CN105467839A - Multi-agent system security consensus control method in malicious environment - Google Patents

Abstract

The invention relates to a multi-agent system against a malicious environment, puts forward a security consensus control method which can resist enemy attack and communication delay, and belongs to the field of multi-agent system distributed coordinated control. The implementation process of the method comprises the following steps: (1) constructing an adaptive cutting parameter rt(k) according to the state information of an individual and the delay information of surrounding neighbor nodes, adaptively cutting the number of pieces of received information in each round, using the retained information in state updating, and finally making all normal agents consistent in state; and (2) analyzing the conditions for the multi-agent system to realize consensus control under malicious attack based on the knowledge of graph theory. Compared with the traditional method, the method of the invention breaks through the limitation that the traditional method is only applicable to a multi-agent system which has a fixed network topology and does not consider the communication delay, and has a strong practical prospect in the industrial sector and military.

Description

The convergent control method of multi-agent system safety under a kind of hostile environments

Technical field

The present invention relates to multi-agent system Coordinated Control field, particularly relate to a kind of have resist malicious attack ability multi-agent system safety convergent control method.

Background technology

Multi-agent system (multi-agentsystems) is the network system being associated to by modes such as communications of intelligent body that a group possesses certain perception, communication, calculating and executive capability.So-called convergent (consensus) control problem, refers to by designing suitable control protocol, the state value of all individualities in multi-agent system is reached unanimity progressively or in finite time.Convergent control has very wide application background in every field such as military affairs, space flight, industry, and the cooperation control etc. as multi-robot formation, multi-satellite system, the scheduling of robotization highway, wireless sensor network is all its typical application example.And the convergent control of safety, then on the basis of convergent control, propose higher control overflow.The basic thought of the convergent control of safety is by applying to control to the normal intelligent body in network, make it in the convergent agreement of execution, the attack of malice intelligent body can be resisted, guarantee that oneself state is in change in a permissible range (security domain) all the time, and finally reach unanimity.In the last few years, along with the development of computer technology and the day by day universal of network system, the safety issue of the convergent control of multi-agent system more and more receives the concern of domestic and international expert.

Mainly there is the deficiency of following two aspects in the convergent control method of traditional safety: on the one hand, and these control methods all suppose that the communication between system individuality is desirable situation, i.e. each intelligent physical efficiency interactive information in real time.But for the communication network of reality, time delay is ubiquity and inevitably.More have even, there is a class malice intelligent body, make communication link produce specific time delay by special attack means; On the other hand, current most of agreement is the network topology for static state, namely carrys out design agreement according to fixing communication line, and this often cannot tackle some moveable malicious attack nodes flexibly, has certain application limitation.

Summary of the invention

The present invention will overcome the deficiency of above-mentioned control method, proposes a kind of under hostile environments, has the convergent control method of multi-agent system safety adapting to time-varying network and communication delay ability.The control method more in the past of control method designed by the present invention, to node flexibly attack pattern there is strong robustness, and be applicable to the network environment with communication delay, formation motivation of the present invention that Here it is.

The object of the invention is to the multi-agent system network to having under malicious attack and communication delay double influence, propose a kind of convergent control method of safety with anti-malicious attack and time delay ability, thus widen the research application category of the convergent control of multi-agent system.

The technical solution adopted for the present invention to solve the technical problems is:

The convergent control method of multi-agent system safety under hostile environments, comprises the following steps:

Step 1. founding mathematical models.Consider the multi-agent system network be made up of n node, node on behalf intelligent body in network.N is included in hypothetical network _sindividual normal node and n _aindividual malicious node, meets n _s+ n _a=n.The dynamic model of i-th normal node is:

x _i(k+1)＝x _i(k)+u _i(k),i∈V _s(1)

Wherein x _i(k) and u _ik () is respectively node i at the state value in k moment and control inputs, V _srepresent the set of all normal node.In supposition system in addition, the dynamic equation of all malicious nodes is unknown, they upgrade oneself state value not in accordance with designed control protocol, there is the ability changing arbitrarily oneself state value, and deceptive information can be manufactured send to surrounding normal node, cause normal node to make a mistake because adopting these deceptive information when more new state, thus reach the object destroying the convergent process of whole network.

Step 2. control method designs.According to the mathematical model of above-mentioned foundation, and the attack characteristics of malicious node, it is subsequent that we provide detailed controller design method.The present invention considers the identification serial number of all normal node other nodes unknown in network, has under to be no more than f neighbours be the prerequisite of malicious node at the most only knowing in surrounding neighbours, namely | and N _i∩ V _a|≤f, f ∈ Z ⁺, wherein V _arepresent the set of all malicious nodes, Z ⁺represent positive integer, according to the time delay status information CONTROLLER DESIGN of oneself state and neighbours.Concrete steps are as follows:

Step 21: initialization system

Make k=0, initialization system, all normal node give original state value;

Step 22: calculate and delete auto-adaptive parameter

In the kth wheel moment, all value of information x that this moment gathers in the crops by normal node i _j(k-d _i,j(k)), j ∈ N _iafter arranging, do descending sort by the size of numerical value, wherein j represents the node now transmitting information to node i, d _i,jk () is the communication delay between i and j, N _ifor the neighbours of node i collect, namely all can send information to node i set of node.Note n _ithe k total number of neighbours that () is k moment node i, r _ik () deletes auto-adaptive parameter, r for controller _ik the value of () is given according to following rule:

$r_i\left(k\right)=\left\{\begin{array}{cc}{n}_i\left(k\right)-f-1,& n_i\left(k\right)<2f+1\\ f,& n_i\left(k\right)\&GreaterEqual;2f+1\end{array}\right.;---\left(2\right)$

Step 23: create and delete rule

That tries to achieve based on step 22 deletes auto-adaptive parameter r _ik (), next we create node and delete rule: be no less than r if had in the sequence of node i arrangement _ik () individual value is strictly greater than oneself state value x _ik (), so by r front in sequence _ik () individual value removes, as less than r _ik () is individual, then these are greater than x _ik the value of () all removes; Similarly, as there being many r in infructescence _ik () individual value is strictly less than oneself state value x _ik (), so by r rear in sequence _ik () individual value removes, as less than r _ik () is individual, then these are less than x _ik the value of () all removes;

Step 24: design con-trol agreement

According to the value of information having deleted rear reservation in step 23, to the following convergent control protocol of node i design:

$u_i\left(k\right)=\frac{1}{\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)}\&times;\left(\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\right(k)\left(x_j\right(k-d_{i,j}\left(k\right))-x_i(k\left)\right))---\left(3\right)$

In conjunction with before individual dynamic equation, control system closed loop equation is:

$x_i(k+1)=x_i\left(k\right)+\frac{1}{\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)}\&times;\left(\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\right(k)\left(x_j\right(k-d_{i,j}\left(k\right))-x_i(k\left)\right))---\left(4\right)$

In formula, each mathematic sign implication is as follows:

D _i,jk (), for node j is to the communication delay of node i, meets constant for the communication delay upper bound, meet $\stackrel{\&OverBar;}{d}={\sup }_{k\&GreaterEqual;0}max\{d_{i,j}\left(k\right),j\&Element;N_i,i\&Element;V_s\}.$ Time delay is there is not, i.e. d when considering that each node obtains oneself state _i,i(k)=0, a _i,j>=0 is the communication weight between node i and j, and order function when node i retains the information of node j in step 2, δ _i,j(k)=1, otherwise δ _i,j(k)=0;

Step 5: be circularly set

Make k=k+1, forward step 22 to.

The convergent condition analysis of step 3..First according to algebraic graph theory knowledge, here propose r ?the concept of robust network: for an oriented communication network network, if any pair subset in set of node V, be denoted as S ₁, S ₂, at least there is a node i ∈ S _k, k=1,2, meet | N _is _k|>=r, r ∈ Z ⁺, then claim this network be r ?robust network.By to r ?the introducing of robust network concept, and then we can obtain following convergent condition:

For the multi-agent system network under a malicious attack environment, f neighbours are no more than for malicious node if had at the most in normal node surrounding neighbours, and meet 2f+1 ?robust network attribute, so each normal node is under control method effect of the present invention, their state value can remain in a safety zone and changes and can finally realize consistent, and has nothing to do with the communication delay of network.

The present invention compared with prior art its remarkable advantage is:

1, the inventive method proposes for dynamic network topology, and compared to the convergent control method of traditional fixed topology, can tackle a class and movably attack node flexibly, applicability is more extensive;

2, the network that there is communication delay is applicable to.In actual environment, communication delay is ubiquity and inevitably, considers that delay problem is extremely necessary when being therefore CONTROLLER DESIGN;

3, controller of the present invention only uses the Delay of surrounding neighbours node as control inputs, without the need to the quantity of information that other are extra, farthest saves network service and assesses the cost.

Accompanying drawing explanation

Fig. 1 is for the multi-agent system Controller gain variations structural drawing under malicious node and communication delay environment in the present invention;

Fig. 2 is the multi-agent system directional topology figure with 4 normal node and 3 malicious node compositions that the embodiment of the present invention is set up;

Fig. 3 is at the displaying chart meeting each moment speed of each dolly under 2-robust network structure;

Fig. 4 is at the displaying chart not meeting each moment speed of each dolly under 2-robust network structure.

Embodiment

See Fig. 1, and the present invention is described in further detail in conjunction with the embodiments.

1) founding mathematical models.Consider the multi-agent system network be made up of n node, node on behalf intelligent body in network.N is included in hypothetical network _sindividual normal node and n _aindividual malicious node, meets n _s+ n _a=n.The dynamic model of i-th normal node is:

x _i(k+1)＝x _i(k)+u _i(k),i∈V _s(1)

Wherein x _i(k) and u _ik () is respectively node i at the state value in k moment and control inputs, V _srepresent the set of all normal node.In supposition system in addition, the dynamic equation of all malicious nodes is unknown, they upgrade oneself state value not in accordance with designed control protocol, there is the ability changing arbitrarily oneself state value, and deceptive information can be manufactured send to surrounding normal node, cause normal node to make a mistake because adopting these deceptive information when more new state, thus reach the object destroying the convergent process of whole network.

2) control method design.According to the mathematical model of above-mentioned foundation, and the attack characteristics of malicious node, it is subsequent that we provide detailed controller design method.The present invention considers the identification serial number of all normal node other nodes unknown in network, has under to be no more than f neighbours be the prerequisite of malicious node at the most only knowing in surrounding neighbours, namely | and N _i∩ V _a|≤f, f ∈ Z ⁺, wherein V _arepresent the set of all malicious nodes, Z ⁺represent positive integer, according to the time delay status information CONTROLLER DESIGN of oneself state and neighbours.Concrete steps are as follows:

Step 1: initialization system

Make k=0, initialization system, all normal node give original state value;

Step 2: calculate and delete auto-adaptive parameter

In the kth wheel moment, all value of information x that this moment gathers in the crops by normal node i _j(k-d _i,j(k)), j ∈ N _iafter arranging, do descending sort by the size of numerical value, wherein j represents the node now transmitting information to node i, d _i,jk () is the communication delay between i and j, N _ifor the neighbours of node i collect, namely all can send information to node i set of node.Note n _ithe k total number of neighbours that () is k moment node i, r _ik () deletes auto-adaptive parameter, r for controller _ik the value of () is given according to following rule:

$r_i\left(k\right)=\left\{\begin{array}{cc}{n}_i\left(k\right)-f-1,& n_i\left(k\right)<2f+1\\ f,& n_i\left(k\right)\&GreaterEqual;2f+1\end{array}\right.;---\left(2\right)$

Step 3: create and delete rule

That tries to achieve based on step 2 deletes auto-adaptive parameter r _ik (), next we create node and delete rule: be no less than r if had in the sequence of node i arrangement _ik () individual value is strictly greater than oneself state value x _ik (), so by r front in sequence _ik () individual value removes, as less than r _ik () is individual, then these are greater than x _ik the value of () all removes; Similarly, as there being many r in infructescence _ik () individual value is strictly less than oneself state value x _ik (), so by r rear in sequence _ik () individual value removes, as less than r _ik () is individual, then these are less than x _ik the value of () all removes;

Step 4: design con-trol agreement

According to the value of information having deleted rear reservation in step 3, to the following convergent control protocol of node i design:

$u_i\left(k\right)=\frac{1}{\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)}\&times;\left(\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\right(k)\left(x_j\right(k-d_{i,j}\left(k\right))-x_i(k\left)\right))---\left(3\right)$

In conjunction with before individual dynamic equation, control system closed loop equation is:

$x_i(k+1)=x_i\left(k\right)+\frac{1}{\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)}\&times;\left(\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\right(k)\left(x_j\right(k-d_{i,j}\left(k\right))-x_i(k\left)\right))---\left(4\right)$

In formula, each mathematic sign implication is as follows:

D _i,jk (), for node j is to the communication delay of node i, meets constant for the communication delay upper bound, meet $\stackrel{\&OverBar;}{d}={\sup }_{k\&GreaterEqual;0}max\{d_{i,j}\left(k\right),j\&Element;N_i,i\&Element;V_s\}.$ Time delay is there is not, i.e. d when considering that each node obtains oneself state _i,i(k)=0, a _i,j>=0 is the communication weight between node i and j, and order function when node i retains the information of node j in step 2, δ _i,j(k)=1, otherwise δ _i,j(k)=0;

Step 5: be circularly set

Make k=k+1, forward step 2 to.

Designed by checking the present invention, the validity of control method, adopts following examples to verify.

Consider a multi-agent system be made up of 7 nodes, communication topology is see Fig. 2.Its interior joint 1,2,4,6 is normal node 3, and 5,7 is hostile node, in figure, single dotted broken line arrow represents the connection channel when time series k is odd number, and be communicated with channel when dash-double-dot arrow represents that k is even number, solid arrow represents constant communication channel, its initial value x (0)=[1,2,3,4,5,6,7], communication step-length is set to 0.1s, and upper delay gets 1s.The security domain of system, is the initial value scope of normal node for [1,6], the communication weight matrix A=[a of system _i,j] value as follows:

$A=\left[\begin{array}{ccccccc}0.2& 0.2& 0& 0& 0& 0.3& 0.3\\ 0.3& 0.2& 0.3& 0.2& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0.2& 0.2& 0.1& 0.1& 0.3& 0.1& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0.1& 0& 0& 0.2& 0.2& 0.2& 0.3\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

In the communication topology of Fig. 2, node 1,2,4, meet between 62 ?the character of robust network, malicious node 3,5,7 give following dynamic equation respectively:

x ₃(k+1)＝0.8x ₃(k)+0.2u _a(k),

x ₅(k+1)＝1.5sin(0.2πk)+4,

x ₇(k+1)＝0.3x ₇(k)+0.7u _a(k),

Make u _a=8, i.e. the cooperating with each other of node 3 and node 7, malice guides the state value of surrounding normal node to be tending towards 8.Above-mentioned communication topology ensure that each normal node malicious neighbor number upper limit is at any time 1.Under the above-mentioned convergence analysis provided, known one meet 2 ?the system of robust network, under controller action of the present invention, can ensure to allow the state value of each normal node in system be in safety zone, and finally realize convergent.

See in Fig. 3, figure, we can see the state trajectory of system, although suffer the attack of 3 malicious nodes, each normal node is under control method of the present invention, and its state value remains at change in security domain, and is finally tending towards identical.As can be seen from Numerical Simulation Results, meet 2 ?robust network character multi-agent system in, the validity of the control method designed by the present invention obtains good checking.

It is subsequent that communicating route between node 1 and node 2 specially cuts off by we, to cause between normal node communication topology no longer meet 2 ?robust network character, in this situation, each node state track is see Fig. 4, and now the state value of all normal node is successfully brought into 8 by malicious node.Although system finally still can reach convergent state, deviate from security domain [1,6].Illustrate that the control method designed by the present invention no longer plays a role in the network of these satisfied 2 ?robust network character.

In the specific embodiment of the present invention, all explanations do not related to belong to the known technology of this area, can be implemented with reference to known technology.

Above embodiment is the concrete support of the convergent control method technological thought of multi-agent system safety under a kind of hostile environments to the present invention's proposition; protection scope of the present invention can not be limited with this; every technological thought proposed according to the present invention; any equivalent variations that technical solution of the present invention basis is done or the change of equivalence, all still belong to the scope of technical solution of the present invention protection.

Claims (1)

1. the convergent control method of multi-agent system safety under hostile environments, comprises the following steps:

Step 1. founding mathematical models; Consider the multi-agent system network be made up of n node, node on behalf intelligent body in network; N is included in hypothetical network _sindividual normal node and n _aindividual malicious node, meets n _s+ n _a=n; The dynamic model of i-th normal node is:

x _i(k+1)＝x _i(k)+u _i(k),i∈V _s(1)

Wherein x _i(k) and u _ik () is respectively node i at the state value in k moment and control inputs, V _srepresent the set of all normal node; In supposition system in addition, the dynamic equation of all malicious nodes is unknown, they upgrade oneself state value not in accordance with designed control protocol, there is the ability changing arbitrarily oneself state value, and deceptive information can be manufactured send to surrounding normal node, cause normal node to make a mistake because adopting these deceptive information when more new state, thus reach the object destroying the convergent process of whole network;

Step 2. control method designs; According to the mathematical model of above-mentioned foundation, and the attack characteristics of malicious node, it is subsequent that we provide detailed controller design method; The present invention considers the identification serial number of all normal node other nodes unknown in network, has under to be no more than f neighbours be the prerequisite of malicious node at the most only knowing in surrounding neighbours, namely | and N _i∩ V _a|≤f, f ∈ Z ⁺, wherein V _arepresent the set of all malicious nodes, Z ⁺represent positive integer, f to represent in neighbours malicious node number at the most, according to the time delay status information CONTROLLER DESIGN of oneself state and neighbours; Concrete steps are as follows:

Step 21: initialization system

Make k=0, initialization system, all normal node give original state value;

Step 22: calculate and delete auto-adaptive parameter

In the kth wheel moment, all value of information x that this moment gathers in the crops by normal node i _j(k-d _i,j(k)), j ∈ N _iafter arranging, do descending sort by the size of numerical value, wherein j represents the node now transmitting information to node i, d _i,jk () is the communication delay between i and j, N _ifor the neighbours of node i collect, namely all can send information to node i set of node; Note n _ithe k total number of neighbours that () is k moment node i, r _ik () deletes auto-adaptive parameter, r for controller _ik the value of () is given according to following rule:

$r_i\left(k\right)=\left\{\begin{array}{cc}{n}_i\left(k\right)-f-1,& n_i\left(k\right)<2f+1\\ f,& n_i\left(k\right)\&GreaterEqual;2f+1\end{array}\right.;---\left(2\right)$

Step 23: create and delete rule

That tries to achieve based on step 22 deletes auto-adaptive parameter r _ik (), next we create node and delete rule: be no less than r if had in the sequence of node i arrangement _ik () individual value is strictly greater than oneself state value x _ik (), so by r front in sequence _ik () individual value removes, as less than r _ik () is individual, then these are greater than x _ik the value of () all removes; Similarly, as there being many r in infructescence _ik () individual value is strictly less than oneself state value x _ik (), so by r rear in sequence _ik () individual value removes, as less than r _ik () is individual, then these are less than x _ik the value of () all removes;

Step 24: design con-trol agreement

According to the value of information having deleted rear reservation in step 23, to the following convergent control protocol of node i design:

$u_i\left(k\right)=\frac{1}{\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)}\&times;\left(\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)\left(x_j\left(k-d_{i,j}\left(k\right)\right)-x_i\left(k\right)\right)\right)---\left(3\right)$

In conjunction with before individual dynamic equation, control system closed loop equation is:

$x_i\left(k+1\right)=x_i\left(k\right)+\frac{1}{\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)}\&times;\left(\underset{j=1}{\overset{n}{\&Sigma;}}{a}_{i,j}{\mathrm{\&delta;}}_{i,j}\left(k\right)\left(x_j\left(k-d_{i,j}\left(k\right)\right)-x_i\left(k\right)\right)\right)---\left(4\right)$

In formula, each mathematic sign implication is as follows:

D _i,jk (), for node j is to the communication delay of node i, meets constant for the communication delay upper bound, meet $\stackrel{\&OverBar;}{d}={\sup }_{k\&GreaterEqual;0}max\{d_{i,j}\left(k\right),j\&Element;N_i,i\&Element;V_s\};$ Time delay is there is not, i.e. d when considering that each node obtains oneself state _i,i(k)=0, a _i,j>=0 is the communication weight between node i and j, and order defined function when node i retains the information of node j in step 2, δ _i,j(k)=1, otherwise δ _i,j(k)=0;

Step 25: be circularly set

Make k=k+1, forward step 22 to;

The convergent condition analysis of step 3.; First according to algebraic graph theory knowledge, the concept of r-robust network is proposed: for an oriented communication network network, if any pair subset in set of node V, be denoted as S here ₁, S ₂, at least there is a node and belong in the middle of one of them subset, be i.e. i ∈ S _κ, κ=1,2, meet | N _is _κ|>=r, r ∈ Z ⁺, then this network is claimed to be r-robust network; By the introducing to r-robust network concept, and then obtain following convergent condition:

For the multi-agent system network under a malicious attack environment, f neighbours are no more than for malicious node if had at the most in normal node surrounding neighbours, and meet 2f+1-robust network attribute, the state value of so each normal node can remain in a safety zone and changes and can finally realize consistent, and has nothing to do with the communication delay of network.