A time-delay pulse control method for intelligent unmanned cluster system to resist deception attacks

Abstract

The present invention belongs to the technical field of intelligent unmanned cluster system control, and specifically relates to a time-delay pulse control method for an intelligent unmanned cluster system for resisting deception attacks, including taking into account the deception attacks existing in the sensor-controller channel of the intelligent unmanned cluster system, adopting the time-delay utilization technology, adding the time-delay into the controller, and using the containment control at the same time, selecting the appropriate containment time-delay parameter, thereby improving the convergence performance of the system; utilizing the discrete pulse control scheme, while saving resources, avoiding the deception attacks at some non-pulse moments, and reducing the impact of the deception attacks on the system; combining the containment time-delay with the pulse control, constructing a consistency control protocol, and ensuring the realization of mean square bounded synchronization of the system; the time-delay pulse control method proposed in the present invention ensures the realization of synchronization of the intelligent unmanned cluster system under the deception attack, and has a certain robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent unmanned cluster system control, and in particular relates to a time-delay pulse control method for an intelligent unmanned cluster system for resisting deception attacks. Background Art

[0002] In recent decades, intelligent unmanned swarm systems have attracted the attention of many researchers due to their wide applications in smart grids, formation control, and collaborative decision-making. The synchronization of intelligent unmanned swarm systems means that all nodes converge to the same state. In order to achieve the synchronization of intelligent unmanned swarm systems, communication is required between individuals in the system. Since the actual intelligent unmanned swarm system is in a complex network environment, it is vulnerable to network attacks. Therefore, the security control of intelligent unmanned swarm systems deserves further study.

[0003] So far, two typical attacks launched by attackers at the communication network layer are denial of service attacks and deception attacks. Deception attacks refer to the attacker modifying control inputs and measurement data, resulting in incomplete or unreliable data resources. According to research, deception attacks can bypass existing detection technologies and cause serious degradation of system performance. Therefore, in recent years, the synchronization problem of intelligent unmanned cluster systems under deception attacks has received widespread attention. For example, in some literature, deception attacks are described as random variables obeying Bernoulli distribution, replaced system control input signals, or desynchronization pulses. Although some progress has been made in the synchronization problem of intelligent unmanned cluster systems under deception attacks, the above literature does not consider some realistic environmental factors when considering intelligent unmanned cluster systems under deception attacks, such as the communication delay between the leader and the follower system. Therefore, it is very meaningful to further study the synchronization problem of intelligent unmanned cluster systems under deception attacks.

[0004] Many synchronization problems of intelligent unmanned cluster systems are solved by pulse control. And due to the widespread existence of time delay, many researchers are very interested in time-delay pulses. In some literature, it is found that time delay has potential practical value, and time delay is not always a bad factor in active controllers. In the controller, the performance and stability of the system can be improved by properly using time delay. In addition, in the leader-follower model, containment control can be used, that is, only controlling some key nodes to reduce the cost of the control strategy. However, most of the existing research on time-delay pulse control is used in ideal environments, and few studies consider the existence of deception attacks in actual communications. Therefore, it is an urgent problem to use time-delay containment pulse control to achieve the synchronization of intelligent unmanned cluster systems and improve the convergence performance of the system under deception attacks. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a time-delay pulse control method for an intelligent unmanned cluster system to resist deception attacks, including constructing a continuous nonlinear intelligent unmanned cluster system with deception attacks, in which the time delay when transmitting information between the leader node and the follower node is considered, and the time-delay pulse control signal generated by the node i at time t is expressed as:

[0006]

[0007] Among them, u i (t) represents the time-delay pulse control signal generated by node i at time t; c is the coupling strength, and N represents the number of individuals in the intelligent unmanned cluster system;; a ij is 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 ≠0, otherwise a ij =0, and a is specified 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; β ij (t) indicates whether node i is subjected to a spoofing attack when receiving the status information of node j. If β ij (t) = 1, it means there is a spoofing attack, and 0 means there is no spoofing attack; q i (t) represents the attack signal suffered by node i at time t; d i represents the control gain of follower node i; p1 represents the control gain of the control pulse; s(t) represents the state vector of the leader; p2 is the control gain of the control delay pulse; τ k Indicates the time lag of the pulse controller; t k represents the time of the kth pulse; δ() is the pulse function.

[0008] Furthermore, in the continuous nonlinear intelligent unmanned cluster system, the follower updates its state according to the input control signal, and the update process is expressed as:

[0009]

[0010] in, is the derivative of the follower state vector, x i (t)∈R n is the state vector of the follower, n is the dimension of the vector; u i (t) is the control input, C and B are constant matrices, g(x i (t))=(g1(x i (t)),g2(x i (t)),...,g n(x i (t))) T g(x i (t)) is a nonlinear function that satisfies the Lipschitz condition and is expressed as g(x i (t))=(g1(x i (t)),g2(x i (t)),...,g n (x i (t))) T , g n (x i (t)) represents the nonlinear function g(x i (t))'s n-th dimension value.

[0011] Furthermore, in the continuous nonlinear intelligent unmanned swarm system, the leader updates the state according to the input control signal, and the update process is expressed as:

[0012]

[0013] in, represents the derivative of the leader's state vector; C and B are constant matrices, and g(s(t)) is the nonlinear part of the leader's dynamic equation.

[0014] Furthermore, the parameter β indicates whether node i has been subjected to a spoofing attack when receiving the status information of node j. ij (t) is a random variable that follows a Bernoulli distribution, ρ ij ∈[0,1) and specify ρ ii =0, random variable β ij (t) are independent of each other.

[0015] Furthermore, in the continuous nonlinear intelligent unmanned cluster system, a directed spanning tree must exist in the directed network topology composed of the leader node and the follower nodes, and the leader node is the root node in the spanning tree.

[0016] Furthermore, the containment gain d of follower node i i The value of is determined by whether the follower node can directly obtain the status of the leader node. When the follower node i can directly obtain the status information of the leader, then d i > 0, otherwise, d i =0.

[0017] Furthermore, the pulse function adopts the Dirac pulse function δ(x), that is, if x≠0, then δ(x)=0; the pulse sequence satisfies 0=t0<t1<…<t k <and The interval between two adjacent pulse times satisfies f1 = inf{tk -t k-1}、f2=sup{t k -t k-1}and 0<f1≤f2<∞.

[0018] The time-delay pulse control protocol designed by the present invention adopts the time-delay utilization technology, and improves the stability performance of the system and accelerates the convergence speed of the system by setting reasonable time-delay control parameters; the continuous system is discretely controlled by the pulse control scheme, which saves system resources and avoids the impact of non-pulse moment deception attacks on the system to a certain extent; the present invention takes into account the nonlinear intelligent unmanned cluster system suffering from deception attacks on the sensor-controller channel, and the system finally achieves mean square bounded synchronization under the time-delay control pulse, so that the method also has a certain robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a system control flow chart of the present invention;

[0020] Figure 2 is an attack position diagram of the deception attack of the present invention;

[0021] Figure 3 is a communication topology diagram of the system of the present invention;

[0022] Figure 4 is an evolution diagram of the node state when the present invention uses time-delay pulse control;

[0023] Figure 5 It is an evolution diagram of the node state when the present invention uses ordinary pulse control;

[0024] Figure 6 is an evolution diagram of the error between each node and the leader when the present invention uses time-delay pulse control;

[0025] Figure 7 It is an evolution diagram of the second norm of the error vector between each node and the leader when the present invention uses time-delay pulse control. DETAILED DESCRIPTION

[0026] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0027] The present invention proposes a time-delay pulse control method for an intelligent unmanned cluster system to resist deception attacks, including constructing a continuous nonlinear intelligent unmanned cluster system with deception attacks, in which the time delay when transmitting information between the leader node and the follower node is considered, and the time-delay pulse control signal generated by the node i at time t is expressed as:

[0028]

[0029] Among them, u i (t) represents the time-delay pulse control signal generated by node i at time t; c is the coupling strength, N represents; a ij is 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 ≠0, otherwise a ij =0, and a is specified 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; β ij (t) indicates whether node i is subjected to a spoofing attack when receiving the status information of node j. If β ij (t) = 1, it means there is a spoofing attack, and 0 means there is no spoofing attack; q i (t) represents the attack signal suffered by node i at time t; d i represents the control gain of follower node i; p1 represents the control gain of the control pulse; s(t) represents the state vector of the leader; p2 is the control gain of the control delay pulse; τ k represents the time lag of the pulse controller; δ() is the pulse function.

[0030] In this embodiment, a time-delay pulse control method for an intelligent unmanned cluster system to resist deception attacks is specifically divided into five steps: Figure 1 , specifically including:

[0031] Step 1: Construct a continuous nonlinear system follower model and a leader reference model to determine the communication topology of the complex intelligent unmanned cluster system, where each individual in the system is regarded as a node in the graph, and the information flow is determined based on the edges between them. Some nodes can obtain the status information of the leader and implement containment control.

[0032] The constructed continuous nonlinear intelligent unmanned swarm system follower model is as follows:

[0033]

[0034] Among them, x i (t)∈R n is the state vector, ui (t) is the control input, C and B are constant matrices, g(x i (t)) is a nonlinear function that satisfies the Lipschitz condition and is represented by g(x i (t))=(g1(x i (t)),g2(x i (t)),...,g n (x i (t))) T , g n (x i (t)) represents the nonlinear function g(x i In the present invention, the nonlinear function is required to satisfy the Lipschitz condition.

[0035] The leader reference model is as follows:

[0036]

[0037] in, is the derivative of the leader's state vector. In order to ensure the synchronization of intelligent unmanned clusters, a directed spanning tree must exist in the directed network topology consisting of the leader and all followers, where the leader node is the root node in the spanning tree. Only in this way can all nodes directly or indirectly obtain the leader's state information and achieve leader-follower consistency. Some nodes in the system topology can directly obtain the leader node's state information, that is, they are controlled by the control method as follows:

[0038] d i (x i (t)-s(t))

[0039] Among them, d i represents the containment gain of the ith node. If the ith node can directly obtain the status information of the leader, then d i > 0, otherwise, d i =0.

[0040] Step 2: Consider the possible deception attacks in the sensor-controller channel, use a random variable that follows the Bernoulli distribution to indicate whether the deception attack occurs, and model the deception attack.

[0041] The present invention considers that the intelligent unmanned cluster system is subjected to deception attacks in the sensor-controller channel. The attack position of the deception attack is as follows: Figure 2 As shown. Using a random variable β that follows a Bernoulli distribution ij(t) indicates whether node i is subjected to a spoofing attack when receiving the status information of node j. If β ij If (t) = 1, it means there is a spoofing attack, and if it is 0, there is no spoofing attack. The probability distribution of the random variable is as follows:

[0042] Prob{β ij (t) = 1} = ρ ij

[0043] Prob{β ij (t) = 0} = 1-ρ ij

[0044] Among them, ij ∈[0,1), and stipulate that ρ ii = 0. Here, it indicates that the probability of a cheating attack in the channel between node i and node j is ρ ij , and the random variable β ij (t) are independent of each other.

[0045] Step 3: The intelligent unmanned cluster system adopts a discrete pulse control scheme. The pulse function will only take effect at the pulse moment. At the non-pulse moment, the control input of the system is 0, and the system will not be able to receive the status information of neighboring nodes. This can avoid some deception attacks and reduce the impact of deception attacks on the system.

[0046] In this embodiment, the intelligent unmanned cluster system adopts a discrete pulse control scheme, using the Dirac pulse function δ(x). If x≠0, then δ(x)=0. That is, the control protocol works only at the discrete pulse control moment. At the same time, if the deception attack happens to occur at a non-pulse moment, it will not affect the control of the system.

[0047] Step 4: Use time delay utilization technology to take into account the time delay in transmitting information between the leader and the follower, and speed up the convergence of the system by setting appropriate control parameters of the time delay pulse.

[0048] The existence of appropriate time delay is conducive to the stability of the system, and it is inevitable that there is a certain time delay in the transmission of information between nodes. Using time-delay pulse control, the system can use the state information of some nodes at non-pulse moments at the pulse moment, which is more conducive to system synchronization.

[0049] Step 5: Set up a consistency control protocol. Each node updates its status according to the status information of neighbor nodes in the consistency control protocol and the status information received from the leader. At the same time, the containment delay term in step 4 is also taken into account, so that the intelligent unmanned cluster system can achieve mean square bounded synchronization in the presence of deception attacks. At the same time, the existence of the delay term can accelerate the convergence of the system.

[0050] The consistency control protocol used in this embodiment is:

[0051]

[0052] The pulse sequence is and Assumptions f2=sup{t k -t k-1}, and satisfies 0<f1≤f2<∞.

[0053] In this embodiment, when the nonlinear intelligent unmanned cluster system meets the following conditions, the intelligent unmanned cluster system achieves mean square bounded synchronization, and the states of all nodes and the leader remain consistent, and the condition met is that the state error between the node and the leader converges to a tight set. That is:

[0054]

[0055] Among them, δ is a constant, indicating the error boundary; E{} indicates the average value, x i (t) represents the state of the ith follower, s(t) represents the state of the leader, and ‖‖ represents the second norm of the vector.

[0056] In this embodiment, Figure 1 A specific implementation method shown includes the following steps:

[0057] Construct a follower model and a leader reference model for a continuous nonlinear system, and determine the communication topology of the intelligent unmanned swarm system;

[0058] Considering the possible deception attacks in the sensor-to-controller channel, a random variable following Bernoulli distribution is used to indicate whether a deception attack occurs, and the deception attack is modeled.

[0059] By adopting a discrete pulse control scheme, at non-pulse moments, the control input of the system is 0, and the system will not be able to receive the status information of neighboring nodes, which can avoid some deception attacks and reduce the impact of deception attacks on the system.

[0060] The time delay utilization technology is used to take the time delay of information transmission between the leader and follower nodes into consideration, and the system convergence speed is accelerated by setting appropriate control parameters of the time delay pulse.

[0061] Taking deception attacks into consideration and combining the communication topology between nodes, a consistency control protocol is designed using a time-delay pulse control scheme, so that the intelligent unmanned multi-turn system can achieve mean square bounded synchronization in the presence of deception attacks.

[0062] like Figure 3 As shown, this embodiment provides a communication topology graph consisting of 6 nodes. The adjacency matrix and Laplace matrix of the communication topology graph are given as follows:

[0063]

[0064] The matrix D = diag{d i} indicates whether there is a path between the node and the leader. In this embodiment, the matrix D is expressed as:

[0065]

[0066] Matrix D shows that only the 2nd and 4th nodes have direct connections to the leader, that is, the 2nd and 4th nodes are pinned down.

[0067] Set the deception attack strength q i The upper bound of is q = 0.2, and the probability matrix of each communication channel between nodes being attacked by spoofing is as follows:

[0068]

[0069] Among them, Prob{β 13 (t)=1}=0.2, indicating that the probability of the communication channel between node 1 and node 3 being subjected to a spoofing attack is 0.2.

[0070] Set the pinning pulse parameter p1 = -0.7, and the time-delay pinning pulse control parameter p2 = -0.08, then the trajectory of each node state is as follows: Figure 4 As shown in the figure, it can be seen that when the calculation step is 0.15, the states of all nodes in the entire system are the same, that is, consistency is achieved, and the entire system is synchronized. When other parameters remain unchanged, the control pulse parameter p1 is set to -0.7, and the time-delay control pulse control parameter is set to p2 = 0, then the trajectory of each node state is as follows Figure 5 As shown in Figure 1, it can be seen that when the calculation step is 0.35, the states of all nodes in the entire system are consistent. Comparing the consistency realization time, the results show that introducing an appropriate amount of time delay in the pinning pulse controller is conducive to the realization of system synchronization.

[0071] Figure 6 The state evolution diagram of the first dimension of the error vector between each node and the leader is described. It can be seen that the errors between all nodes and the leader eventually fluctuate around 0, and the entire system achieves follower-leader synchronization. Figure 7The graph describes the evolution of the square of the binary norm of the error vector between the node and the leader over time. It can be seen that the final error vector is very close to 0, and the theoretical upper bound of the binary norm of the error vector can be calculated to be 2.3841. The error in the figure is obviously smaller than the theoretical upper bound, which meets the conditions for the system to achieve mean square bounded synchronization. The intelligent unmanned cluster system finally achieved mean square bounded synchronization in the presence of deception attacks.

[0072] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A time-delay pulse control method for an intelligent unmanned cluster system to resist deception attacks, characterized in that: A continuous nonlinear intelligent unmanned cluster system with deception attacks is constructed. In this system, the time delay in information transmission between the leader node and the follower node is considered. The time-delay pulse control signal generated by node i at time t is expressed as: Among them, u i (t) represents the time-delay pulse control signal generated by node i at time t; c is the coupling strength, N represents the number of individuals in the intelligent unmanned cluster system; a ij is 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 ≠0, otherwise a ij =0, and a is specified 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; β ij (t) indicates whether node i is subjected to a spoofing attack when receiving the status information of node j. If β ij (t) = 1, it means there is a spoofing attack, 0 means there is no spoofing attack, β ij (t) is a random variable that follows a Bernoulli distribution. The probability distribution of this random variable is represents the probability of a deception attack in the channel between node i and node j, ρ ii = 0 and the random variable β ij (t) are independent of each other; q i (t) represents the attack signal suffered by node i at time t; d i represents the control gain of follower node i; p1 represents the control gain of the control pulse; s(t) represents the state vector of the leader; p2 is the control gain of the control delay pulse; τ k represents the time lag of the control pulse controller; tk represents the time of the kth pulse; δ() is the pulse function; In the continuous nonlinear intelligent unmanned swarm system, the follower updates its state according to the input control signal. The update process is expressed as: in, is the derivative of the follower state vector, n is the dimension of the vector; C and 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))=(g1(x i (t)),g2(x i (t)),...,g n (x i (t))) T , g n (x i (t)) represents the nonlinear function g(x i (t))’s nth dimension value; In the continuous nonlinear intelligent unmanned swarm system, the leader updates the state according to the input control signal. The update process is expressed as: in, represents the derivative of the leader’s state vector; g(s(t)) is the nonlinear part of the leader’s dynamics equation.

2. The method for controlling time-delay pulses of an intelligent unmanned cluster system for resisting deception attacks according to claim 1 is characterized in that: In a continuous nonlinear intelligent unmanned cluster system, a directed spanning tree must exist in the directed network topology composed of a leader node and follower nodes, and the leader node is the root node in the spanning tree.

3. The time-delay pulse control method for an intelligent unmanned cluster system for resisting deception attacks according to claim 1 is characterized in that: The containment gain d of follower node i i The value of is determined by whether the follower node can directly obtain the status of the leader node. When the follower node i can directly obtain the status information of the leader, then d i > 0, otherwise, d i =0.

4. The method for controlling time-delay pulses of an intelligent unmanned cluster system for resisting deception attacks according to claim 1 is characterized in that: The pulse function adopts the Dirac pulse function δ(x), that is, if x≠0, then δ(x)=0; the pulse sequence satisfies 0=t0<t1<…<t k <… and The interval between two adjacent pulse times satisfies f1 = inf{t k -t k-1 }、f2=sup{t k -t k-1 } and 0<f1≤f2<∞, inf{} means finding the infimum, and sup{} means finding the supremum.

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