CN109491249B - Method for determining consistency event trigger controller in presence of DoS attack - Google Patents

Method for determining consistency event trigger controller in presence of DoS attack Download PDF

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CN109491249B
CN109491249B CN201811451504.XA CN201811451504A CN109491249B CN 109491249 B CN109491249 B CN 109491249B CN 201811451504 A CN201811451504 A CN 201811451504A CN 109491249 B CN109491249 B CN 109491249B
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刘皓
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Benxi Steel Group Information Automation Co ltd
Dragon Totem Technology Hefei Co ltd
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Abstract

The invention relates to the technical field of networked control systems, in particular to a method for determining a consistency event trigger controller by utilizing a modal-dependent average residence time method aiming at the condition that a multi-agent system with a leader has a Denial-of-Service (DoS), which comprises the following steps: firstly, establishing a leader-follower multi-agent system model and a design event triggering condition; step two, establishing a DoS attack model and a switching system model; and step three, designing an event trigger controller and corresponding switching conditions. The invention provides a method for adopting modal dependence average residence time, which solves the design problem of a consistency event trigger controller when a leader-follower multi-agent system has a DoS network attack.

Description

Method for determining consistency event trigger controller in presence of DoS attack
Technical Field
The invention relates to the technical field of networked control systems, in particular to a method for determining a consistency event trigger controller by utilizing a modal-dependent average residence time method aiming at the condition that a multi-agent system with a leader has a Denial-of-Service (DoS) attack.
Background
The multi-agent system is an important research direction of the network control system, and the leader-follower system is an important research topic of the multi-agent system, and has wide practical application values, such as multi-unmanned formation control, cluster control, intelligent vehicle formation control and the like.
Because the intelligent agent has limited data processing capacity, if the data amount is excessive, the processing speed can be delayed and even cause network congestion, and therefore, the calculation for reducing the data amount by adopting an appropriate method has practical significance. Event trigger control provides a good idea for solving the problem, so that data can be transmitted and calculated only when certain trigger conditions are met, and the transmission, storage and calculation of the data can be greatly reduced. However, most leader-follower multi-agent systems do not consider the situation of the DoS network attack between the leader and the follower at present, so that the research on the situation has strong practical significance.
The invention provides a method for average residence time by adopting modal dependence, which solves the design problem of a consistency event trigger controller when a leader-follower multi-agent system has a DoS network attack.
Disclosure of Invention
The invention aims to provide a modal dependence-based average residence time method, which aims at the design of a consistency event trigger controller of a multi-agent system and solves the problem that consistency control cannot be realized when a DoS attack exists between a leader and a follower in the prior art. The technical scheme of the invention is implemented as follows:
1) establishing a leader-follower multi-agent system model and designing event triggering conditions;
2) establishing a DoS attack model and a switching system model;
3) the design event triggers the controller and the corresponding switching conditions.
The first step is as follows: considering that the leader is a high-order system and is not influenced by the dynamic of the follower, the model is
Figure GDA0003219508040000021
The model of the ith follower is
Figure GDA0003219508040000022
Therefore, the consistency control protocol of the ith follower of the multi-agent system is designed to be
Figure GDA0003219508040000023
The corresponding event trigger condition is designed as
Figure GDA0003219508040000024
Wherein
Figure GDA0003219508040000025
The second step is as follows: assuming that the DoS attack satisfies: (1)
Figure GDA0003219508040000026
(2)
Figure GDA0003219508040000027
when attack exists, communication between a leader and a follower is interrupted, a communication topological structure is changed, and the system is changed from stable to unstable at the moment, so that a switching system is adopted to describe the leader-follower multi-agent system when DoS attack exists; the system under attack corresponds to the unstable subsystem of the switching system, and the system under no attackThe system corresponds to a stabilizing subsystem; also, the switching system model may be expressed as follows:
Figure GDA0003219508040000028
the third step is as follows: in step two, the feedback gain is unknown, and the following method is adopted for design; given the parameters alpha > 0, beta > 0, mu1> 1 and 0 < mu2< 1, if matrix X is present1＞0，X2> 0 and Y1, Y2 is such that
Figure GDA0003219508040000029
Figure GDA00032195080400000210
X1≤μ2X2；X2≤μ1X1
Wherein,
Figure GDA00032195080400000211
p is 1, 2; then, the controller gain can be designed to be
Figure GDA0003219508040000031
P is 1, 2; if leader-follower multi-agent consistency is met, the switching signals of the switching system also need to be met
Figure GDA0003219508040000032
Figure GDA0003219508040000033
The method is suitable for large-scale unmanned aerial vehicle formation flight control or intelligent vehicle formation control in the presence of network attacks.
The invention has the beneficial effects that:
the invention designs a consistency event triggering controller which can ensure that a multi-agent system can still ensure consistency when a leader-follower multi-agent system has a DoS attack. A multi-agent system under DoS attack is described by adopting a switching system, and a switching condition meeting the system consistency is provided by utilizing a mode-dependent average residence time method, and the condition that an event trigger condition does not have a Zeno phenomenon is ensured. Due to the design of the event trigger controller, the data volume processed by the system can be greatly reduced, and the calculation and transmission energy is saved. The method is suitable for large-scale unmanned aerial vehicle formation flight control or intelligent vehicle formation control in the presence of network attacks, and has great practical application value.
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In order to facilitate understanding for those skilled in the art, the present invention will be further described with reference to the accompanying drawings.
FIG. 1 is a distributed event-triggered delivery strategy for the ith follower.
Detailed Description
In order to make the technical embodiments of the present invention more clearly understood, specific embodiments are given below: the distributed event-triggered delivery strategy for the ith follower of the present invention is shown in FIG. 1.
Establishing leader-follower multi-agent system model and designing event triggering conditions
Assume leader satisfaction
Figure GDA0003219508040000034
The kinetic equation of the ith follower is
Figure GDA0003219508040000035
Wherein,
Figure GDA0003219508040000036
n is the number of followers. The invention aims to realize the limsup when the DoS attack existst→∞||z(t)||≤δ，z(t)＝col{z1(t)，z2(t)，...zN(t)}，zi(t)＝xi(t)-x0(t)。
For follower i, consider the following measurement error:
Figure GDA0003219508040000041
wherein,
Figure GDA0003219508040000042
the kth event for follower i triggers the time. Definition of
Figure GDA0003219508040000043
Selecting a coherency control protocol
Figure GDA0003219508040000044
Wherein, the matrix K is a feedback gain required to be designed.
Event trigger time of follower i
Figure GDA0003219508040000045
The following method may be employed for determination:
Figure GDA0003219508040000046
it should be noted that only in
Figure GDA0003219508040000047
At that moment, the i-th follower sends the current state information to its neighbors and updates the control data, and then the measurement error is reset to zero. In addition, the designed event triggering condition must ensure that the Zeno phenomenon is removed, otherwise, the system cannot normally operate, namely, the requirement of meeting the requirement
Figure GDA0003219508040000048
1) Establishing DoS attack model and switching system model
Suppose the DoS attack time is
Figure GDA0003219508040000049
Definition of Rn＝[rn，rn+τn) And represents the nth time period of the DoS attack. Tau isnActual interval lasting for nth attack and satisfying taun＜rn+1-rnAnd Tmax≥τn≥τminIs greater than 0. Is defined as follows
Figure GDA00032195080400000410
And
Figure GDA00032195080400000411
wherein
Figure GDA00032195080400000412
And
Figure GDA00032195080400000413
respectively, indicating the time intervals of communication interruption and communication. Thus, the control protocol of the follower i can be expressed as
Figure GDA00032195080400000414
Wherein,
Figure GDA0003219508040000051
Figure GDA0003219508040000052
the DoS attack is assumed to satisfy the following frequency and duration constraints:
Figure GDA0003219508040000053
Figure GDA0003219508040000054
wherein, T is more than or equal to 01≤T2，Nσ2(T1，T2) Is represented in the time interval T1，T2) Number of intra-DoS attacks.
Definition of zi(t)＝xi(t)-x0(t)，
Figure GDA0003219508040000055
And z (t) col { z1(t)，z2(t)，...zN(t) }, then one can obtain
Figure GDA0003219508040000056
As can be seen from equation (8), in the presence of a DoS attack, the leader-follower multi-agent system model can be described by the switching system. The switching system comprises two subsystems, a stable subsystem and an unstable subsystem. The multi-agent system corresponds to an unstable subsystem when an attack exists.
2) Designing event-triggered controllers and corresponding switching conditions
Assuming that a supporting tree exists in the communication topology of the leader-follower system when no DoS attack exists, the leader agent is a root node. Given the parameters alpha > 0, beta > 0, mu1> 1 and 0 < mu2< 1, if matrix X is present1＞0，X2> 0 and Y1, Y2 is such that
Figure GDA0003219508040000057
Figure GDA0003219508040000058
X1≤μ2X2，X2≤μ1X1(11) Wherein,
Figure GDA0003219508040000059
p is 1, 2, and the DoS attack satisfies constraint (6) (7),
Figure GDA0003219508040000061
Figure GDA0003219508040000062
then, leader-follower multi-agent coherence can be satisfied, and z (t) satisfies
Figure GDA0003219508040000063
Wherein,
Figure GDA0003219508040000064
Figure GDA0003219508040000065
Figure GDA00032195080400000621
c＝exp{N01lnμ1+N02lnμ2}
Figure GDA00032195080400000620
Figure GDA00032195080400000610
Figure GDA00032195080400000611
thus, the controller gain can be designed to be
Figure GDA00032195080400000612
P is 1, 2. In addition, the selected event trigger condition is satisfied
Figure GDA00032195080400000613
Wherein,
ω＝λmax{(A+AT)/2}，
Figure GDA00032195080400000615
Figure GDA00032195080400000619
the preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (2)

1. A method for determining a coherence event triggered controller in the presence of a DoS attack, comprising the steps of:
the method comprises the following steps: establishing a leader-follower multi-agent system model and designing event triggering conditions;
step two: establishing a DoS attack model and a switching system model;
step three: designing an event trigger controller and corresponding switching conditions;
the first step is as follows: considering that the leader is a high-order system and is not influenced by the dynamic of the follower, the model is
Figure FDA0003219508030000011
The model of the ith follower is
Figure FDA0003219508030000012
Wherein,
Figure FDA0003219508030000013
n is the number of followers; therefore, the consistency control protocol of the ith follower of the multi-agent system is designed to be
Figure FDA0003219508030000014
Wherein, the matrix K is a feedback gain required to be designed; the corresponding event trigger condition is designed as
Figure FDA0003219508030000015
Wherein
Figure FDA0003219508030000016
Figure FDA0003219508030000017
Triggering time for the kth event of the follower i;
the second step is as follows: assuming that the DoS attack satisfies: (1)
Figure FDA0003219508030000018
(2)
Figure FDA0003219508030000019
wherein, T is more than or equal to 01≤T2，Nσ2(T1，T2) Is represented in the time interval T1，T2) The number of intra-DoS attacks; when attack exists, communication between a leader and a follower is interrupted, a communication topological structure is changed, and the system is changed from stable to unstable at the moment, so that a switching system is adopted to describe the leader-follower multi-agent system when DoS attack exists; the system under attack corresponds to an unstable subsystem of the switching system, and the system under attack corresponds to a stable subsystem; and,the switching system model can be expressed as follows:
Figure FDA00032195080300000110
the third step is as follows: in step two, the feedback gain is unknown, and the following method is adopted for design; given the parameters alpha > 0, beta > 0, mu1> 1 and 0 < mu2< 1, if matrix X is present1＞0，X2> 0 and Y1，Y2So that
Figure FDA00032195080300000111
Figure FDA00032195080300000112
X1≤μ2X2；X2≤μ1X1
Wherein,
Figure FDA0003219508030000021
p is 1, 2; then, the controller gain can be designed to be
Figure FDA0003219508030000022
P is 1, 2; if leader-follower multi-agent consistency is met, the switching signals of the switching system also need to be met
Figure FDA0003219508030000023
2. The method for determining the consistency event trigger controller in the presence of a DoS attack as claimed in claim 1, wherein the method is suitable for large-scale unmanned aerial vehicle formation flight control or intelligent vehicle formation control in the presence of a network attack.
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