Heterogeneous unmanned cluster system security immunity control method under distributed denial of attack

Abstract

The invention discloses a security immunity control method for a heterogeneous unmanned cluster system under distributed denial of attack. According to the method, an event triggering mechanism is adopted, so that continuous information interaction between followers is avoided, discrete communication is realized, a sesame phenomenon is effectively eliminated, and the limitation of limited communication bandwidth under an actual condition is eliminated; in addition, the design requirement for a distributed observer in a traditional method is eliminated, and extra information transmission caused by state variables of the observer is avoided. A controller is designed based on a matching thought to get rid of a system model prior information constraint, and state tracking can be realized under the conditions that the system model is uncertain and different communication links suffer from independent attacks; meanwhile, the equivalent attenuation rate of the communication channel is introduced, the attenuation condition is analyzed under the condition that each communication link is subjected to independent attacks, and the uncertainty of a system model and the diversity of network attacks in the actual situation are effectively dealt 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] The unmanned swarm system is a large and complex system composed of multiple intelligent unmanned platforms such as drones, unmanned vehicles, and unmanned boats. Multiple platforms perform special tasks through collaborative cooperation, and can complete complex tasks that are difficult or even impossible for a single system to complete. It has the advantages of stronger adaptability, better fault tolerance, and better parallelism, and has broad application prospects in civil and military fields. Distributed collaboration between unmanned platforms reduces the computational complexity of complex problems and improves system performance, but at the same time, this collaborative control mechanism also puts higher requirements on network security, communication resources, and uncertainty response capabilities.

[0003] In an unmanned swarm system, unmanned platforms exchange information through network topology to collaboratively perform tasks. In an open environment, communication topology often faces many external threats, and network attacks are one of the main threats. Denial of Service (DoS) attack is one of the most common attacks. Attackers block communication channels to make some or all components of the control system inaccessible, thereby endangering the stability of the system. Most of the current research results on network security assume that all communication channels in the system have the same attack model. However, in actual situations, due to the complexity of the communication network and the diversity of attackers, this synchronous attack is less practical. Distributed attacks take into account the attacker's independent attacks on different communication links, that is, the attacker can attack any channel at different times. The establishment of this attack model can better simulate the complex situation in the actual environment and has stronger versatility.

[0004] Traditional cooperative controllers often work under ideal communication conditions, that is, assuming that continuous data transmission can be carried out between adjacent unmanned platforms with communication links in the system. At the same time, designing distributed observers is an effective method for state tracking control of heterogeneous multi-agent systems. Most of the existing research on cooperative control through output regulation theory uses distributed observers to estimate leader information. However, in actual situations, the resources of the system are limited, the transmission of auxiliary variable information observed in the system adds additional communication burden, and continuous communication is difficult to achieve under the limited communication bandwidth, which brings major challenges to the design of more cost-effective communication strategies. Event-triggered control strategy provides an effective method to solve this problem. By adopting an event-based data transmission scheme between adjacent unmanned platforms, that is, the system only updates or transmits data when the pre-designed trigger conditions are met, the discrete communication of the system is realized, which greatly reduces the communication burden of the system, effectively avoids continuous communication in unmanned cluster systems, and saves the communication resources of the system.

[0005] In addition, the existing design of cooperative control methods for multi-agent systems has a strong dependence on accurate system models. However, in practical applications, due to factors such as external disturbances, the model of unmanned swarm systems is difficult to obtain accurately and has high uncertainty, which poses a severe challenge to the implementation of cooperative control. The matching idea has opened up new ideas for dealing with the problem of uncertain systems, making the accurate dynamic model of the system no longer a necessary prerequisite for cooperative 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, and designs an event-triggered security controller under distributed attack based on the matching idea. It can perform collaborative control without the need for system model information, and get rid of the design requirements for 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 invention discloses a safe immune control method for heterogeneous unmanned cluster systems under distributed denial of attack. The heterogeneous uncertain unmanned cluster system is composed of N followers and 1 leader. The unmanned platforms communicate with each other through a directed topology graph. The heterogeneous unmanned cluster system adopts an event trigger 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 the non-trigger period.

[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, and 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; For the 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 ith agent, respectively. is the local estimation error of the ith 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 ith 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;

[0021] The leader's system model is

[0022]

[0023] Here, 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 with dimension s×n;

[0024] 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

[0025]

[0026] 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;

[0027] 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 ;

[0028] 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 .

[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 from DoS attack within t∈(0,∞);

[0032] Attack duration limit

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

[0034] Where D (i,j) (t0,t) is the set of time periods during which the edge (i,j) of the directed graph is subjected to DoS attack 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 ith follower, is the kth triggering moment of the ith follower, is the triggering time sequence of the ith 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 state estimation error e at the initial moment 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 with respect to the 0 eigenvalue 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 max are the smallest and largest 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 The 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 for 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, and 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 The figure is a 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 present invention provides a method for controlling the safety immunity of a heterogeneous unmanned cluster system under a distributed denial of attack, comprising the following steps:

[0050] Step 1: Establish a heterogeneous uncertain unmanned cluster system model. Assume that it consists of N followers and 1 leader. The unmanned platforms communicate through a topology graph, and the communication between any two unmanned platforms is directional.

[0051] Directed Graph is the follower topology graph, where 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 .

[0052] Directed Graph It is the system topology diagram, which consists of the leader and all followers, where 0 is the leader index. is a strongly connected graph. H is the system topology graph The corresponding communication link matrix satisfies H≠H T .

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

[0054]

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

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

[0057]

[0058] Here, 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] 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-by-m.

[0062] The heterogeneous uncertain unmanned cluster system model only requires the above model matching conditions to be met without knowing the exact 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 uncertain models and difficulty in explicit acquisition in actual complex environments.

[0063] Step 2: Due to the complexity of the communication network 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] Where D(i,j) (t0,t) is the set of time periods during which edge (i,j) is attacked by DoS within t∈(t0,t), ζ ij >0 is a positive scalar, 0<μ ij <1 is the attack strength parameter.

[0067] Attack model building

[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 ith 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 : The local estimation error in Represents the neighborhood of node i in the communication topology graph of the unmanned system, and the state estimation error e at the initial moment 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 with respect to the 0 eigenvalue 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 max are the smallest and largest 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 The communication link matrix.

[0080] Step 4: In the actual heterogeneous unmanned cluster system, there are external disturbances and other factors, which leads to the system model (i.e., the system matrix A i With the input matrix B i ) has large uncertainty and is difficult to obtain in advance. Therefore, in order to achieve the state tracking goal of heterogeneous uncertain unmanned cluster 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 ith follower; is the local estimation error of agent i. 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 and calculate the interval between adjacent trigger events to eliminate the Zeno phenomenon of the event trigger 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 must be 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 cluster system can achieve the tracking control target.

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

[0100]

[0101] in, is the kth triggering moment of the ith agent, is the k+1th triggering time of the ith 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 interval between adjacent trigger events is 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 protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for security immune control of heterogeneous unmanned cluster systems under distributed denial of attack, characterized in that: 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 adopts an event trigger 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 the non-trigger period. 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, and 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; For the 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 ith agent, respectively. is the local estimation error of the ith 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, characterized in that In the heterogeneous uncertain unmanned cluster system, The system model of N followers is Among them, x i is the state of the ith 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 Here, 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 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, H is the system topology graph The corresponding communication link matrix satisfies H≠H T .

3. The method according to claim 2, characterized in that 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) Where D (i,j) (t0,t) is the set of time periods during which the edge (i,j) of the directed graph is subjected to DoS attack 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, characterized in that The open-loop estimator based on the event-triggered mechanism is: in, is the state estimate of the ith follower, is the kth triggering moment of the ith follower, is the triggering time sequence of the ith 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 state estimation error e at the initial moment 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. Follower topology diagram The left eigenvector of the Laplace matrix L with respect to the 0 eigenvalue 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 max are the smallest and largest elements in the eigenvector ξ, respectively. is the system topology under the attack model Γ Communication link matrix.

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