Adaptive event-triggered cooperative control method for unmanned system under denial-of-service attack

Abstract

The application discloses a self-adaptive event-triggered cooperative control method of an unmanned system under a denial-of-service attack, relates to the technical field of unmanned cluster systems, and comprises the following steps: firstly, an unmanned cluster system model is established; the unmanned cluster system is composed of one leader and N followers; it is assumed that they communicate through a directed spanning tree graph; the leader serves as a root node; starting from the root node, any node in the graph can be reached, that is, each follower can directly or indirectly receive information of the leader; then, based on an existing edge denial-of-service attack model, an event-triggered mechanism is designed, and a local event-triggered leader observer is constructed; then, based on the leader observer, a fault-tolerant controller is designed; finally, based on existing Lyapunov stability theory, a sufficient condition for stability is obtained. The controller design method provided by the application guarantees that the unmanned cluster system can achieve safety and stability in a communication network with limited resources and denial-of-service attacks.

Description

Technical Field

[0001] This invention relates to the field of unmanned cluster system technology, specifically to an adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks. More specifically, it proposes a design method for an adaptive event-triggered cooperative secure elastic controller when the communication edge between unmanned systems is subjected to a denial-of-service attack under limited communication resources. Background Technology

[0002] Unmanned swarm systems are an emerging type of multi-agent system, comprising multiple cooperating drones, vehicles, or underwater robots. With the continuous development of unmanned technology, unmanned swarm systems have been widely applied in many fields, such as exploration, monitoring, and search and rescue. Due to their advantages such as reconfigurability, robustness, and adaptability, unmanned swarm systems have attracted increasing attention and research in practical applications.

[0003] From a practical application perspective, it is essential to ensure the system possesses strong reliability and robustness. In reality, low measurement accuracy and a lack of understanding of the external environment make it difficult to obtain precise mathematical models. Furthermore, the modeling process is susceptible to various factors such as strong nonlinearity, uncertainty, and interference. Therefore, the dynamics model of unmanned swarm individuals needs to consider these factors to better approximate the real system.

[0004] On the other hand, it is essential to ensure the system's communication capabilities. With the ever-increasing volume of data in the network, redundant data consumes a growing amount of network resources. Therefore, reducing the waste of communication and computing resources and extending the lifespan of network hardware is a critical issue. Another key issue is that in insecure networks, denial-of-service attacks can cause network congestion, interrupting information transmission and leading to the failure of unmanned cluster collaboration.

[0005] How to implement adaptive and collaborative security control for unmanned cluster systems under denial-of-service attacks to avoid information transmission interruptions caused by network congestion is a problem that existing technical solutions have not yet solved. Summary of the Invention

[0006] In view of this, the present invention provides an adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks. It can take into account the situation where the communication links between agents are subjected to denial-of-service attacks, and designs a local distributed event-triggered leader observer to effectively reduce the communication load, thereby avoiding network congestion caused by denial-of-service attack network threats.

[0007] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0008] Step 1: Establish an unmanned swarm system model. The unmanned swarm system consists of 1 navigator and N followers. It is assumed that they communicate with each other through a directed spanning tree graph. The navigator is the root node. Starting from the root node, any node in the graph can be reached. That is, each follower can receive information from the navigator directly or indirectly.

[0009] Step 2: Based on the existing edge denial-of-service attack model, design an event triggering mechanism and construct a local event-triggered leader observer.

[0010] Step 3: Based on the leader observer obtained in Step 2, design a fault-tolerant controller.

[0011] Step 4: Based on the existing Lyapunov stability theory, the sufficient condition for stability is:

[0012] Except for the design parameters related to the controller's control input, all other design parameters related to the controller are greater than 3, the design parameters related to the controller's control input are greater than 0, and the design parameters related to the update rate are greater than 0.

[0013] Furthermore, in step one, the unmanned swarm system model is established, wherein each unmanned system is modeled as follows:

[0014]

[0015] Where, x i,m and x i,n Let p be the m-th and n-th states of the i-th unmanned system, respectively, and let p be the state exponent. im and p in All are positive odd integers, and the maximum exponent is p. i =max{p i1 ,…,p in}, where i = 1, ..., N is the number of unmanned systems, m = 1, ..., n-1, and m and n are the system orders. Let i be the state of the i-th unmanned system. Let x be the m-th state of the i-th unmanned system. i,m The first derivative, Let be an unknown nonlinear function of order m for the i-th unmanned system. Let u be an unknown nonlinear function of order n for the i-th unmanned system. iF =b i u i +u i,f For the controller input of the i-th unmanned system that is faulted, u i For actuator input, b i ∈(0,1] represents the multiplicative actuator fault of the i-th unmanned system, u i,fThe ith unmanned system's adder actuator is faulty; y i This is the output of the i-th unmanned system.

[0016] The navigator's output is y0, and the upper bound of its derivative is y0. 0,max .

[0017] Furthermore, in step two, based on the existing edge denial-of-service attack model, an event triggering mechanism is designed, and a local event-triggered leader observer is constructed, specifically including the following steps:

[0018] The existing edge denial-of-service attack model satisfies the attack frequency and attack duration, and also satisfies:

[0019]

[0020] Among them, Ξ A (t p ,t q ) represents the time interval (t) p ,t q The duration of the attack on t p t is the lower bound of the time interval. q a is the upper limit of the time interval. * ∈(0,a max ), a max =max{a1,a2}, parameter parameter P v In (N), the superscript v represents a parameter that is greater than 0 and less than 1; N is the number of followers, k is a preset parameter, 0 <k<1,ρ i,1 ,ρ i,2 ,ρ i,3 These are positive design parameters related to the event triggering conditions.

[0021] Construct the following trigger function φ i :

[0022]

[0023]

[0024] Where e i The measurement error is represented by t, which is time, and σ represents the topology switch caused by a denial-of-service attack. Let a be the communication weight between unmanned systems i and j under the σ topology. When unmanned system i cannot directly receive information from j, a i,j It is 0 if it is not 0 otherwise; similarly, Let be the communication weight between unmanned system i and the navigator in the σ-topology. When unmanned system i cannot directly receive information from the navigator... It is 0 if it is not 0 otherwise; θ i (t) represents the observer state of the unmanned system i at time t, θ j θ(t) represents the observer state of the unmanned system j at time t, and θ0(t) represents the output of the navigator at time t.

[0025] If φ is satisfied i If the value is greater than or equal to 0, update the data; otherwise, keep the original data.

[0026] Design the following local event-triggered leader observer.

[0027]

[0028] in, For state θ i The first derivative, t k To meet the data update timing that triggers the conditions, For unmanned systems i in The observer state at time t. For unmanned systems j in The observer state at time t. For the navigator Output at any moment Let θ be the state of unmanned system i. i The sequence of events in time, The observer state θ of unmanned system j j The last time this happened, Let θ be the observer state of unmanned system j. j At the last event moment, N + Γ is a positive natural number, and s is a positive natural number; when the connectivity of the unmanned swarm network is disrupted, the parameter Γ... i (t) = 0, otherwise Γ i (t) = 1, v is a parameter greater than 0 and less than 1; sat(*) is a saturation function.

[0029] Furthermore, in step three, the design of the fault-tolerant controller specifically involves:

[0030] Design the control input u of the unmanned system i i for:

[0031]

[0032] Among them, intermediate variables k i,n and For design parameters greater than 0, Let n be the adaptive update rate of the unmanned system i at order n, obtained through the differential function. get, Let c be a known Gaussian function vector of order n for unmanned system i. i,n , β i,n and All are positive design parameters, z i,n =x i,n -α i,n-1 Let x be the nth state of the unmanned system i. i,n With intermediate variable α i,n-1 Error, intermediate variables k i,n-1 and For design parameters greater than 0, Let be the adaptive update rate of the (n-1)th order of the unmanned system i, obtained through the differential function. get, Let c be a known Gaussian function vector of order n-1 for unmanned system i. i,n-1 and β i,n-1 All are positive design parameters, ..., and so on, with intermediate variables. k i,1 , and For design parameters greater than 0, Let be the first-order adaptive update rate of unmanned system i, obtained through the differential function. get, Let c be a known first-order Gaussian function vector of unmanned system i. i,1 and β i,1 All are positive design parameters. Let the first-order compensation update rate of unmanned system i be obtained through the differential function. get, and All are positive design parameters, z i,1 =x i,1 -θ i,1 Let be the error between the first-order state of unmanned system i and the leader observer.

[0033] Furthermore, in step four, based on the existing Lyapunov stability theory, a sufficient condition for stability is obtained, which specifically includes:

[0034]

[0035] Where k i,1 ,…,k i,n-1 ,k i,n They are respectively related to controller α i,1 ,…,α i,n-1 ,u i Relevant design parameters; β i,1,…,β i,n Respectively with update rate Relevant design parameters, To match the update rate The relevant design parameters, that is, as long as each parameter meets the above-mentioned sufficient conditions for stability, the designed controller can guarantee the stability of the system, and the output of the follower will track the output of the leader.

[0036] Beneficial effects:

[0037] This invention offers the following advantages: The controller design method provided by this invention first considers the scenario where the communication links between agents are subjected to denial-of-service attacks. A locally distributed event-triggered leader observer is designed to effectively reduce communication load, thereby avoiding network congestion caused by denial-of-service attack threats. Then, using the backstepping method, exponential integration technique, and Lyapunov stability theory, a distributed fault-tolerant controller is designed, and the stability of the unmanned swarm system is proven. The controller design method provided by this invention guarantees that the unmanned swarm system can achieve security and stability in communication networks with limited resources and denial-of-service attacks, and the output of the followers can track the output of the leader. Detailed Implementation

[0038] The present invention will now be described in detail with reference to the embodiments.

[0039] This invention provides an adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks, comprising the following steps:

[0040] Step 1: Establish an unmanned swarm system model. The unmanned swarm system consists of 1 leader and N followers. It is assumed that they communicate through a directed spanning tree graph. The leader is the root node, and any node in the graph can be reached from the root node. That is, each follower can receive information from the leader directly or indirectly.

[0041] Each unmanned system is modeled as follows:

[0042]

[0043] Where, x i,m and x i,n Let p be the m-th and n-th states of the i-th unmanned system, respectively, and let p be the state exponent. im and p in All are positive odd integers, and the maximum exponent is p. i =max{p i1 ,…,p in}, where i = 1, ..., N is the number of unmanned systems, m = 1, ..., n-1, and m and n are the system orders. Let i be the state of the i-th unmanned system. is the m-th order state x of the i-th unmanned system i,m first-order derivative of, is an unknown nonlinear function of the m-th order of the i-th unmanned system, is an unknown nonlinear function of the n-th order of the i-th unmanned system, u iF =b i u i +u i,f is the controller input subjected to a fault of the i-th unmanned system, u i is the actuator input, b i ∈(0,1] is a multiplicative actuator fault of the i-th unmanned system, u i,f is an additive actuator fault of the i-th unmanned system; y i is the output of the i-th unmanned system;

[0044] the output of the leader is y0, and the upper bound of its derivative is assumed to be y 0,max .

[0045] Step 2: Based on the existing edge denial-of-service attack model, design an event-triggered mechanism and construct a local event-triggered leader observer. Specifically, it includes:

[0046] it is assumed that the denial-of-service attack satisfies requirements on attack frequency and attack duration, and satisfies

[0047]

[0048] wherein, Ξ A (t p , t q ) is the attack duration on the time interval (t p , t q ), which can generally be set as t p =0, t q =∞, a * ∈(0, a max ), a max =max{a1,a2}, parameter parameter P v the superscript v in (N) is a parameter greater than 0 and less than 1; N is the number of followers, k is a preset parameter satisfying 0<k<1, ρ i,1 , ρ i,2 , ρ i,3 are positive design parameters related to the event triggering condition, their values need to be adjusted according to the specific system model, as long as the conditions are satisfied, for example, they can be 3, 2, 1.

[0049] construct the triggering function as follows: if φ is satisfiedi If the value is ≥0, update the data; otherwise, keep the original data.

[0050]

[0051] Where e i The measurement error is represented by t, where t is time. k To meet the data update timing that triggers the conditions, in, For unmanned systems i in The observer state at time t. For unmanned systems j in The observer state at time t. For the navigator Output at any moment Let θ be the state of unmanned system i. i The sequence of events in time, The observer state θ of unmanned system j j The last time this happened, Let θ be the observer state of unmanned system j. j At the last event moment, N + Let be a positive natural number, s be a positive natural number, and σ represent the topology switch caused by a denial-of-service attack. Let a be the communication weight between unmanned systems i and j under the σ topology. When unmanned system i cannot directly receive information from j, a i,j It is 0 if it is not 0 otherwise. Similarly, Let be the communication weight between unmanned system i and the navigator in the σ-topology. When unmanned system i cannot directly receive information from the navigator... It is 0 if it is not 0 otherwise.

[0052] Design the following local event-triggered leader observer.

[0053]

[0054] in, For state θ i The first derivative of Γ, when the connectivity of the unmanned swarm network is disrupted. i (t) = 0, otherwise Γ i (t) = 1, where v is a parameter greater than 0 and less than 1, such as 0.5, 0.3, etc. The saturation function sat(x) has the following form:

[0055]

[0056] Where δ is a small non-negative constant.

[0057] Step 3: Based on the leader observer obtained in Step 2, design a fault-tolerant controller. This specifically includes:

[0058] Design the control input for the unmanned system.

[0059]

[0060] Among them, intermediate variables k i,n and For design parameters greater than 0, where k i,n A larger value results in better control, but also requires more controller energy. Variable values ​​such as 20 or 200 can be designed. It can be designed to be slightly smaller, such as 2; Let the nth-order update rate of unmanned system i be obtained through the differential function. get, Let c be a known Gaussian function vector of order n for unmanned system i. i,n , β i,n and All are positive design parameters, such as 0.5, 2, 2, 3, etc.; z i,n =x i,n -α i,n-1 Let i be the nth-order state of the unmanned system and the intermediate variable α. i,n-1 Error, intermediate variables k i,n-1 and For design parameters greater than 0, Let be the adaptive update rate of the (n-1)th order of the unmanned system i, obtained through the differential function. get, Let c be a known Gaussian function vector of order n-1 for unmanned system i. i,n-1 and β i,n-1 All are positive design parameters, ..., and so on, with intermediate variables. k i,1 , and For design parameters greater than 0, Let be the first-order adaptive update rate of unmanned system i, obtained through the differential function. get, Let c be a known first-order Gaussian function vector of unmanned system i. i,1 and β i,1 All are positive design parameters. Let the first-order compensation update rate of unmanned system i be obtained through the differential function. get, and All are positive design parameters, zi,1 =x i,1 -θ i,1 Let be the error between the first-order state of unmanned system i and the leader observer.

[0061] Step 4: Based on the existing Lyapunov stability theory, the sufficient condition for stability is as follows:

[0062]

[0063] Where k i,1 ,...,k i,n-1 ,k i,n They are respectively related to controller α i,1 ,…,α i,n-1 ,u i Relevant design parameters; β i,1 ,...,β i,n Respectively with update rate Relevant design parameters, To match the update rate The relevant design parameters, that is, as long as each parameter meets the above conditions, the designed controller can guarantee the stability of the system, and the output of the follower can track the output of the leader.

[0064] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks, characterized in that, Includes the following steps: Step 1: Establish an unmanned swarm system model, which consists of one navigator and... The system consists of several followers, and they communicate with each other through a directed spanning tree graph. The leader is the root node, and any node in the graph can be reached from the root node. That is, each follower can receive information from the leader directly or indirectly. Step 2: Based on the existing edge denial-of-service attack model, design an event triggering mechanism and construct a local event-triggered leader observer; Step 3: Based on the leader observer obtained in Step 2, design a fault-tolerant controller; Step 4: Based on the existing Lyapunov stability theory, the sufficient condition for stability is: Except for the design parameters related to the controller's control input, all other design parameters related to the controller are greater than 3, the design parameters related to the controller's control input are greater than 0, and the design parameters related to the update rate are greater than 0.

2. The adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks as described in claim 1, characterized in that, In step one, the unmanned cluster system model is established, wherein each unmanned system is modeled as follows: in, and The first The first unmanned system Rank, number Order state, state exponent and All are positive odd integers, and the maximum exponent is , The number of unmanned systems. , m and Let be the system order. For the first The nth order state of an unmanned system For the first The m-th order state of an unmanned system. For the first The first unmanned system first state The first derivative, For the first The first unmanned system first state The first derivative, For the first The first unmanned system An unknown nonlinear function of order 1 For the first The first unmanned system An unknown nonlinear function of order 1 For the first An unmanned system receives a faulty controller input. For actuator input, For the first A multiplicative actuator failure in an unmanned system For the first A fault occurred in the adder actuator of an unmanned system. For the first The output of an unmanned system; The Navigator's output is Its derivative has an upper bound of . .

3. The adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks as described in claim 1 or 2, characterized in that, In step two, based on the existing edge denial-of-service attack model, an event triggering mechanism is designed, and a local event-triggered leader observer is constructed, specifically including the following steps: The existing edge denial-of-service attack model satisfies the attack frequency and attack duration, and also satisfies: in, Time interval The duration of the attack on the surface, This is the lower limit of the time interval. The upper limit of the time interval, , ,parameter ,parameter , The superscript v in the text represents a parameter that is greater than 0 and less than 1; , The number of followers These are preset parameters. , These are positive design parameters related to event triggering conditions; Construct the following trigger function : in To account for measurement error, For time, This indicates a topology switch caused by a denial-of-service attack. for Unmanned systems under topology and The communication weight between them, when unmanned systems Cannot receive directly When receiving information, It is 0 if it is not 0 otherwise; similarly, for Unmanned systems under topology The communication weight between the navigator and the unmanned system When you cannot receive information directly from the navigator, It is 0 if it is not 0 otherwise; For unmanned systems exist t The observer state at time t. For unmanned systems exist t The observer state at time t. For the navigator t Output at any moment; If satisfied If the condition is met, update the data; otherwise, keep the original data. Design the following local event-triggered leader observer. in, For state The first derivative, To meet the data update timing that triggers the conditions, For unmanned systems exist The observer state at time t. For unmanned systems exist The observer state at time t. For the navigator Output at any moment For unmanned systems status The sequence of events in time, It is an unmanned system Observer state The last event time, subscript , For unmanned systems Observer state The last time this happened, It is a positive natural number. It is a positive natural number; when the connectivity of the unmanned swarm network is disrupted, the parameter... ,otherwise , Parameters that are greater than 0 and less than 1; It is a saturation function.

4. The adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks as described in claim 3, characterized in that, In step three, the design of the fault-tolerant controller specifically involves: Design unmanned systems control input for: Among them, intermediate variables , and For design parameters greater than 0, For unmanned systems No. The adaptive update rate of order is obtained through the differential function. get, For unmanned systems No. A known Gaussian function vector of order, , , and All are positive design parameters. For unmanned systems No. first state With intermediate variables Error, intermediate variables , and For design parameters greater than 0, For unmanned systems No. The adaptive update rate of order is obtained through the differential function. get, For unmanned systems No. A known Gaussian function vector of order, and All are positive design parameters, and the process is repeated sequentially, with intermediate variables included. , , and For design parameters greater than 0, For unmanned systems No. The adaptive update rate of order is obtained through the differential function. get, For unmanned systems No. A known Gaussian function vector of order, and All are positive design parameters. For unmanned systems No. The compensation update rate of the order is obtained through the differential function. get, and All are positive design parameters. For unmanned systems No. Error between the first-order state and the leader observer.

5. The adaptive event-triggered cooperative control method for unmanned systems under denial-of-service attacks as described in claim 4, characterized in that, In step four, based on the existing Lyapunov stability theory, a sufficient condition for stability is obtained. Specifically, the sufficient condition for stability is: in respectively with the controller Relevant design parameters; Respectively with update rate Relevant design parameters, To match the update rate The relevant design parameters, that is, as long as each parameter meets the above-mentioned sufficient conditions for stability, the designed controller can guarantee the stability of the system, and the output of the follower will track the output of the leader.

Images