Security immune control method for heterogeneous unmanned cluster system under distributed denial of service attack

Abstract

The application discloses a kind of heterogeneous unmanned cluster system security immune control methods under distributed denial of service attack.The application uses event triggering mechanism to avoid continuous information interaction between followers,achieves discrete communication,and effectively excludes Zeno phenomenon,gets rid of the limitation of limited communication bandwidth in actual situation;In addition,getting rid of the design requirement of distributed observer in traditional method,avoiding the extra information transmission caused by observer state variable;And based on the design of controller with matching idea to get rid of the prior information constraint of system model,can realize state tracking under the condition that system model is uncertain and different communication links are attacked independently;At the same time,communication channel equivalent decay rate is introduced,under the condition that each communication link is attacked independently,decay condition is analyzed,system model uncertainty and network attack diversity in actual situation are effectively coped with.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned cluster systems, and in particular to a security immune control method for heterogeneous unmanned cluster systems under distributed denial of attack. Background Art

[0002] Unmanned swarm systems are large, complex systems composed of multiple intelligent unmanned platforms, including drones, vehicles, and boats. These platforms collaborate to perform specialized tasks, enabling them to accomplish complex tasks that would be difficult or even impossible for a single system. These systems offer advantages such as greater adaptability, improved fault tolerance, and enhanced parallelism, and hold broad application prospects in both civil and military fields. Distributed collaboration among these platforms reduces the computational complexity of complex problems and improves system performance. However, this collaborative control mechanism also places higher demands on network security, communication resources, and the ability to cope with uncertainty.

[0003] In unmanned swarm systems, unmanned platforms exchange information through network topology to collaboratively execute tasks. In open environments, communication topologies often face numerous external threats, with cyberattacks being a primary one. Denial-of-Service (DoS) attacks are a common attack, where attackers block communication channels, rendering some or all components of a control system inaccessible, thereby compromising system stability. Current research on network security mostly assumes that all communication channels in a system have the same attack model. However, in practice, due to the complexity of communication networks and the diversity of attackers, such synchronized attacks are less practical. Distributed attacks consider independent attacks on different communication links, meaning attackers can attack any channel at different times. This attack model better simulates the complexities of real-world environments and offers greater versatility.

[0004] Traditional cooperative controllers often operate under ideal communication conditions, assuming continuous data transmission between adjacent unmanned platforms with communication links. Designing distributed observers is an effective approach for state tracking control of heterogeneous multi-agent systems. Existing research on cooperative control through output regulation theory mostly employs distributed observers to estimate leader information. However, in practical situations, system resources are limited, and the transmission of observed auxiliary variable information imposes an additional communication burden. Furthermore, continuous communication is difficult to achieve within the constraints of limited communication bandwidth, posing a significant challenge to designing more cost-effective communication strategies. Event-triggered control strategies offer an effective approach to addressing this issue. By employing an event-based data transmission scheme between adjacent unmanned platforms, data is updated or transmitted only when pre-designed trigger conditions are met, enabling discrete communication within the system. This significantly reduces the communication burden, effectively avoiding continuous communication within unmanned cluster systems, and conserving system communication resources.

[0005] Furthermore, existing collaborative control methods for multi-agent systems rely heavily on precise system models. However, in practice, due to factors such as external disturbances, accurate models of unmanned swarm systems are difficult to obtain and exhibit high uncertainty, posing a significant challenge to collaborative control. The matching concept offers a new approach to addressing uncertain systems, eliminating the need for a precise dynamic model of the system as a prerequisite for collaborative control. Summary of the Invention

[0006] In view of this, the present invention provides a security immune control method for heterogeneous unmanned cluster systems under distributed denial of attack. Based on the matching idea, an event-triggered security controller under distributed attack is designed, which can perform collaborative control without the need for system model information, and get rid of the design requirements of distributed observers, realize discrete communication, reduce the communication burden of the system, and better cope with the uncertainty of system models and the diversity of network attacks in actual situations.

[0007] The present invention provides a method for secure immune control of heterogeneous unmanned swarm systems under distributed denial of service (DDoS) attacks. The heterogeneous uncertain unmanned swarm system consists of N followers and one leader, and the unmanned platforms communicate with each other via a directed topology graph. The heterogeneous unmanned swarm system uses an event-triggered mechanism, that is, data transmission is performed only when the trigger condition is met, and state estimation is performed using an open-loop estimator during non-trigger periods.

[0008] Among them, the event-triggered tracking controller is:

[0009]

[0010] Among them, x i ∈Rn is the state of the i-th follower; is the local estimation error of agent i; x0∈R n It is the state of a leader. is the state estimate of the i-th follower; the controller parameter k i ∈R m×n is the feedback gain matrix, l i ∈R is the coupling gain;

[0011] is the state error feedback matrix, P is a symmetric positive definite matrix that satisfies the following linear matrix inequality conditions:

[0012]

[0013] PA0+A0 T P-α Γ P-γφ2I<0

[0014] Where X = P -1 >0;α Γ is the attack attenuation rate corresponding to the attack model Γ; is a matrix The smallest characteristic root of is the system topology diagram under attack model Γ The communication link matrix; φ1>0 and φ2>0 are the designed event trigger parameters, γ>0 is the selected performance parameter; I is the unit matrix; A0 is the reference system matrix, b0 is the reference input matrix;

[0015] Moreover, the interval between adjacent trigger events satisfies:

[0016]

[0017] in, are the kth and k+1th triggering moments of the i-th agent, is the local estimation error of the i-th agent exist The norm value of is the norm exist The upper bound of the inner is the trigger parameter.

[0018] Preferably, in the heterogeneous uncertain unmanned cluster system, the system model of N followers is

[0019]

[0020] Among them, x i is the state of the i-th follower; denotes the derivative of the ith follower state; u i is the control input of the ith follower; y i is the output of the ith follower; A i denotes the follower system matrix, B i denotes the follower input matrix, C i denotes the follower output matrix;

[0021] The system model of the leader is

[0022]

[0023] where all eigenvalues of the matrix A0have non-positive real parts. x0∈R n is the state of the leader, which is also the desired state that the follower needs to track, and n denotes the dimension of the leader state x0; denotes the derivative of the leader state; y0∈R s is the output of the leader, and s denotes the dimension of the leader output y0; A0∈R n×n denotes the leader system matrix with dimension n x n, C0∈R s ×n denotes the leader output matrix with dimension s x n;

[0024] For the above heterogeneous unmanned cluster system, it is assumed that there exists a matrix k i ∈R m×n and a scalar l i ∈R, such that the system matrix A i and the input matrix B i satisfy

[0025]

[0026] where the reference matrix pair (A0, b0) is known, A0∈R n×n denotes the reference system matrix with dimension n x n, b0∈R n×m denotes the reference input matrix with dimension n x m;

[0027] The follower topology graph is a directed graph where is the node set composed of followers, v i denotes the ith node, is the edge set between nodes; L is the follower topology graph corresponding Laplacian matrix, which represents the communication link between followers, and satisfies L≠L T ;

[0028] The system topology graph is a directed graph It consists of a leader and all followers, where 0 is the leader index; is a strongly connected graph, and H is the system topology graph The corresponding communication link matrix satisfies H≠H T .

[0029] The better attack model is:

[0030] Γ(t)={(i,j)∈ε|t∈D (i,j) (0,∞)}

[0031] Where Γ(t) is the attack model corresponding to time t, D (i,j) (0,∞) is the set of time periods during which edge (i,j) suffers DoS attack within t∈(0,∞);

[0032] Attack duration limit

[0033] |D (i,j) (t0,t)|≤ζ ij +μ ij (t-t0)

[0034] Among them D (i,j) (t0,t) is the set of time periods during which the edge (i,j) of the directed graph is attacked by DoS within t∈(t0,t), ζ ij >0 is a positive scalar, 0<μ ij <1 is the attack strength parameter;

[0035] When Γ = ε, it is a full attack model.

[0036] The optimal open-loop estimator based on the event-triggered mechanism is:

[0037]

[0038] in, is the state estimate of the i-th follower, is the kth triggering moment of the ith follower, is the triggering time sequence of the i-th follower; assuming that the followers in the system that have a communication link with the leader can continuously receive the information transmitted by the leader, that is,

[0039] Define the state estimation error e of the i-th agent i ∈R n : in Represents the neighborhood of node i in the communication topology graph of the unmanned system, and the initial state estimation error e i (0)=0.

[0040] Event trigger mechanism design

[0041]

[0042] Trigger parameters satisfy

[0043]

[0044] Where φ1>0 and φ2>0 are the designed event trigger parameters, and γ>0 is a sufficiently large performance parameter. Follower topology diagram The left eigenvector of the Laplace matrix L about the eigenvalue 0 is ξ=[ξ1,ξ2,...,ξ N ] T , satisfying ξ T L=0,ξ i >0 is the i-th element of the eigenvector ξ, min and ξ max are the minimum and maximum elements in the eigenvector ξ, that is, ξ min =min i∈v {ξ i},ξ max =max i∈v {ξ i}. is the system topology under attack model Γ Communication link matrix.

[0045] Beneficial effects:

[0046] The present invention adopts an event trigger mechanism to avoid continuous information interaction between followers, realizes discrete communication, and effectively eliminates the Zeno phenomenon, getting rid of the limitation of limited communication bandwidth in actual situations; in addition, it gets rid of the design requirements of distributed observers in traditional methods, and avoids the additional information transmission brought by the observer state variables; and designs a controller based on the matching idea to get rid of the prior information constraints of the system model, which can realize state tracking when the system model is uncertain and different communication links are attacked independently; at the same time, the equivalent attenuation rate of the communication channel is introduced to analyze the attenuation conditions when each communication link is attacked independently, effectively dealing with the uncertainty of the system model and the diversity of network attacks in actual situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0048] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0049] The application provides a security immune control method for a heterogeneous unmanned cluster system under a distributed denial of service attack.

[0050] Step 1: establishing a heterogeneous uncertain unmanned cluster system model. It is assumed that the model is composed of N followers and one leader, unmanned platforms communicate through a topological graph, and the communication between any two unmanned platforms has directionality.

[0051] A directed graph is a follower topological graph, wherein is a node set composed of followers, v i represents the i th node, is an edge set between nodes. L is a follower topological graph is a corresponding Laplacian matrix, representing the communication link between followers, and satisfying L≠L T .

[0052] A directed graph is a system topological graph composed of a leader and all followers, wherein 0 is a leader index. is a strongly connected graph. H is a system topological graph is a corresponding communication link matrix, satisfying H≠H T .

[0053] The system model of the N followers is established as

[0054]

[0055] wherein the matrix pair (A i ,B i ) is controllable. x i ∈R n is the state of the i th follower, and n represents the dimension of the state x i of the i th follower; represents the derivative of the state of the i th follower; u i ∈R m is the control input of the i th follower, and m represents the dimension of the control input u i of the i th follower; y i ∈R s is the output of the i th follower, and s represents the dimension of the output y i of the i th follower; A i ∈R n×n represents a follower system matrix with a dimension of n×n, B i ∈R n×m represents a follower input matrix with a dimension of n×m, C i ∈R s×n represents a follower output matrix with a dimension of s×n.

[0056] The leader's system model is established as

[0057]

[0058] In which all eigenvalues ​​of the matrix A0 have non-positive real parts. n is the state of the leader and the expected state that the follower needs to track. n represents the dimension of the leader state x0; represents the derivative of the leader state; y0∈R s is the output of the leader, s represents the dimension of the leader output y0; A0∈R n×n represents the leader system matrix with dimension n×n, C0∈R s ×n Represents the leader output matrix of dimension s×n.

[0059] For the above heterogeneous uncertain unmanned cluster system, assume that there is a matrix k i ∈R m×n With scalar l i ∈R 1 , so that the system matrix A i With the input matrix B i satisfy

[0060]

[0061] Where the matrix pair (A0, b0) is known, A0∈R n×n represents the reference system matrix with dimension n×n, b0∈R n×m Represents the reference input matrix of dimension n×m.

[0062] The heterogeneous uncertain unmanned swarm system model only requires the above model matching conditions to be met without the need to know the precise system matrix A in advance. i 、B i The introduction of this matching condition releases the dependence on the precise model of the system, and can better deal with the problem of model uncertainty and difficulty in explicit acquisition in actual complex environments.

[0063] Step 2: Due to the complexity of communication networks and the diversity of attack behaviors, attackers can attack any communication channel at different times. Considering the attacker's independent attacks on different communication links, a distributed DoS attack model is established.

[0064] Attack duration limit

[0065] |D (i,j) (t0,t)|≤ζ ij +μ ij (t-t0)

[0066] Among them D(i,j) (t0,t) is the set of time periods during which edge (i,j) suffers DoS attack within t∈(t0,t), ζ ij >0 is a positive scalar, 0<μ ij <1 is the attack strength parameter.

[0067] Attack model establishment

[0068] Γ(t)={(i,j)∈ε|t∈D (i,j) (0,∞)}

[0069] Where Γ(t) is the attack model corresponding to time t, D (i,j) (0,∞) is the set of time periods during which edge (i,j) suffers DoS attack within t∈(0,∞).

[0070] Step 3: Considering that the continuous exchange of explicit information between unmanned platforms will generate a large communication burden, an event trigger mechanism is designed so that the system only transmits data when the trigger conditions are met, and the state estimation is performed through the open-loop estimator during the non-trigger period.

[0071] Open-loop estimator design

[0072]

[0073] in, is the state estimate of the i-th follower, is the kth triggering moment of the ith follower, is the triggering time sequence of the ith follower. Assume that the followers in the system that have a communication link with the leader can continuously receive the information transmitted by the leader, that is,

[0074] Define the state estimation error e of the i-th agent i ∈R n : and local estimation error in Represents the neighborhood of node i in the communication topology graph of the unmanned system, and the initial state estimation error e i (0)=0.

[0075] Event trigger mechanism design

[0076]

[0077] Trigger parameters satisfy

[0078]

[0079] Where v1>0 and v2>0 are the designed event trigger parameters, and γ>0 is a sufficiently large performance parameter. Follower topology diagram The left eigenvector of the Laplace matrix L about the eigenvalue 0 is ξ=[ξ1,ξ2,...,ξ N ] T , satisfying ξ T L=0,ξ i >0 is the i-th element of the eigenvector ξ, min and ξ max are the minimum and maximum elements in the eigenvector ξ, that is, ξ min =min i∈v {ξ i},ξ max =max i∈v {ξ i}. is the system topology under attack model Γ Communication link matrix.

[0080] Step 4: Due to the existence of external disturbances and other factors in the actual heterogeneous unmanned cluster system, the system model (i.e., the system matrix A i With the input matrix B i ) has high uncertainty and is difficult to obtain in advance. Therefore, in order to achieve the state tracking goal of heterogeneous uncertain unmanned swarm systems, an event-triggered tracking controller under distributed DoS attacks is designed based on the matching idea.

[0081] Controller Design

[0082]

[0083] where x i ∈R n is the state of the i-th follower; is the local estimation error of agent i. The controller parameter k i ∈R m×n is the feedback gain matrix, l i ∈R 1 is the coupling gain, satisfying the following matching conditions:

[0084]

[0085] Where (A0, b0) is the reference matrix pair. State error feedback matrix P∈R n×n is a symmetric positive definite matrix that satisfies the following linear matrix inequality conditions:

[0086]

[0087] PA0+A0 T P-α Γ P-γφ2I<0

[0088] Where X = P -1 >0,α Γ is the attack attenuation rate corresponding to the attack model Γ, φ1>0 and φ2>0 are event trigger parameters, and γ>0 is the selected performance parameter.

[0089] Step 5: Use the Lyapunov stability analysis method to design decay conditions to analyze the coordinated behavior of the system. Calculate the interval between adjacent trigger events to eliminate the Zeno phenomenon of the event triggering mechanism.

[0090] Lyapunov function design

[0091]

[0092] where Ξ=diag{ξ1,ξ2,...,ξ N}.

[0093] Under the designed event-triggered safety tracking controller, the attenuation of the Lyapunov function can be achieved, that is, Among them, the decay rate α of the Lyapunov function Γ The following conditions are met:

[0094]

[0095]

[0096]

[0097] Among them, ω>0 is the convergence parameter, 0<μ ij <1 is the attack strength parameter, and are the equivalent attenuation rates when edge (i, j) suffers DoS attack and normal communication, respectively.

[0098] Under the above attenuation conditions, lim t→∞ V(t)=0, that is, lim t→∞ ‖δ(t)‖=0, the unmanned swarm system can achieve tracking control targets.

[0099] The interval between adjacent trigger events of the system meets the

[0100]

[0101] in, is the kth triggering moment of the i-th agent, is the k+1th triggering moment of the i-th agent, is the local estimation error exist The norm value of For The norm of the local estimation error within The upper bound of .

[0102] Under the designed event trigger mechanism, the intervals between adjacent trigger events are strictly positive, that is, within any finite time, there is no Zeno behavior for all unmanned platforms.

[0103] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A security immune control method for heterogeneous unmanned cluster systems under distributed denial of attack, characterized by: The heterogeneous uncertain unmanned swarm system consists of N followers and one leader. The unmanned platforms communicate with each other through a directed topology graph. The heterogeneous unmanned swarm system uses an event-triggered mechanism, that is, data transmission is performed only when the trigger condition is met, and state estimation is performed through an open-loop estimator during non-trigger periods. Among them, the event-triggered tracking controller is: Among them, x i ∈R n is the state of the i-th follower; is the local estimation error of agent i; x0∈R n It is the state of a leader. is the state estimate of the i-th follower; the controller parameter k i ∈R m×n is the feedback gain matrix, l i ∈R is the coupling gain; is the state error feedback matrix, P is a symmetric positive definite matrix that satisfies the following linear matrix inequality conditions: PA0+A0 T P-a Γ P-γφ2I<0 Where X = P -1 >0;α Γ is the attack attenuation rate corresponding to the attack model Γ; is a matrix The smallest characteristic root of is the system topology diagram under attack model Γ The communication link matrix; φ1>0 and φ2>0 are the designed event trigger parameters, γ>0 is the selected performance parameter; I is the unit matrix; A0 is the reference system matrix, b0 is the reference input matrix; Moreover, the interval between adjacent trigger events satisfies: in, are the kth and k+1th triggering moments of the i-th agent, is the local estimation error of the i-th agent exist The norm value of is the norm exist The upper bound of the inner is the trigger parameter.

2. The method according to claim 1, wherein In the heterogeneous uncertain unmanned cluster system, The system model of N followers is Among them, x i is the state of the i-th follower; represents the derivative of the i-th follower state; u i is the control input of the ith follower; y i is the output of the ith follower; A i represents the follower system matrix, B i represents the follower input matrix, C i represents the follower output matrix; The leader's system model is Among them, all eigenvalues ​​of the matrix A0 have non-positive real parts, x0∈R n is the state of the leader and the expected state that the follower needs to track. n represents the dimension of the leader state x0; represents the derivative of the leader state; y0∈R s is the output of the leader, s represents the dimension of the leader output y0; A0∈R n×n represents the leader system matrix with dimension n×n, C0∈R s×n represents the leader output matrix with dimension s×n; For the above heterogeneous unmanned cluster system, assume that there is a matrix k i ∈R m×n With scalar l i ∈R, so that the system matrix A i With the input matrix B i satisfy The reference matrix pair (A0, b0) is known, A0∈R n×n represents the reference system matrix with dimension n×n, b0∈R n×m represents the reference input matrix with dimension n×m; The follower topology is a directed graph in is the set of nodes consisting of followers, v i represents the i-th node, is the edge set between nodes; L is the follower topology graph The corresponding Laplace matrix represents the communication link between followers, satisfying L≠L T ; The system topology is a directed graph It consists of a leader and all followers, where 0 is the leader index; is a strongly connected graph, and H is the system topology graph The corresponding communication link matrix satisfies H≠H T .

3. The method according to claim 2, wherein The attack model is: Γ(t)={(i,j)∈ε|t∈D (i,j) (0,∞)} Where Γ(t) is the attack model corresponding to time t, D (i,j) (0,∞) is the set of time periods during which edge (i,j) suffers DoS attack within t∈(0,∞); Attack duration limit |D (i,j) (t0,t)|≤ζ ij +μ ij (t-t0) Among them D (i,j) (t0,t) is the set of time periods during which the edge (i,j) of the directed graph is attacked by DoS within t∈(t0,t), ζ ij >0 is a positive scalar, 0<μ ij <1 is the attack strength parameter; When Γ = ε, it is a full attack model.

4. The method according to claim 3, wherein The open-loop estimator based on the event-triggered mechanism is: in, is the state estimate of the i-th follower, is the kth triggering moment of the ith follower, is the triggering time sequence of the i-th follower; assuming that the followers in the system that have a communication link with the leader can continuously receive the information transmitted by the leader, that is, Define the state estimation error e of the i-th agent i ∈R n : in Represents the neighborhood of node i in the communication topology graph of the unmanned system, and the initial state estimation error e i (0)=0; Event trigger mechanism design Trigger parameters satisfy Where φ1>0 and φ2>0 are the designed event trigger parameters, and γ>0 is a sufficiently large performance parameter selected; follower topology diagram The left eigenvector of the Laplace matrix L about the eigenvalue 0 is ξ=[ξ1,ξ2,...,ξ N ] T , satisfying ξ T L=0,ξi>0 is the i-th element of the eigenvector ξ, min and ξ max are the minimum and maximum elements in the eigenvector ξ, respectively. is the system topology under attack model Γ Communication link matrix.

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