CN115022031B - Safety consistency control method for solving influence of FDI attack on multi-agent system - Google Patents
Safety consistency control method for solving influence of FDI attack on multi-agent system Download PDFInfo
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- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
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Abstract
The invention belongs to the field of multi-agent system control, and discloses a safety consistency control method for solving the influence of FDI attack on a multi-agent system, which comprises the following steps: under the Kalman filtering framework, an estimator capable of estimating the state of the neighbor intelligent agent is designed; based on the proposed state estimator, a safety protection mechanism is designed, so that each intelligent agent adopts a safety value to update the state, the influence of false data injection attack on the system is eliminated, and the system asymptotically realizes the mean square bipartite consistency; establishing event triggering conditions by using the estimated value and the value received from the network so as to reduce the transmission of state information and relieve network congestion; the invention considers that the communication channel between the intelligent bodies and the communication channel from the sensor to the controller are simultaneously attacked by malicious attackers, and the influence of process noise and measurement noise exists in the system, thereby being applicable to complex network environment and having better robustness and anti-interference performance.
Description
Technical Field
The invention belongs to the technical field of multi-agent system control, and particularly relates to a safety consistency control method for solving the problem that FDI attack affects a multi-agent system.
Background
Multi-intelligent system grouping consistency is a fundamental requirement for intelligent emergence of complex system groups and coordinated control of clusters. In recent years, as the multi-intelligent system grouping consistent cooperative control is widely applied in the fields of intelligent power grids, unmanned aerial vehicle formation control and the like, the multi-intelligent system grouping consistent cooperative control gradually draws a great deal of attention from researchers in a plurality of fields. For multi-agent systems, the conventional design of robustness and fault tolerance mechanisms cannot meet the security control requirements when the system encounters an external malicious attack. In view of the current complex network environment, the tolerance of multi-agent systems to harsh environments, the stability of cooperatively implementing task goals, and the like face greater challenges.
When network attack exists in the multi-agent system, communication information among agents can be stolen or tampered, so that the performance of the agents is reduced, and even the expected task cannot be completed. The network attacks existing in the multi-agent system at present mainly comprise the following forms: denial-of-Service (DoS) attacks, spoofing attacks, FDI attacks. Among other things, FDI attacks can be considered a subclass of spoofing attacks. FDI attacks are the replacement of real information by injecting a different signal or the change of the integrity of real information. The purpose of DoS attacks is to break the communication channel and prevent the exchange of information between agents. FDI attacks are more hidden and more difficult to detect than DoS attacks. The attacker easily injects spurious data into the channel, which makes FDI attacks common in multi-agent systems. However, the study of the consistency problem of multi-agent systems under FDI challenge is still in the onset phase. Therefore, the research on the safety consistency problem of the multi-agent system under the FDI attack is of more practical significance.
Currently, for research on the presence of FDI attacks in multi-agent systems, researchers have mainly considered the following aspects: firstly, considering the position of malicious attackers for injecting false data, a communication channel between intelligent agents can be attacked by the attackers, a sensor-to-controller channel is injected with the false data and a sensor-to-controller channel, two parts of channels from the controller to the executor are simultaneously attacked by the attackers, most students only consider the situation that a single position is attacked, and only consider that the single position is attacked, so that a multi-intelligent agent system cannot work in a complex environment. Secondly, considering interaction relation and cooperation mode among the intelligent agents, FDI attack exists in the multi-intelligent-agent system, and many scholars only consider single cooperation interaction or competition interaction among the intelligent agents and less consider cooperation-competition interaction relation among the intelligent agents. For example: in railway transportation, trains meet both as transportation goods and competing for use of the track. Thus, research into inter-agent collaboration-competition interactions is more practical. Moreover, most of the existing documents only consider the overall consistency of the system, but group consistency is not suitable for a multi-task grouping collaboration scenario that is more widely applied in reality. For example: unmanned aerial vehicles are generally divided into a plurality of groups, each group employing a different formation according to different control actions. Therefore, it is more practical to study the problem of security packet consistency of multi-agent systems. Thirdly, consider how to eliminate the impact of the attack. Researchers have proposed a control method with attack compensators that aim to ensure the final connectivity of multi-agent systems under FDI attacks. Notably, this control method contemplates a continuous attack model that facilitates the design of attack compensators.
In combination with the above analysis, the following problems can be found: first, when considering the location where the FDI attack occurs, most research results have studied that the attack occurs at a single location, for example, the attack occurs only in the channel between agents or in the channel from the sensors inside the agents to the controller, while there are fewer documents about the more complex locations that are simultaneously under attack. Theoretically, considering that attacks occur at multiple locations simultaneously, the system can be made to operate in a more hostile environment. Thus, it is particularly important to study multiple locations that are under attack. Secondly, the scholars mainly study the cooperation or competition interaction among the intelligent agents when FDI attacks exist, and the research on the cooperation-competition interaction which is wider in practical application is less. Third, the safety consistency of multi-agent systems in most research in the presence of FDI attacks is based on the noiseless situation, and the dynamics model of the agent is usually not modeled accurately. Process noise is used to describe the uncertainty of the multi-agent system. Uncertainty is mainly reflected in two aspects, firstly, that a mathematical model of a system cannot be accurately described, and secondly, that disturbance of the system is uncontrollable and difficult to model. Measurement noise is used to represent the error between the measured value and the agent's true state value.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A security consistency control method for solving the influence of FDI attack on a multi-agent system is provided.
The technical scheme adopted by the invention is as follows: the safety consistency control method for solving the influence of FDI attack on the multi-agent system is characterized by comprising the following steps:
step 1: constructing a discrete multi-agent system model with process noise, determining the communication topology of a complex multi-agent system, and designing a state estimator capable of estimating the states of neighbor agents based on cooperative competition interaction among agents;
step 2: obtaining an estimated value of each intelligent embedded state estimator and a state value which is received from a network and possibly influenced by an attack signal, comparing the two values, and judging whether data transmitted in the network are influenced by a malicious attacker or not;
step 3: establishing a safety protection mechanism according to the state estimation value obtained in the step 2, the state value received from the communication network and a given threshold value, and updating the state of the intelligent body by adopting the safety value through the help of the safety protection mechanism;
step 4: the security protection mechanism and the event triggering mechanism are combined into the security control protocol, the event triggering mechanism can also lighten the influence of an attacker on the system to a certain extent, even if the attacker exists in the network when the event triggering condition is not satisfied, the consistency process of the system can not be influenced, and the security protection mechanism promotes the multi-agent system to eliminate the influence of the attacker and asymptotically realize the mean square bipartite consistency.
Preferably, the discrete multi-agent system is composed of first-order agents, the kinetic behavior of which is represented by the following formula:
x i (k+1)＝x i (k)+u i (k)+w i (k)，i∈V
wherein x is i (k) Representing state information transmitted by agent i to its neighbor agent at time k, u i (k) Representing the control input, w, of agent i at time k i (k) Representing process noise for agent i at time k.
Preferably, determining the communication topology of the complex multi-agent system in step 1 includes exchanging state information between each agent and the neighboring agents, and modeling attack signals between the agents and between the sensor and the controller communication channel.
Preferably, in a practical scenario, attacks initiated by malicious attackers in the network tend to be random. Modeling attacks to follow bernoulli distribution is therefore more consistent with realistic applications.
Preferably, the intelligent agents in the multi-intelligent agent system are divided into two groups, the intelligent agents in the same group adopt cooperative interaction, and the intelligent agents in different groups adopt competitive interaction.
The technical scheme of the invention has the following beneficial effects: the state estimator based on measurement designed by the invention can estimate the state of the neighbor intelligent agent, compares the estimated value with the state value which is possibly influenced by attack signals and is received from the network, judges whether a malicious attacker injects false data into the network or not, and then adopts different values to update the state of the intelligent agent according to the judging result.
In the invention, cooperation and competition interaction among the intelligent agents are considered, a novel algorithm capable of estimating the state of the neighbor intelligent agents is designed under a Kalman filtering framework, and the stability of the algorithm is proved in theory; the algorithm considers the state correlation of the intelligent agent in the measuring range and outside the measuring range of the estimator embedded in each intelligent agent; a safety protection mechanism is designed based on the proposed state estimation algorithm, so that each intelligent agent adopts a safety value to update the state, the influence of false data injection attack on the system is eliminated, and the system asymptotically realizes the mean square bipartite consistency; establishing event triggering conditions by using the estimated value and the value received from the network so as to reduce the transmission of state information and relieve network congestion; the invention considers that the communication channel between the intelligent bodies and the communication channel from the sensor to the controller are simultaneously attacked by malicious attackers, and the influence of process noise and measurement noise exists in the system, thereby being applicable to complex network environment and having better robustness and anti-interference performance.
Drawings
FIG. 1 is a system control flow diagram of the present invention;
FIG. 2 is a functional block diagram of a security mechanism;
FIG. 3 is a communication topology of a system;
FIG. 4 is a graph of estimation error;
FIG. 5 is an event trigger timing diagram of an agent;
FIG. 6 is a state evolution diagram without the action of a safety protection mechanism;
fig. 7 is a state evolution diagram under the action of a security protection mechanism.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and specifically described below with reference to the drawings in the embodiments of the present invention. The described embodiments are only a few embodiments of the present invention.
A security consistency control method for solving the problem of the influence of FDI attack on a multi-agent system, as shown in fig. 1, the method comprising:
step 1: and (3) determining a communication topological structure of the discrete multi-agent system with process noise by considering the interaction process between the agents, wherein each agent exchanges state information with the neighbor agents respectively, and models the attack signals.
The discrete multi-agent system is composed of first-order agents, and the dynamic behavior of the system can be represented by the following formula:
x i (k+1)＝x i (k)+u i (k)+w i (k)，i∈V
wherein, the liquid crystal display device comprises a liquid crystal display device,respectively representing the state information of the intelligent agent i and controlling input; />Is assumed to have a positive definite covariance matrix Q i (k) > 0, and uncorrelated gaussian white noise, i.e. w i (k)∈(0,Q i (k) A kind of electronic device. V represents all agent sets.
The control inputs depend on the state of the neighboring nodes, as follows:
wherein c > 0 is the uniformity gain; n (N) Qi And N Ri Representing sets of adjacent agents belonging to the same group as agent i and to different groups, respectively. a, a ij Representing the interaction of adjacent agents.
Attacks on the agent i and agent j communication channels can be modeled as:
wherein, the liquid crystal display device comprises a liquid crystal display device,state value, mu representing information sent by node j after being injected with dummy data ij (k) Attack signal representing attacker injection, assuming μ ij (k) Is a bounded real number. Beta ij (k) Representing the attack decision variables. Likewise, inside agent i, the attack on the sensor-to-controller channel can be modeled as:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the state value after being affected by the attack. The present invention assumes that the node j to node i channel and the node i internal sensor to controller channel are injected with the same attack signal by an attacker. Therefore, attack decision variable β ij (k) And attack signal mu ij (k) Is thatThe same applies. Definition beta ij (k) Is a variable obeying Bernoulli distribution, when FDI attacks occur, the variable beta ij (k) =1, otherwise β ij (k) =0. The probability of FDI attacks occurring and not occurring is respectively:
where τ ε [0,1 ] is a constant, when (i, j) + (u, v), β ij Independent of beta uv 。
Step 2, based on the cooperation-competition interaction between the agents, a state estimator based on measurement is designed with the help of a Kalman filtering framework to estimate the states of the neighbor agents, and a safety protection mechanism schematic block diagram is designed, as shown in fig. 2. And estimating the states of the neighbor intelligent agents, establishing event triggering conditions according to the estimated values and the real values transmitted from the sensors, and designing a safety protection mechanism according to the estimated values and the values received from the network so that the safety values are used for updating the states of the multi-intelligent agent system.
The cooperative competition interaction mechanism considered in the invention is as follows: all the agents are divided into two groups, cooperative relationships exist among the agents in the same group, and competing relationships exist among the agents in different groups. Obviously, the neighbor node of agent i will only be at N Qi Or N Ri Thus N i ＝N Qi ∪N Ri . Suppose the first U agents are in a group and the last N-U agents are in a group.
Each agent is equipped with a measurement-based estimator to estimate the state of the neighboring agents, and an attack detector and event generator are also designed. X is x i (k)，x j (k) States, v, of agent i and agent j, respectively ij (k) Representing the measurement noise of the agent i in-line estimator,is the state of agent j received by node i from the communication network,representing the status of agent i received from the communication network, the estimate of the status of agent i is denoted +.>The estimate of the state of agent j is denoted +.>And->Is the detected safety value.
From the functional block diagram of the security protection mechanism, the main idea of the mechanism is to design an estimator and a detector to ensure that the controller updates the state of the agent with the security value. Assuming that the multi-agent system is operating at time k, the built-in estimator of agent i calculatesAnd->And sends these two values to the detector, which will receive +.>And->The detector then determines if the network is under attack and ultimately sends the security value to the controller. Furthermore, the event generator utilizes x received from the sensor i (k) And estimator sent +.>And establishing event triggering conditions. An event triggering mechanism is used to avoid the continuous transmission of the state of the agent, which is sent to the network only when a triggering condition is reached.
And step 3, the estimated value of the estimator is subjected to difference absolute value and the state value received from the communication network, and then the absolute value is compared with a given threshold value, so that whether false data injection attack exists in the multi-agent system is detected. And establishing event triggering conditions between the state estimation value and the state value transmitted by the sensor.
The measurement-based estimator is as follows:
wherein K is ij (k+1) is the estimator gain. Y is Y i (k+1) represents a measurement set,representing an a priori state estimate.
Based on binary decision variable f ij The following safety protection mechanism is designed:
c represents the consistency gain, N represents the number of intelligent agents, f ij (k) Representing binary decision variables, b ij Indicating the connection condition of the intelligent agent.
The main idea of the security protection mechanism is that when the difference between the state value received from the network and the estimated value is smaller than a given threshold, the state of the agent is updated directly with the value received from the network, if not, the state of the agent is updated with the estimated value of the estimator.
The event triggering mechanism is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,delta is a constant, ">Is the kth trigger instant.
Step 4: and (3) using the detection result in the step (3) to design a safety protection mechanism, wherein the safety protection mechanism can enable the state of the intelligent body to be updated by adopting a safety value. In addition, the event triggering mechanism can reduce the transmission of state information, relieve network congestion, reduce the influence of network attack on the multi-agent system to a certain extent, and finally enable the system to realize mean square dichotomy consistency asymptotically.
The noisy multi-agent system cannot directly use the state feedback control protocol, and the presence of observation noise renders the actual state of the agent unavailable. Therefore, while maintaining the structure, the real information of the agent is replaced with the measured value of the corresponding measuring device, and { y }, is used ij (k) I j e V represents the measurement set of agent i, then:
wherein y is ij (k) The state of agent j observed by agent i at time k; v ij (k) Assumed to have zero mean and covariance R i (k) Independent co-distributed random variables > 0, i.e. v ij (k)∈(0,R i (k))；d ij Is a variable indicating whether agent j is within the measurement range of agent i,
N i representing a neighbor set of agent i, the control input of agent i may be rewritten as:
wherein y is ii (k) Indicating the measured state of agent i at time k.
Preferably, the process noise of agent i is gaussian white noise that is uncorrelated with the process noise of other agents.
In the invention, when the discrete multi-agent system meets the following conditions, all agents can realize the consistence of mean square bisection asymptotically, and the conditions are that the states of the agents in the same group are converged to one value, and the states of the agents in different groups are converged to state values with opposite signs.
N Qi ，N Ri Representing two different sets of agents.
As shown in fig. 3, the communication topology is composed of 6 agents, from which it can be seen that agents 1,2,3 are grouped together and agents 4,5,6 are grouped together. The adjacency matrix and the laplace matrix of the communication topology are given as follows:
the communication channel between agent 3 and agent 4 receives a false data injection attack, and the graph of the estimated error in estimating the state using a state estimator based on measurements is shown in fig. 4, and fig. 5 is an event-triggered timing graph of 6 agents. Setting the probability of FDI attack occurrence to be tau=0.33, and the attacker is in k epsilon [20,30 ]]K E [50,60 ]]An attack is initiated. The attack signal is set to μ=2. As can be seen from fig. 3, when an attacker injects dummy data into the communication network of agents 3 and 4, both agents 3 and 4 send data to each other, and it is considered herein that the data transmitted by the sensors within agents 3 and 4 to the controller channels are also affected by the dummy data. The intelligent agent 3 receivesThe agent 4 receives +.>The state trajectories when the agents 3 and 4 do not use the security protection mechanism, but directly use the values received from the network for state updating are shown in fig. 6. As can be seen from fig. 6, in case of an attack, the state trajectories of agents 3 and 4 are severely shifted, and more seriously, the same set of agent state trajectories is caused. Therefore, multi-agent systems cannot achieve mean square binary agreement without the use of a safety protection mechanism. Fig. 7 is a state evolution diagram of 6 agents using a security protection mechanism, and finally, two groups of agents converge to different state values, so that the mean square binary agreement is realized.
Claims (2)
1. The safety consistency control method for solving the influence of FDI attack on the multi-agent system is characterized by comprising the following steps:
step 1: constructing a discrete multi-agent system model with process noise, determining the communication topology of a complex multi-agent system, and designing a state estimator capable of estimating the states of neighbor agents based on cooperative competition interaction among agents;
the discrete multi-agent system is composed of first-order agents, and the dynamic behavior of the discrete multi-agent system is represented by the following formula:
x i (k+1)＝x i (k)+u i (k)+w i (k)，i∈V
wherein x is i (k) Representing state information transmitted by agent i to its neighbor agent at time k, u i (k) Representing the control input, w, of agent i at time k i (k) Process noise representing agent i at time k;
the control inputs depend on the state of the neighboring nodes, as follows:
wherein c > 0 is the uniformity gain; n (N) Qi And N Ri Respectively representing adjacent agent sets belonging to the same group and different groups with the agent i;
the communication topology of the complex multi-agent system is determined to comprise that each agent exchanges state information with a neighbor agent respectively, attack signals between the agents and between a sensor and a controller communication channel are modeled, and attack modeling on the communication channel of the agent i and the agent j is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,state value, mu representing information sent by node j after being injected with dummy data ij (k) Representing an attacker-injected attack signal, beta ij (k) Representing attack decision variables;
inside agent i, the attack on the sensor-to-controller channel is modeled as:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the state value after being affected by the attack; definition beta ij (k) Is a variable obeying Bernoulli distribution, when FDI attacks occur, the variable beta ij (k) =1, otherwise β ij (k) =0; the probability of FDI attacks occurring and not occurring is respectively:
where τ.epsilon.0, 1 is a constant, when (i, j) is equal to (u,v) beta ij Independent of beta uv ；
The estimator is as follows:
wherein K is ij (k+1) is the estimator gain, Y i (k+1) represents a measurement set,representing a priori state estimates;
step 2: obtaining an estimated value of each intelligent embedded state estimator and a state value received from a network, comparing the two values, and judging whether data transmitted in the network are influenced by malicious attackers or not;
step 3: establishing a safety protection mechanism according to the state estimation value obtained in the step 2, the state value received from the communication network and a given threshold value, and updating the state of the intelligent body by adopting the safety value through the help of the safety protection mechanism;
the safety protection mechanism specifically comprises that a multi-agent system is assumed to run at the moment k, and an estimator embedded in an agent i calculatesAnd->And sends these two values to the detector, which will receive +.>Andthe detector judges whether the network is attacked or not, and finally sends the security value to the controller; furthermore, the event generator utilizes slave sensor interfacesReceived x i (k) And estimator sent +.>Establishing event triggering conditions; using an event triggering mechanism to avoid continuous transmission of the state of the agent, the state of the agent being sent to the network only when a triggering condition is reached;
based on binary decision variable f ij The following safety protection mechanism is designed:
c represents the consistency gain, N represents the number of intelligent agents, f ij (k) Representing binary decision variables, b ij Representing the connection condition of the intelligent agent;
the event triggering mechanism is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,delta is a constant, ">Is the kth trigger instant;
step 4: the security protection mechanism and event triggering mechanism are incorporated into the security control protocol.
2. The security consistency control method for solving the problem of the impact of the FDI attack on the multi-agent system according to claim 1, wherein: the process noise w i (k) Is provided with a positive definite covariance matrix Q i (k) And uncorrelated gaussian white noise, i.e. w i (k)∈(0,Q i (k))。
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