δ22＝diag{-Ω,-γ2I,-I}
Figure BDA0003179753370000044
Figure BDA0003179753370000045
Figure BDA0003179753370000046
where α represents the expected value of the Bernoulli variable α (t), I represents the identity matrix of the appropriate dimension, Ω, L represent known matrices, ηm、ρ、β1Indicating a given positive parameter, U, R1、M1Representing a matrix of suitable dimensions, K representing the controller gain
Preferably: xi2The following were used:
Figure BDA0003179753370000051
Y11＝-2β2P2+P2A+ATP2+Q2-g2Z2+U-g2R2
Y21＝g2(Z2+M2+R2+S2)
Figure BDA0003179753370000052
Figure BDA0003179753370000053
Y31＝-g2M2-g2S2
Y32＝g2(Z2+M2+R2+S2)
Y33＝-g2(Q2+Z2+R2)
Y51＝ηmP2A
Y54＝ηmP2
Y55＝-P2(R2+Z2)-1P2
wherein, beta2Representing a known vector, Z2、M2Representing a matrix with appropriate dimensions.
Preferably: controller gain K of the tracking controller:
Figure BDA0003179753370000054
give DoS parameters
Figure BDA0003179753370000058
zmin、ηm、γ、ιDAnd positive scalar parameters alpha, h, c, beta1、β2、τ1、τ2Matrix L, if present
Figure BDA0003179753370000055
Figure BDA0003179753370000056
Matrix array
Figure BDA0003179753370000057
Y has a suitable dimension and is obtained using the linear inequality:
Γ1＜0
Γ2＜0
the constraint conditions are as follows:
Figure BDA0003179753370000061
Figure BDA0003179753370000062
Figure BDA0003179753370000063
Figure BDA0003179753370000064
Figure BDA0003179753370000065
Figure BDA0003179753370000066
Figure BDA0003179753370000067
Figure BDA0003179753370000068
Figure BDA0003179753370000069
Figure BDA00031797533700000610
Figure BDA00031797533700000611
Figure BDA00031797533700000612
Figure BDA00031797533700000613
Figure BDA0003179753370000071
Figure BDA0003179753370000072
Figure BDA0003179753370000073
Figure BDA0003179753370000074
Figure BDA0003179753370000075
Figure BDA0003179753370000076
Figure BDA0003179753370000077
Figure BDA0003179753370000078
Figure BDA0003179753370000079
Figure BDA00031797533700000710
Figure BDA00031797533700000711
Figure BDA0003179753370000081
Figure BDA0003179753370000082
Λ51＝ηmAX2
Λ54＝ηm
Figure BDA0003179753370000083
wherein i is 1, 2; y denotes a matrix, X1Representing a positive definite matrix, X2Denotes a positive definite matrix, τ1Denotes a positive real number, τ2Which represents a positive real number, is,
Figure BDA0003179753370000084
a positive definite matrix is represented and,
Figure BDA0003179753370000085
a positive definite matrix is represented and,
Figure BDA0003179753370000086
a positive definite matrix is represented and,
Figure BDA0003179753370000087
a positive definite matrix is represented and,
Figure BDA0003179753370000088
a matrix representing a suitable dimension is then formed,
Figure BDA0003179753370000089
a matrix representing a suitable dimension is then formed,
Figure BDA00031797533700000810
a positive definite matrix is represented and,
Figure BDA00031797533700000811
denotes positive real number, beta2Which represents a positive real number, is,
Figure BDA00031797533700000812
a matrix representing a suitable dimension is then formed,
Figure BDA00031797533700000813
a matrix representing a suitable dimension is then formed,
Figure BDA00031797533700000814
a positive definite matrix is represented and,
Figure BDA00031797533700000815
a positive definite matrix is represented and,
Figure BDA00031797533700000816
representing a positive definite matrix.
Preferably: the method comprises the following steps of:
the data transmitted under a spoofing attack is represented as:
Figure BDA00031797533700000817
wherein,
Figure BDA00031797533700000818
representing transmitted data under a spoofing attack, α (t) being a Bernoulli variable for use in transmitting data under a spoofing attackIndicates whether a spoofing attack has occurred, where 0 indicates occurrence, 1 indicates non-occurrence, and h (e (t)k,nh) A non-linear function representing a spoofing attack, e (t)k,nh) Representing the transmitted data after passing through the transmission mechanism, e (t)k,nh)＝εk,n(t)+e(t-ηk,n(t))，εk,n(t) represents the error threshold, η, between the last transmitted signal and the current sampled signalk,n(t) represents a time delay, and t represents a time;
the transmission data under DoS attack is represented as:
Figure BDA00031797533700000819
wherein,
Figure BDA00031797533700000820
showing the transmission data under the DoS attack, and zeta (t) represents the state of the DoS attack. ζ (t) ═ 1 denotes when t ∈ [ F ]n,Fn+zn) Meanwhile, the DoS attack is in a sleep state. ζ (t) ═ 0 denotes when t ∈ [ F ]n+zn,Fn+1) Meanwhile, the DoS attack is in an active state, and the system is attacked by the DoS. FnIndicating the start of the nth active period, Fn+1Indicating the end of the nth active period and the beginning of the (n + 1) th sleep period. z is a radical ofnIndicating the length of the sleep period. Therefore, the start and end of DoS attack sleep cycle need to satisfy:
0≤F0＜F1＜F1+z1＜F2＜…＜Fn＜Fn+zn＜Fn+1。
a design method of a tracking controller based on an event trigger mechanism under hybrid network attack mainly aims at designing a tracking controller for a networked control system with an event trigger mechanism and hybrid network attack. An event-triggered mechanism is employed to alleviate network bandwidth load. By utilizing the Lyapunov stability theory, a sufficient condition for ensuring the good tracking performance of the tracking controller is obtained. In addition, the controller gain is obtained by solving a set of linear matrix inequalities. Finally, the effectiveness of the method is verified through a simulation example, and the method specifically comprises the following steps:
step 1: and establishing a system preliminary model and a preliminary reference model based on a networked control system, and designing a preliminary tracking controller.
Step 2: firstly, an event trigger mechanism is introduced, the problem of network resource limitation can be solved by reducing unnecessary data transmission by introducing the event trigger mechanism, and specifically, a trigger condition based on the event trigger mechanism is established according to current sampling data and latest transmission data;
and step 3: and respectively considering the influence of the deception attack and the DoS attack on the transmission data, and establishing a hybrid network attack model.
And 4, step 4: and (3) establishing an error system of the tracking controller and giving a tracking performance index according to the system initial model, the initial reference model and the initial tracking controller established in the step (1), the trigger condition based on the event trigger mechanism established in the step (2) and the hybrid network attack model established in the step (3).
And 5: and obtaining sufficient conditions for ensuring the tracking performance of the tracking system by utilizing the Lyapunov stability theory.
Step 6: and solving the linear inequality to obtain a controller gain K of the tracking controller.
Preferably: the system preliminary model, the preliminary reference model and the preliminary tracking controller in the step 1 are as follows:
and (3) a system preliminary model:
Figure BDA0003179753370000091
a primary reference model:
Figure BDA0003179753370000092
definitions e (t) ═ x (t) — xr(t), designing the following preliminary tracking controller:
Figure BDA0003179753370000093
wherein,
Figure BDA0003179753370000094
denotes the derivative of x (t), x (t) denotes the system vector, u (t) denotes the controller output vector, ω (t) denotes the external input disturbance,
Figure BDA0003179753370000095
denotes xrDerivative of (t), xr(t) represents the reference model system vector, r (t) represents the bounded reference input vector, A, B, C, D, E all represent matrices of suitable dimensions, e (t) represents the tracking error, and K is the controller gain required;
Figure BDA0003179753370000096
representing the actual input to the controller.
Preferably: triggering conditions based on an event triggering mechanism in the step 2:
Figure BDA0003179753370000101
wherein epsilonk(t) represents the error threshold between the last transmitted signal and the current sampled signal, Ω represents a free weight matrix of suitable dimensions, c represents an event trigger scalar parameter, e (t)kh + sh) represents the current sample data, e (t)kh) Indicating the latest transmitted data, tkh denotes the latest transmission time, sh denotes the current sampling time, s denotes a positive integer, and h denotes the sampling period
εk(t)＝e(tkh+sh)-e(tkh)，Ω＞0。
The next transmission instant tk+1h is expressed as:
Figure BDA0003179753370000102
wherein,
Figure BDA0003179753370000103
representing a positive integer.
Preferably: and 4, establishing an error system of the tracking controller and giving a tracking performance index:
due to the existence of DoS attacks, the transmission data will be affected, and the trigger condition based on the event trigger mechanism established in step 2 will no longer be applicable, so in consideration of the influence of DoS attacks, the transmission time is redefined as:
tk,nh＝{tk,ahsatisfying(1)|tk,ah∈Vn-1,1}∪{Fn}
wherein, tk,nh denotes the trigger time, t, of the cycle in the nth DoS attackk,ah represents the trigger time of the a-th DoS period, n represents n DoS attack periods, a represents the a-th DoS period, k represents the number of trigger times in the n-th DoS period, and tk,ah. n, a are all non-negative integers;
definition of
Figure BDA0003179753370000104
Event interval Xk,nThe method is divided into the following cells:
Figure BDA0003179753370000105
the inter-cell representation of the event interval is as follows:
Figure BDA0003179753370000106
and is
Figure BDA0003179753370000111
V1,nThe method is divided into the following steps:
Figure BDA0003179753370000112
wherein,
Figure BDA0003179753370000113
two piecewise functions are defined:
Figure BDA0003179753370000114
and
Figure BDA0003179753370000115
then, the transmission data after the event triggering mechanism is represented as:
e(tk,nh)＝εk,n(t)+e(t-ηk,n(t)), wherein ηk,n(t)∈[0,ηM)。
The event triggering conditions at this time are:
Figure BDA0003179753370000116
wherein eta isk,n(t) represents the system time delay, ∈k,n(t) represents the error threshold, η, between the last transmitted signal and the current sampled signalMRepresents the time lag upper limit, and Ω represents a matrix of suitable dimensions;
and establishing an error system of the tracking controller according to the event triggering condition at the moment.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention establishes a mathematical model of complex network attack aiming at a networked control system on the basis of considering deception attack and DoS attack.
2. And limited bandwidth is saved by adopting an event triggering scheme.
3. And (4) giving sufficient conditions of the tracking performance of the tracking controller by utilizing the Lyapunov theory.
4. The gain of the controller can be derived by solving a series of linear matrix inequalities.
Drawings
FIG. 1: the networked control system tracks the control plan.
FIG. 2: system x1(t) state trajectory and reference system xr1(t) state trace.
FIG. 3: system x2(t) state trajectory and reference system xr2(t) state trace.
FIG. 4: signal of DoS attack.
FIG. 5: the event triggers the release time and interval.
FIG. 6: and (4) spoofing the attack occurrence moment.
Detailed Description
The present invention is further illustrated by the following description in conjunction with the accompanying drawings and the specific embodiments, it is to be understood that these examples are given solely for the purpose of illustration and are not intended as a definition of the limits of the invention, since various equivalent modifications will occur to those skilled in the art upon reading the present invention and fall within the limits of the appended claims.
A method for designing a tracking controller based on an event trigger mechanism under a hybrid network attack, as shown in fig. 1, includes the following steps:
step 1: and establishing a system preliminary model and a preliminary reference model based on a networked control system, and designing a preliminary tracking controller.
And (3) a system preliminary model:
Figure BDA0003179753370000121
a primary reference model:
Figure BDA0003179753370000122
definitions e (t) ═ x (t) — xr(t), designing the following preliminary tracking controller:
Figure BDA0003179753370000123
in (1),
Figure BDA0003179753370000124
denotes the derivative of x (t), x (t) denotes the system vector, u (t) denotes the controller output vector, ω (t) denotes the external input disturbance,
Figure BDA0003179753370000125
denotes xrDerivative of (t), xr(t) represents the reference model system vector, r (t) represents the bounded reference input vector, A, B, C, D, E all represent matrices of suitable dimensions, e (t) represents the tracking error, and K is the controller gain required;
Figure BDA0003179753370000126
representing the actual input to the controller.
Step 2: in order to effectively save bandwidth, an event triggering scheme is introduced: according to the current sampling data and the latest transmission data, establishing a trigger condition based on an event trigger mechanism;
Figure BDA0003179753370000131
wherein epsilonk(t) represents the error threshold between the last transmitted signal and the current sampled signal, Ω represents a free weight matrix of suitable dimensions, c represents an event trigger scalar parameter, e (t)kh + sh) represents the current sample data, e (t)kh) Indicating the latest transmitted data, tkh represents the latest transmission time, sh represents the current sampling time, s represents a positive integer, and h represents the sampling period;
εk(t)＝e(tkh+sh)-e(tkh)，Ω＞0。
the next transmission instant tk+1h is expressed as:
Figure BDA0003179753370000132
wherein,
Figure BDA0003179753370000133
representing a positive integer.
And step 3: and respectively considering the influence of the deception attack and the DoS attack on the transmission data, and establishing a hybrid network attack model.
The data transmitted under a spoofing attack is represented as:
Figure BDA0003179753370000134
wherein,
Figure BDA0003179753370000135
representing the transmitted data under the spoofing attack, alpha (t) is a Bernoulli variable used for representing whether the spoofing attack occurs or not, wherein 0 represents occurrence, 1 represents non-occurrence, and h (e (t) isk,nh) A non-linear function representing a spoofing attack, e (t)k,nh) Representing the transmitted data after passing through the transmission mechanism, e (t)k,nh)＝εk,n(t)+e(t-ηk,n(t))，εk,n(t) represents the error threshold, η, between the last transmitted signal and the current sampled signalk,n(t) represents a time delay, and t represents a time;
the transmission data under DoS attack is represented as:
Figure BDA0003179753370000136
wherein,
Figure BDA0003179753370000137
represents the transmission data under DoS attack, and ζ (t) represents the state of DoS attack. ζ (t) ═ 1 denotes when t ∈ [ F ]n,Fn+zn) Meanwhile, the DoS attack is in a sleep state. ζ (t) ═ 0 denotes when t ∈ [ F ]n+zn,Fn+1) Meanwhile, the DoS attack is in an active state, and the system is attacked by the DoS. FnIndicating the start of the nth active period, Fn+1Indicating the end of the nth active period and the beginning of the (n + 1) th sleep period. z is a radical ofnIndicating the length of the sleep period. Therefore, the start and end of DoS attack sleep cycle need to satisfy:
0≤F0＜F1＜F1+z1＜F2＜…＜Fn＜Fn+zn＜Fn+1。
and 4, step 4: and (3) establishing an error system of the tracking controller and giving a tracking performance index according to the system initial model, the initial reference model and the initial tracking controller established in the step (1), the trigger condition based on the event trigger mechanism established in the step (2) and the hybrid network attack model established in the step (3).
Due to the existence of DoS attacks, the transmission data will be affected, and the trigger condition based on the event trigger mechanism established in step 2 will no longer be applicable, so in consideration of the influence of DoS attacks, the transmission time is redefined as:
tk,nh＝{tk,ahsatisfying(1)|tk,ah∈Vn-1,1}∪{Fn}
wherein, tk,nh denotes the trigger time, t, of the cycle in the nth DoS attackk,ah represents the trigger time of the a-th DoS period, n represents n DoS attack periods, a represents the a-th DoS period, and t representsk,ah. n, a are all non-negative integers.
Definition of
Figure BDA0003179753370000141
Event interval Xk,nThe method is divided into the following cells:
Figure BDA0003179753370000142
the inter-cell representation of the event interval is as follows:
Figure BDA0003179753370000143
and is
Figure BDA0003179753370000144
V1,nThe method is divided into the following steps:
Figure BDA0003179753370000145
wherein,
Figure BDA0003179753370000146
two piecewise functions are defined:
Figure BDA0003179753370000147
and
Figure BDA0003179753370000151
then, the transmission data after the event triggering mechanism is represented as:
e(tk,nh)＝εk,n(t)+e(t-ηk,n(t)), wherein ηk,n(t)∈[0,ηM)。
The event triggering conditions at this time are:
Figure BDA0003179753370000152
wherein eta isk,n(t) represents the system time delay, ∈k,n(t) represents the error threshold, η, between the last transmitted signal and the current sampled signalMRepresents the time lag upper limit, and Ω represents a matrix of suitable dimensions;
the following tracking controller error system was set up:
Figure BDA0003179753370000153
wherein e (t) x (t) -xr(t), x (t) denotes a systematic vector, xr(t) denotes the reference model system vector, A, B, C, D, E denotes a matrix of appropriate dimensions, e (t) denotes the tracking error, and K is the required controller gain。
Figure BDA0003179753370000154
Representing the actual input to the controller. α (t) is a bernoulli variable used to describe whether a spoofing attack occurred, where a value of 1 indicates no occurrence and 0 indicates occurrence. Suppose h (e (t)k,nh) ) represents a non-linear function of a spoofing attack. Eta of 0 ≦k,n(t)≤ηmRepresenting a time delay. We(t)＝(A-D)xr(t)+Cω(t)-Er(t)。
The tracking performance indexes to be met are set as follows:
Figure BDA0003179753370000155
where U is a positive definite matrix. Gamma > 0 is a tracking performance indicator. t is tfIndicating the termination time.
And 5: and a Lyapunov stability theory is utilized to obtain a sufficient condition for ensuring the tracking performance of the tracking system.
Give DoS parameters
Figure BDA0003179753370000156
zmin、ηm、γ、ιDAnd positive scalar parameters alpha, h, c, beta1、β2、τ1、τ2A matrix K, L, P if there is a matrix Ω > 01>0、P2>0、Q1＞0,Q2＞0,R1＞0,R2＞0,Z1＞0,Z2> 0, matrix U, S1,S2,M1,M2With the dimensions in place, the following inequality holds:
Ξ1＜0
Ξ2＜0
the constraint conditions are as follows:
Figure BDA0003179753370000161
Figure BDA0003179753370000162
wherein:
Figure BDA0003179753370000163
Figure BDA0003179753370000164
Σ11＝2β1P1+P1A+ATP1+Q1-g1R1-g1Z1n+U,Σ32＝g1(R1+S1+Z1+M1)
Σ21＝αKTBTP1+g1R1+g1S1+g1Z1+g1M1
Figure BDA0003179753370000171
Figure BDA0003179753370000172
Figure BDA0003179753370000173
Δ22＝diag{-Ω,-γ2I,-I}
Figure BDA0003179753370000174
Figure BDA0003179753370000175
Figure BDA0003179753370000176
Figure BDA0003179753370000177
Y11＝-2β2P2+P2A+ATP2+Q2-g2Z2+U-g2R2
Y31＝-g2M2-g2S2
Y21＝g2(Z2+M2+R2+S2)
Figure BDA0003179753370000181
Y32＝g2(Z2+M2+R2+S2)
Y33＝-g2(Q2+Z2+R2)
Y51＝ηmP2A,Y54＝ηmP2,Y55＝-P2(R2+Z2)-1P2
step 6: and solving the linear inequality to obtain a controller gain K of the tracking controller.
Give DoS parameters
Figure BDA0003179753370000185
zmin、ηm、γ、ιDAnd positive scalar parameters alpha, h, c, beta1、β2、τ1、τ2Matrix L, if present
Figure BDA0003179753370000182
Figure BDA0003179753370000183
Matrix array
Figure BDA0003179753370000184
Y has a suitable dimension and can be obtained using the linear inequality:
Γ1＜0
Γ2＜0
the constraint conditions are as follows:
Figure BDA0003179753370000191
Figure BDA0003179753370000192
Figure BDA0003179753370000193
Figure BDA0003179753370000194
Figure BDA0003179753370000195
the required controller gains are:
Figure BDA0003179753370000196
wherein:
Figure BDA0003179753370000197
Figure BDA0003179753370000198
Figure BDA0003179753370000199
Figure BDA00031797533700001910
Figure BDA00031797533700001911
Figure BDA00031797533700001912
Figure BDA00031797533700001913
Figure BDA0003179753370000201
Figure BDA0003179753370000202
Figure BDA0003179753370000203
Figure BDA0003179753370000204
Figure BDA0003179753370000205
Figure BDA0003179753370000206
Figure BDA0003179753370000207
Figure BDA0003179753370000208
Figure BDA0003179753370000209
Figure BDA0003179753370000211
Figure BDA0003179753370000212
Figure BDA0003179753370000213
Figure BDA0003179753370000214
Figure BDA0003179753370000215
simulation analysis:
the Matlab program is written to solve the linear matrix inequality to solve the gain of the tracking controller and draw a simulation curve, and the effectiveness of the method is demonstrated by using a simulation example.
Consider the parameters in the system model as:
Figure BDA0003179753370000216
B＝[0 1]T,C＝[0 1]T
and the external disturbance input is: ω (t) ═ 8sin (t-0.5).
The reference model is:
Figure BDA0003179753370000217
wherein: r (t) sin (t + 0.5).
The nonlinear function under a spoofing attack is: h (e (t) [ -tanh [)T(0.15e1(t)) -tanhT(0.05e2(t))]T；
The following scalar parameters are set: beta is a1＝0.15,β2＝2,τ1＝1.02,τ2＝1.02,ηm＝0.2,zmin＝1.3，
Figure BDA0003179753370000218
The event trigger parameter c is 0.4; the index parameter of the tracking performance is gamma which is 0.7; the bernoulli variable α is 0.6, indicating that the system is subject to spoofing and DoS attacks. Initial conditions were set to x (0) ═ 0.2-0.1]T,xr(0)＝[0.5 0.1]T. By solving the linear inequality by Matlab, the following matrix parameters can be obtained:
Y＝[0.6030 -1.8109]，
Figure BDA0003179753370000221
Figure BDA0003179753370000222
by expression
Figure BDA0003179753370000223
The controller gain can be obtained as
K＝[0.0560 -0.0245]。
FIGS. 2-5 are graphs derived from Matlab, obtaining by simulation. FIGS. 2 and 3 show the state traces of system x (t) and reference system xr(t), therefore, the designed method can ensure that the system state can track the state of the reference model and has good tracking performance; FIG. 4 shows signals of a DoS attack; FIG. 5 shows the event-triggered release times and intervals; fig. 6 shows the occurrence time of a spoofing attack.
From the images obtained above, the following conclusions can be drawn: the controller of the networked control system based on the event trigger and the hybrid network attack can realize good tracking control.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (10)

1. A tracking controller based on an event trigger mechanism under hybrid network attack is characterized in that: the error system of the tracking controller is as follows:
Figure FDA0003179753360000011
wherein,
Figure FDA0003179753360000012
denotes the derivative of e (t), t denotes the time, e (t) denotes the tracking error, e (t) x (t) -xr(t), x (t) denotes a systematic vector, xr(t) represents a reference model system vector, alpha (t) is a Bernoulli variable used for describing whether the spoofing attack occurs or not, wherein when the value is 1, the value does not occur, and when the value is 0, the value occurs; A. b, C, D, E, K is the required controller gain,
Figure FDA0003179753360000013
representing the actual input to the controller; h (e (t)k,nh) Is shown in (a)A non-linear function of a spoofing attack; eta of 0 ≦k,n(t)≤ηmRepresenting a time delay, ηk,n(t) represents the time delay, ηmAn upper bound of the time lag is indicated,
definition of We(t)＝(A-D)xr(t) + Cω (t) -Er (t), ω (t) representing the system external disturbance, r (t) representing the bounded reference input vector, εk,n(t) represents the error threshold between the last transmitted signal and the current sampled signal, V1,n-1Indicating the moment at which DoS attack does not occur, V2,n-1Representing the moment of occurrence of the DoS attack;
the tracking performance indexes to be met are set as follows:
Figure FDA0003179753360000014
wherein U is a positive definite matrix; gamma > 0 is a tracking performance index; t is tfIndicating the termination time.
2. The tracking controller based on the event trigger mechanism under the hybrid network attack according to claim 1, wherein: the sufficient conditions of the tracking performance of the tracking controller are as follows:
Ξ1＜0
Ξ2＜0
the constraint conditions are as follows:
Figure FDA0003179753360000021
Figure FDA0003179753360000022
wherein: i is 1, 2; xi1Denotes the intermediate parameter one, xi2Representing the intermediate parameter two, P1、P2、Qi、Q3-i、Ri、R3-i、Zi、Z3-iAll represent positive definite matrices; tau is2、τ1、β1、β2、τ3-i、
Figure FDA0003179753360000026
zmin、ιDRepresents a given positive parameter; h denotes a sampling period.
3. The tracking controller based on the event trigger mechanism under the hybrid network attack according to claim 2, wherein: intermediate parameter xi1The following were used:
Figure FDA0003179753360000023
Figure FDA0003179753360000024
Σ11＝2β1P1+P1A+ATP1+Q1-g1R1-g1Z1+U
Σ32＝g1(R1+S1+Z1+M1)
Σ21＝αKTBTP1+g1R1+g1S1+g1Z1+g1M1
Figure FDA0003179753360000025
Σ31＝-g1S1-g1M1
Σ32＝g1(R1+S1+Z1+M1)
Σ33＝-g1Q1-g1R1-g1Z1
Figure FDA0003179753360000031
Figure FDA0003179753360000032
Δ22＝diag{-Ω,-γ2I,-I}
Figure FDA0003179753360000033
Figure FDA0003179753360000034
Figure FDA0003179753360000035
Δ22＝diag{-Ω,-γ2I,-I}
Figure FDA0003179753360000036
Figure FDA0003179753360000037
Δ33＝diag{-I,-P1(R1+Z1)-1P1,-P1(R1+Z1)-1P1},
Figure FDA0003179753360000038
where α represents the expected value of the Bernoulli variable α (t), I represents the identity matrix of the appropriate dimension, Ω, L represent known matrices, ηm、ρ、β1Indicating a given positive parameter, U, R1、M1A matrix with appropriate dimensions is shown and K represents the controller gain.
4. The tracking controller based on the event trigger mechanism under the hybrid network attack according to claim 3, wherein: intermediate (II)
Parameter two xi2The following were used:
Figure FDA0003179753360000041
Y11＝-2β2P2+P2A+ATP2+Q2-g2Z2+U-g2R2
Y21＝g2(Z2+M2+R2+S2)
Figure FDA0003179753360000042
Figure FDA0003179753360000043
Y31＝-g2M2-g2S2
Y32＝g2(Z2+M2+R2+S2)
Y33＝-g2(Q2+Z2+R2)
Y51＝ηmP2A
Y54＝ηmP2
Y55＝-P2(R2+Z2)-1P2
wherein, beta2Representing a known vector, Z2、M2Representing a matrix with appropriate dimensions.
5. The tracking controller based on the event trigger mechanism under the hybrid network attack according to claim 4, wherein: controller gain K of the tracking controller:
Figure FDA0003179753360000044
give DoS parameters
Figure FDA0003179753360000045
zmin、ηm、γ、ιDAnd positive scalar parameters alpha, h, c, beta1、β2、τ1、τ2Matrix L, if present
Figure FDA0003179753360000051
Figure FDA0003179753360000052
Matrix array
Figure FDA0003179753360000053
Y has a suitable dimension and is obtained using the linear inequality:
Γ1＜0
Γ2＜0
the constraint conditions are as follows:
Figure FDA0003179753360000054
Figure FDA0003179753360000055
Figure FDA0003179753360000056
Figure FDA0003179753360000057
Figure FDA0003179753360000058
Figure FDA0003179753360000059
Figure FDA00031797533600000510
Figure FDA00031797533600000511
Figure FDA0003179753360000061
Figure FDA0003179753360000062
Figure FDA0003179753360000063
Figure FDA0003179753360000064
Figure FDA0003179753360000065
Figure FDA0003179753360000066
Figure FDA0003179753360000067
Figure FDA0003179753360000068
Figure FDA0003179753360000069
Figure FDA00031797533600000610
Figure FDA00031797533600000611
Figure FDA0003179753360000071
Figure FDA0003179753360000072
Figure FDA0003179753360000073
Figure FDA0003179753360000074
Figure FDA0003179753360000075
Figure FDA0003179753360000076
Figure FDA0003179753360000077
Λ51＝ηmAX2
Λ54＝ηm
Figure FDA0003179753360000078
where i ═ 1,2, Y denotes a matrix, X1Representing a positive definite matrix, X2Denotes a positive definite matrix, τ1Denotes a positive real number, τ2Which represents a positive real number, is,
Figure FDA0003179753360000079
a positive definite matrix is represented and,
Figure FDA00031797533600000710
a positive definite matrix is represented and,
Figure FDA00031797533600000711
a positive definite matrix is represented and,
Figure FDA00031797533600000712
a positive definite matrix is represented and,
Figure FDA00031797533600000713
a matrix representing a suitable dimension is then formed,
Figure FDA00031797533600000714
a matrix representing a suitable dimension is then formed,
Figure FDA00031797533600000715
denotes a positive definite matrix, ζ1Denotes positive real number, beta2Which represents a positive real number, is,
Figure FDA00031797533600000716
a matrix representing a suitable dimension is then formed,
Figure FDA00031797533600000717
a matrix representing a suitable dimension is then formed,
Figure FDA00031797533600000718
a positive definite matrix is represented and,
Figure FDA00031797533600000719
a positive definite matrix is represented and,
Figure FDA00031797533600000720
representing a positive definite matrix.
6. The tracking controller based on the event trigger mechanism under the hybrid network attack according to claim 5, wherein: the method comprises the following steps of:
the data transmitted under a spoofing attack is represented as:
Figure FDA00031797533600000721
wherein,
Figure FDA00031797533600000722
representing a spoofing attackTransmitted data under attack, α (t) is a Bernoulli variable used to indicate whether a spoofing attack has occurred, where 0 indicates occurrence, 1 indicates non-occurrence, and h (e (t) isk,nh) A non-linear function representing a spoofing attack, e (t)k,nh) Representing the transmitted data after passing through the transmission mechanism, e (t)k,nh)＝εk,n(t)+e(t-ηk,n(t))，εk,n(t) represents the error threshold, η, between the last transmitted signal and the current sampled signalk,n(t) represents a time delay, and t represents a time;
the transmission data under DoS attack is represented as:
Figure FDA0003179753360000081
wherein,
Figure FDA0003179753360000082
represents the transmission data under the DoS attack, and ζ (t) represents the state of the DoS attack; ζ (t) ═ 1 denotes when t ∈ [ F ]n,Fn+zn) Meanwhile, the DoS attack is in a dormant state; ζ (t) ═ 0 denotes when t ∈ [ F ]n+zn,Fn+1) When the system is in the active state, the system is attacked by the DoS; fnIndicating the start of the nth active period, Fn+1Indicating the end of the nth active period and the beginning of the (n + 1) th sleep period; z is a radical ofnRepresents the length of the sleep period; therefore, the start and end of DoS attack sleep cycle need to satisfy:
0≤F0＜F1＜F1+z1＜F2＜…＜Fn＜Fn+zn＜Fn+1；
for writing convenience, order
Figure FDA0003179753360000083
7. A method for designing a tracking controller based on an event trigger mechanism under the hybrid network attack according to claim 1, comprising the following steps:
step 1: establishing a system preliminary model and a preliminary reference model based on a networked control system, and designing a preliminary tracking controller;
step 2: according to the current sampling data and the latest transmission data, establishing a trigger condition based on an event trigger mechanism;
and step 3: respectively considering the influence of the deception attack and the DoS attack on the transmission data, and establishing a hybrid network attack model;
and 4, step 4: establishing a tracking controller error system and giving a tracking performance index according to the system initial model, the initial reference model and the initial tracking controller established in the step 1, the trigger condition based on the event trigger mechanism established in the step 2 and the hybrid network attack model established in the step 3;
and 5: obtaining sufficient conditions for ensuring the tracking performance of the tracking system by utilizing the Lyapunov stability theory;
step 6: and solving the linear inequality to obtain a controller gain K of the tracking controller.
8. The method for designing a tracking controller based on an event trigger mechanism under the hybrid network attack as claimed in claim 7, wherein: the system preliminary model, the preliminary reference model and the preliminary tracking controller in the step 1 are as follows:
and (3) a system preliminary model:
Figure FDA0003179753360000084
a primary reference model:
Figure FDA0003179753360000091
definitions e (t) ═ x (t) — xr(t), designing the following preliminary tracking controller:
Figure FDA0003179753360000092
wherein,
Figure FDA0003179753360000093
denotes the derivative of x (t), x (t) denotes the system vector, u (t) denotes the controller output vector, ω (t) denotes the external input disturbance,
Figure FDA0003179753360000094
denotes xrDerivative of (t), xr(t) represents the reference model system vector, r (t) represents the bounded reference input vector, A, B, C, D, E all represent matrices of suitable dimensions, e (t) represents the tracking error, and K is the controller gain required;
Figure FDA0003179753360000095
representing the actual input to the controller.
9. The method for designing a tracking controller based on an event trigger mechanism under the hybrid network attack as claimed in claim 8, wherein: triggering conditions based on an event triggering mechanism in the step 2:
Figure FDA0003179753360000096
wherein epsilonk(t) represents the error threshold between the last transmitted signal and the current sampled signal, Ω represents a free weight matrix of suitable dimensions, c represents an event trigger scalar parameter, e (t)kh + sh) represents the current sample data, e (t)kh) Indicating the latest transmitted data, tkh represents the latest transmission time, sh represents the current sampling time, s represents a positive integer, and h represents the sampling period;
εk(t)＝e(tkh+sh)-e(tkh)，Ω＞0；
the next transmission instant tk+1h is expressed as:
Figure FDA0003179753360000097
wherein,
Figure FDA0003179753360000098
representing a positive integer.
10. The method for designing a tracking controller based on an event trigger mechanism under the hybrid network attack according to claim 9, wherein: and 4, establishing an error system of the tracking controller and giving a tracking performance index:
due to the existence of DoS attacks, the transmission data will be affected, and the trigger condition based on the event trigger mechanism established in step 2 will no longer be applicable, so in consideration of the influence of DoS attacks, the transmission time is redefined as:
tk,nh＝{tk,ah satisfying formula (1) | tk,ah∈V1,n-1}∪{Fn}
Wherein, tk,nh denotes the trigger time, t, of the cycle in the nth DoS attackk,ah represents the trigger time of the a-th DoS period, n represents n DoS attack periods, a represents the a-th DoS period, k represents the number of trigger times in the n-th DoS period, and tk,ah. n, a are all non-negative integers;
definition of
Figure FDA0003179753360000101
Event interval Xk,nThe method is divided into the following cells:
Figure FDA0003179753360000102
Figure FDA0003179753360000103
the inter-cell representation of the event interval is as follows:
Figure FDA0003179753360000104
and is
Figure FDA0003179753360000105
V1,nThe method is divided into the following steps:
Figure FDA0003179753360000106
wherein,
Figure FDA0003179753360000107
two piecewise functions are defined:
Figure FDA0003179753360000108
and
Figure FDA0003179753360000109
then, the transmission data after the event triggering mechanism is represented as:
e(tk,nh)＝εk,n(t)+e(t-ηk,n(t)), wherein ηk,n(t)∈[0,ηM)；
The event triggering conditions at this time are:
Figure FDA0003179753360000111
wherein eta isk,n(t) represents the system time delay, ∈k,n(t) represents the error threshold, η, between the last transmitted signal and the current sampled signalMRepresents the time lag upper limit, and Ω represents a matrix of suitable dimensions;
and establishing an error system of the tracking controller according to the event triggering condition at the moment.
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