CN115913704A - Intelligent unmanned cluster system time-lag pulse control method for resisting spoofing attack - Google Patents
Intelligent unmanned cluster system time-lag pulse control method for resisting spoofing attack Download PDFInfo
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Abstract
The invention belongs to the technical field of intelligent unmanned cluster system control, and particularly relates to an intelligent unmanned cluster system time-lag pulse control method for resisting cheating attacks, which comprises the steps of considering the cheating attacks existing in a sensor-controller channel of an intelligent unmanned cluster system, adopting a time-lag utilization technology, adding time lags into a controller, simultaneously using containment control, selecting proper containment time-lag parameters, and improving the convergence performance of the system; by utilizing a discrete pulse control scheme, a part of deception attacks at non-pulse moments are avoided while resources are saved, and the influence of the deception attacks on a system is reduced; the containment time lag is combined with pulse control to construct a consistency control protocol, so that the realization of bounded synchronization of the system mean square is ensured; the time-lag pulse control method provided by the invention ensures the realization of synchronization of the intelligent unmanned cluster system under deception attack, and has certain robustness.
Description
Technical Field
The invention belongs to the technical field of intelligent unmanned cluster system control, and particularly relates to a time-lag pulse control method for an intelligent unmanned cluster system for resisting cheating attacks.
Background
In recent decades, due to the wide application of intelligent unmanned cluster systems in smart grids, formation control and cooperative decision-making, the intelligent unmanned cluster system attracts the attention of many researchers. The synchronization of the intelligent unmanned cluster system means that all nodes converge to one and the same state. To achieve synchronization of intelligent unmanned cluster systems, communication between individuals in the system is required. Since the actual intelligent unmanned cluster system is in a complex network environment, the system is vulnerable to network attacks. Therefore, the safety control of the intelligent unmanned cluster system is worthy of further research.
Two typical attacks that attackers launch at the communication network layer to date are denial of service attacks and spoofing attacks. Spoofing attacks refer to attackers modifying control inputs and measurement data, resulting in incomplete or unreliable data resources. According to research, existing detection technologies can be bypassed by a spoofing attack, so that the performance of the system is seriously reduced, and therefore, in recent years, the problem of synchronization of the intelligent unmanned cluster system under the spoofing attack is widely concerned. For example, spoofing attacks are described in some documents as random variables that obey bernoulli distributions, replaced system control input signals, or desynchronization pulses. Although some progress has been made in the synchronization problem of intelligent unmanned cluster systems under spoofing attacks, the above document does not take into account some real-world factors such as communication time lag between the leader follower system and the leader when considering intelligent unmanned cluster systems under spoofing attacks. Therefore, it is very meaningful to further study the synchronization problem of the intelligent unmanned cluster system under the spoofing attack.
The synchronization problem of the intelligent unmanned cluster system is solved by pulse control. And because of the wide spread of skew, many researchers are interested in skew pulses. Skew is found in some literature to be of potential practical value and is not always a bad factor in active controllers. In the controller, the performance and stability of the system can be improved by appropriately using the time delay. Furthermore, in the leader-follower model, containment control, i.e., controlling only some of the key nodes, may be used to reduce the cost of the control strategy. However, most of the existing research on dead-time pulse control is used in an ideal environment, and few researches consider the existence of spoofing attacks in actual communication. Therefore, it is an urgent problem to solve the problem of implementing synchronization of an intelligent unmanned cluster system and improving the convergence performance of the system by adopting time lag containment pulse control under the spoofing attack.
Disclosure of Invention
In order to solve the problems, the invention provides an intelligent unmanned cluster system time-lag pulse control method for resisting cheating attacks, which comprises the steps of constructing a continuous nonlinear intelligent unmanned cluster system with cheating attacks, considering the time lag when information is transmitted between a leader node and a follower node in the system, and expressing time-lag pulse control signals generated by a node i at a time t as follows:
wherein u is i (t) a time lag pulse control signal generated at node i at time t; c is coupling strength, and N represents the number of individuals in the intelligent unmanned cluster system; (ii) a a is ij For the adjacency matrix of the graph corresponding to the intelligent unmanned cluster system, if node j has a path to node i, then a ij Not equal to 0, otherwise a ij =0, and specifies a ii ＝0；x j (t) represents the state vector, x, of the follower node j at time t i (t) represents the state vector of follower node i at time t; beta is a ij (t) indicates whether node i has suffered a spoofing attack while accepting the state information of node j, if β ij (t) =1, this means that there is a spoofing attack, and 0 means that there is a spoofing attackNone; q. q of i (t) represents an attack signal suffered by the node i at the time t; d i Representing the containment gain of follower node i; p is a radical of formula 1 Representing a containment pulse control gain; s (t) represents the leader's state vector; p is a radical of 2 Is a hold-down time-lag pulse control gain; tau. k Representing the time lag of the holdback pulse controller; t is t k Represents the time of the kth pulse; δ () is a pulse function.
Further, the state of a follower in the continuous nonlinear intelligent unmanned cluster system is updated according to an input control signal, and the updating process is represented as follows:
wherein the content of the first and second substances,
is the derivative of the follower state vector, x i (t)∈R n Is the state vector of the follower, and n is the dimension of the vector; u. of i (t) is the control input, C, B are constant matrices, g (x) i (t))＝(g 1 (x i (t)),g 2 (x i (t)),...,g n (x i (t))) T g(x i (t)) is a non-linear function satisfying the Lipschitz condition and is expressed as g (x) i (t))＝(g 1 (x i (t)),g 2 (x i (t)),...,g n (x i (t))) T ，g n (x i (t)) represents a non-linear function g (x) i (t)) the nth dimensional value.
Further, a leader in the continuous nonlinear intelligent unmanned cluster system updates the state according to an input control signal, and the updating process is represented as follows:
wherein, the first and the second end of the pipe are connected with each other,
a derivative of a state vector representing the leader; C. b is a constant matrix, and g (s (t)) is a nonlinear part in the leader kinetic equation.
Further, a parameter β indicating whether or not the node i has suffered a spoofing attack while receiving the state information of the node j ij (t) is a random variable, ρ, following a Bernoulli distribution ij Belongs to [0, 1) and specifies ρ ii =0, random variable β ij (t) are independent of each other.
Furthermore, in the continuous nonlinear intelligent unmanned cluster system, a directed spanning tree must exist in a directed network topology formed by the leader node and the follower nodes, and the leader node is a root node in the spanning tree.
Further, the containment gain d of follower node i i The value of d is determined by whether the following node can directly acquire the state of the leader node, and when the following node i can directly acquire the state information of the leader, d i > 0, otherwise, d i ＝0。
Further, the pulse function is a dirac pulse function δ (x), i.e. if x ≠ 0, then δ (x) =0; the pulse sequence satisfies 0= t 0 ＜t 1 ＜…＜t k < and
the interval between two adjacent pulse time satisfies f 1 ＝inf{t k -t k-1 }、f 2 ＝sup{t k -t k-1 And 0 < f 1 ≤f 2 ＜∞。
The time-lag pulse control protocol designed by the invention adopts a time-lag utilization technology, and improves the stability of the system and accelerates the convergence speed of the system by setting reasonable time-lag control parameters; the pulse control scheme is utilized to carry out discrete control on the continuous system, thereby saving system resources and avoiding the influence on the system caused by the occurrence of non-pulse cheating attack to a certain extent; the invention considers that the nonlinear intelligent unmanned cluster system suffers deception attack on a sensor-controller channel, and finally realizes mean square bounded synchronization under the control of time-delay containment pulses, so that the method also has certain robustness.
Drawings
FIG. 1 is a system control flow diagram of the present invention;
FIG. 2 is a diagram of the attack location of the spoofing attack of the present invention;
FIG. 3 is a communication topology of the system of the present invention;
FIG. 4 is an evolution diagram of node states when the invention is controlled using a time-lag pulse;
FIG. 5 is an evolution diagram of node states when the present invention uses normal pulse control;
FIG. 6 is an evolution diagram of the error between each node and the leader when the time-lag pulse control is used in the present invention;
FIG. 7 is a diagram of the evolution of the two-norm error vector between each node and the leader when the invention uses time-lag pulse control.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a time lag pulse control method of an intelligent unmanned cluster system for resisting cheating attacks, which comprises the steps of constructing a continuous nonlinear intelligent unmanned cluster system with cheating attacks, considering time lag when information is transmitted between a leader node and a follower node in the system, and expressing time lag pulse control signals generated by a node i at a time t as follows:
wherein u is i (t) a time lag pulse control signal generated at a node i at time t; c is coupling strength, N represents; a is ij For the adjacency matrix of the graph corresponding to the intelligent unmanned cluster system, if node j has a path to node i, then a ij Not equal to 0, otherwise a ij =0, and specifies a ii ＝0；x j (t) represents the state vector of follower node j at time t, x i (t) represents the state vector of follower node i at time t; beta is a beta ij (t) indicates whether node i has suffered a spoofing attack while accepting the state information of node j, if β ij (t) =1, which means that there is a spoofing attack, and 0, which means not; q. q of i (t) represents an attack signal suffered by the node i at the time t; d i Representing the containment gain of follower node i; p is a radical of 1 Representing a holdoff pulse control gain; s (t) represents the leader's state vector; p is a radical of 2 Is a hold-down skew pulse control gain; tau is k Representing the dead time of the holddown pulse controller; δ () is a pulse function.
In this embodiment, the method for implementing the intelligent unmanned cluster system time-lag pulse control for resisting spoofing attack is specifically divided into 5 steps, as shown in fig. 1, and specifically includes:
step 1: and constructing a follower model and a leader reference model of the continuous nonlinear system, and determining the communication topology of the complex intelligent unmanned cluster system, wherein each individual in the system is seen as a node in the graph, and the information flow is determined according to the edges between the individual individuals. And part of nodes can acquire the state information of the leader and carry out containment control.
The constructed continuous nonlinear intelligent unmanned cluster system follower model is as follows:
wherein x is i (t)∈R n Is a state vector u i (t) is the control input, C, B are constant matrices, g (x) i (t)) is a non-linear function satisfying the Lipschitz condition and is expressed as g (x) i (t))＝(g 1 (x i (t)),g 2 (x i (t)),...,g n (x i (t))) T ，g n (x i (t)) watchShows a non-linear function g (x) i (t)) the nth dimensional value. In the present invention, the nonlinear function is required to satisfy the Lipschitz condition.
The leader reference model is as follows:
wherein the content of the first and second substances,
is the derivative of the leader's state vector. In order to ensure the implementation of intelligent unmanned cluster synchronization, a directed spanning tree must exist in a directed network topology composed of a leader and all followers, wherein the leader node is a root node in the spanning tree. Only in this way, all nodes can directly or indirectly acquire the state information of the leader, and the leader-follower consistency is realized. Some nodes in the system topology can directly acquire the state information of the leader node, namely, the state information is controlled by the containment, and the containment mode is as follows:
d i (x i (t)-s(t))
wherein, d i The containment gain of the ith node is represented, and if the ith node can directly acquire the state information of the leader, d i > 0, otherwise, d i ＝0。
Step 2: the method comprises the steps of considering possible cheating attacks in a sensor-controller channel, representing whether the cheating attacks occur or not by utilizing a random variable subjected to Bernoulli distribution, and modeling the cheating attacks.
The invention considers that the intelligent unmanned cluster system is subjected to the spoofing attack in the sensor-controller channel, and the attack position of the spoofing attack is shown in figure 2. Using a random variable beta obeying a Bernoulli distribution ij (t) to indicate whether node i has suffered a spoofing attack while accepting the state information of node j, if β ij (t) =1, which means there is a spoofing attack, and 0, which means there is no spoofing attack, and the probability distribution of the random variable is as follows:
Prob{β ij (t)＝1}＝ρ ij
Prob{β ij (t)＝0}＝1-ρ ij
where ρ is ij E [0, 1), and specifies ρ ii And =0. The probability of being subjected to spoofing attack in a channel for transmitting information between a node i and a node j is shown as rho ij And satisfies a random variable beta ij (t) are independent of each other.
And step 3: the intelligent unmanned cluster system adopts a discrete pulse control scheme, the pulse function can only act at the pulse time, the control input of the system is 0 at the non-pulse time, the system cannot receive the state information of the neighbor nodes, so that part of deception attacks can be avoided, and the influence of the deception attacks on the system is reduced.
In this embodiment, the intelligent unmanned cluster system adopts a discrete pulse control scheme, and adopts a dirac pulse function δ (x), if x ≠ 0, then δ (x) =0. I.e. the control protocol is active only at discrete pulsed control instants. At the same time, if the spoofing attack happens to occur at a non-pulse time, the control of the system will not be affected.
And 4, step 4: the time lag utilization technology is adopted, the time lag during information transmission between a leader and a follower is taken into account, and the convergence speed of the system is accelerated by setting proper time lag pulse control parameters.
The stability of the system is facilitated by the existence of proper time lag, and a certain time lag for information transfer between nodes cannot be avoided. The time lag pulse control is used, so that the system can use the state information of some nodes at non-pulse time at the pulse time, and the synchronization of the system is facilitated.
And 5: and (4) setting a consistency control protocol, updating the state of each node according to the state information of the neighbor nodes in the consistency control protocol and the received state information of the leader, and simultaneously taking the containment time lag item in the step (4) into consideration, so that the mean-square bounded synchronization can be realized in the intelligent unmanned cluster system under the condition that the deception attack exists, and the convergence of the system can be accelerated due to the existence of the time lag item.
The consistency control protocol adopted in the embodiment is as follows:
wherein the pulse sequence is
And->
Suppose that
f 2 ＝sup{t k -t k-1 And satisfies 0 < f 1 ≤f 2 ＜∞。
In this embodiment, when the nonlinear intelligent unmanned cluster system satisfies the following condition, the intelligent unmanned cluster system achieves mean square bounded synchronization, states of all nodes and the leader are kept consistent, and the satisfied condition is that a state error between the nodes and the leader converges to a tight set. Namely:
wherein δ is a constant representing the error bound; e { } denotes averaging, x i (t) represents the state of the ith follower, s (t) represents the state of the leader, | represents the binorm of the vector.
In this embodiment, a specific implementation is shown in fig. 1, which includes the following steps:
constructing a follower model and a leader reference model of a continuous nonlinear system, and determining the communication topology of the intelligent unmanned cluster system;
considering the possible cheating attack in the controller channel from the sensor, whether the cheating attack occurs or not is represented by a random variable obeying Bernoulli distribution, and the cheating attack is modeled;
a discrete pulse control scheme is adopted, the control input of the system is 0 at the non-pulse moment, the system cannot receive the state information of the neighbor node, so that part of deception attacks can be avoided, and the influence of the deception attacks on the system is reduced;
by adopting a time lag utilization technology, the time lag of information transmission between a leader node and a follower node is taken into account, and the convergence speed of the system is accelerated by setting a proper control parameter of a time lag pulse;
the spoofing attack is taken into consideration, the communication topology between the nodes is combined, and a time-lag pulse control scheme is utilized to design a consistency control protocol, so that the intelligent unmanned system can realize mean-square bounded synchronization under the condition that the spoofing attack exists.
As shown in fig. 3, the present embodiment provides a communication topology diagram consisting of 6 nodes. The adjacency matrix and laplacian matrix of the communication topology are given as follows:
matrix D = diag { D } i Denotes whether there is a path between the node and the leader, and in this embodiment, the matrix D is expressed as:
the matrix D shows that only the 2 nd node and the 4 th node have a direct connection path with the leader, namely the 2 nd node and the 4 th node are restrained.
Setting spoofing attack strength q i Q =0.2, and the probability matrix of each communication channel between nodes being subject to spoofing attacks is as follows:
wherein, Prob{β 13 (t) =1} =0.2, indicating that the probability that the communication channel between node 1 to node 3 is subject to a spoofing attack is 0.2.
Setting the holdback pulse parameter p 1 = 0.7, the time-lag hold-down pulse control parameter is set to p 2 = 0.08, the trace of the state of each node is as shown in fig. 4, and it can be seen that when the step size is calculated at 0.15, the states of all nodes in the whole system are the same, that is, consistency is achieved, and the whole system achieves synchronization. Setting the holdback pulse parameter p in contrast with other parameters unchanged 1 = 0.7, the time-lag hold-down pulse control parameter is set to p 2 =0, the trace of the state of each node is as shown in fig. 5, and it can be seen that when the step size is calculated at 0.35, the states of all nodes in the whole system are consistent. Compared with the realization time of consistency, the result shows that the introduction of a proper amount of time lag in the holddown pulse controller is beneficial to the realization of system synchronization.
Fig. 6 depicts a state evolution diagram of the first dimension of the error vector between each node and the leader, and it can be seen that finally the errors between all the nodes and the leader fluctuate around 0, and the whole system achieves the synchronization of the follower leader. Fig. 7 depicts an evolution diagram of squares of two norms of error vectors of nodes and a leader over time, and it can be seen that a final error vector is very close to 0, an upper bound of the theoretical error vector two norms can be calculated to be 2.3841, and an error in the diagram is obviously smaller than the theoretical upper bound, so that a condition that a system realizes mean-square bounded synchronization is met, and the intelligent unmanned cluster system finally realizes mean-square bounded synchronization in the presence of spoofing attacks.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (7)
1. A time lag pulse control method of an intelligent unmanned cluster system for resisting cheating attacks is characterized in that a continuous nonlinear intelligent unmanned cluster system with cheating attacks is constructed, time lag when information is transmitted between a leader node and a follower node is considered in the system, and a time lag pulse control signal generated by a node i at time t is expressed as:
wherein u is i (t) a time lag pulse control signal generated at node i at time t; c is coupling strength, and N represents the number of individuals in the intelligent unmanned cluster system; a is ij For the adjacency matrix of the graph corresponding to the intelligent unmanned cluster system, if the node j has a path to the node i, then a ij Not equal to 0, otherwise a ij =0, and specifies a ii ＝0；x j (t) represents the state vector, x, of the follower node j at time t i (t) represents the state vector of follower node i at time t; beta is a ij (t) indicates whether node i has suffered a spoofing attack while accepting the state information of node j, if β ij (t) =1, which means that there is a spoofing attack, and 0, which means not; q. q.s i (t) represents an attack signal suffered by the node i at the time t; d is a radical of i Representing the containment gain of follower node i; p is a radical of 1 Representing a holdoff pulse control gain; s (t) represents the leader's state vector; p is a radical of 2 Is a hold-down skew pulse control gain; tau. k Representing the time lag of the holdback pulse controller; t is t k Represents the time of the kth pulse; δ () is a pulse function.
2. The intelligent unmanned cluster system time-lag pulse control method for defending against spoofing attacks, as set forth in claim 1, is characterized in that a follower in the continuous nonlinear intelligent unmanned cluster system performs state updating according to an input control signal, and the updating process is represented as:
wherein the content of the first and second substances,
is the derivative of the follower state vector, x i (t)∈R n Is the state vector of the follower, and n is the dimension of the vector; u. of i (t) is the control input, C, B are constant matrices, g (x) i (t)) is a nonlinear function that satisfies the Lipschitz condition and is expressed as g (x) i (t))＝(g 1 (x i (t)),g 2 (x i (t)),...,g n (x i (t))) T ，g n (x i (t)) represents a non-linear function g (x) i (t)) the nth dimensional value.
3. The intelligent unmanned cluster system time-lag pulse control method for defending against spoofing attacks as recited in claim 1, characterized in that a leader in the continuous nonlinear intelligent unmanned cluster system performs state update according to an input control signal, and the update process is represented as:
wherein, the first and the second end of the pipe are connected with each other,
a derivative of a state vector representing the leader; C. b is a constant matrix, and g (s (t)) is a nonlinear part in the leader dynamics equation.
4. The intelligent unmanned cluster system time lag pulse control method for defending against spoofing attacks as recited in claim 1, wherein a parameter β representing whether or not a node i suffers from spoofing attacks when receiving state information of a node j ij (t) is a random variable, ρ, following a Bernoulli distribution ij Belongs to [0, 1) and specifies ρ ii =0, random variable β ij (t) are independent of each other.
5. The intelligent unmanned cluster system time-lag pulse control method for defending against spoofing attacks of claim 1, wherein in the continuous nonlinear intelligent unmanned cluster system, one directed spanning tree must exist in a directed network topology formed by a leader node and a follower node, and the leader node is a root node in the spanning tree.
6. The intelligent unmanned cluster system time-lag pulse control method for resisting spoofing attack as claimed in claim 1, wherein the containment gain d of follower node i i The value of d is determined by whether the following node can directly acquire the state of the leader node, and when the following node i can directly acquire the state information of the leader, d i > 0, otherwise, d i ＝0。
7. The intelligent unmanned cluster system time-lag pulse control method for defending against spoofing attacks as claimed in claim 1, characterized in that the pulse function adopts a dirac pulse function δ (x), that is, if x ≠ 0, then δ (x) =0; the pulse sequence satisfies 0= t 0 ＜t 1 ＜…＜t k < 8230am
The interval between two adjacent pulse time satisfies f 1 ＝inf{t k -t k-1 }、f 2 ＝sup{t k -t k-1 And 0 < f 1 ≤f 2 Infinity, inf { } represents the definite boundary found below, and { } represents the definite boundary found above. />
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| CN116679753A (en) * | 2023-06-25 | 2023-09-01 | 中国矿业大学 | Formation tracking control method for anti-spoofing attack of heterogeneous unmanned system |
| CN116820100A (en) * | 2023-06-25 | 2023-09-29 | 中国矿业大学 | Unmanned vehicle formation control method under spoofing attack |
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| CN116679753A (en) * | 2023-06-25 | 2023-09-01 | 中国矿业大学 | Formation tracking control method for anti-spoofing attack of heterogeneous unmanned system |
| CN116820100A (en) * | 2023-06-25 | 2023-09-29 | 中国矿业大学 | Unmanned vehicle formation control method under spoofing attack |
| CN116679753B (en) * | 2023-06-25 | 2024-01-26 | 中国矿业大学 | Formation tracking control method for anti-spoofing attack of heterogeneous unmanned system |
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