An adaptive consensus control method for multi-spacecraft formation system based on dynamic event-triggering under DoS attack

Abstract

The application discloses a kind of under DoS attack based on dynamic event triggering's spacecraft formation system's self-adapting consistency control method.The method is first based on multi-agent consistency model theory, establishes the multi-agent system model of multi-agent spacecraft formation system, then consider based on time series DoS attack, by the frequency and duration of DoS attack are analyzed and researched, to solve the consistency problem of multi-agent spacecraft formation under DoS attack, then design a dynamic event triggering mechanism to reduce communication transmission frequency, and it is proved that there is no Zeno behavior existence, finally based on Lyapunov stability theory analysis, design a kind of event triggered distributed adaptive controller, solve the consistency problem of multi-spacecraft formation.The method is applied to multi-spacecraft formation system, guarantee the normal operation of system under DoS attack.

Description

TECHNICAL FIELD

[0001] The present application relates to a dynamic event-triggered adaptive control method, and particularly designs an adaptive control method for a multi-spacecraft formation system based on dynamic event triggering. BACKGROUND

[0002] Multi-spacecraft formation is a key challenge in space missions, requiring multiple spacecraft to work together to perform specific tasks. To improve the efficiency and robustness of the formation, researchers have adopted some advanced control strategies, among which dynamic event triggering and adaptive consensus control are two aspects of great concern.

[0003] Dynamic event triggering is a novel control strategy that dynamically triggers controller updates based on changes in system state, rather than traditional time-triggered. In multi-agent spacecraft formation, the application of this strategy helps to reduce communication frequency and improve system energy efficiency. The key to dynamic event triggering is to communicate and control operations only when the system state changes significantly. This can be achieved through monitoring and analyzing the system state, such as spacecraft position, velocity, attitude, etc. Once the system state changes beyond a predetermined threshold, the controller is triggered to update. This strategy effectively reduces communication resources, making the formation system more flexible and adaptable.

[0004] Adaptive consensus control is another control strategy with important applications in multi-agent formation. Its goal is to ensure that multiple agents maintain consistency while performing tasks, even in the face of dynamic uncertainty or external disturbances. In spacecraft formation, this is crucial for coordinating task execution, preventing collisions, and maintaining overall formation performance. The core idea of adaptive consensus control is to adjust the control strategy based on the dynamics of the system to maintain the consistency of the formation. This includes the relative position and velocity between agents, as well as possible angle or attitude adjustments. By adopting adaptive control algorithms, the system can better adapt to different environmental conditions, thereby improving the robustness and adaptability of the formation.

[0005] Combining dynamic event triggering and adaptive consensus control can further enhance the performance of multi-spacecraft formation. Dynamic event triggering ensures that the controller is updated when needed, while adaptive consensus control ensures that the formation maintains consistency in the face of changing system dynamics. This integration can be achieved through advanced control algorithms and communication protocols. The threshold for dynamic event triggering can be adjusted based on feedback from adaptive consensus control, thereby achieving optimal performance in different environments. Such integration improves the flexibility, robustness of the system, while reducing communication resources and computational burden. SUMMARY

[0006] The purpose of the present application is to propose a kind of multi-spacecraft formation system adaptive consensus control method based on dynamic event triggering under DoS attack, which can effectively reduce communication transmission frequency, improve the flexibility and robustness of system in different environments.

[0007] The specific technical solutions of the present application are as follows: a kind of multi-spacecraft formation system adaptive consensus control method based on dynamic event triggering under DoS attack, comprising the following steps:

[0008] Based on the consensus theory of multiple agents, for the spacecraft formation system in reference [1], the following dynamic model is established:

[0009]

[0010]

[0011]

[0012] In the formula, is the system state, wherein is the expected deviation distance in X, Y and Z axes, is the velocity in three directions, and ω0 is the angular velocity of the aircraft.

[0013] Further consider the DoS attack based on time series, by analyzing and researching the frequency and duration of DoS attack, to solve the consensus problem of multi-spacecraft formation under DoS attack, the specific steps are as follows:

[0014] When DoS attack occurs, although the communication ability between agents is still maintained, the data availability is affected. In order to understand more comprehensively, it is assumed that the attacker can attack the communication network in different active periods, after the attacker attacks for a period of time, the attacker must stop the attack, store energy and prepare for the next attack. It is assumed that represents the attack sequence launched at time during DoS attack. Consider a time interval represents the length of the mth attack. Then on [τ, t], the total DoS attack time length is

[0015] That means the length of time allowed for communication is For the attack frequency of DoS Where N a (T1, T2) represents the number of attacks in the time region [T1, T2), and the attack duration satisfies

[0016] Then, a dynamic event-triggered mechanism is designed to reduce the communication frequency, and it is proved that there is no Zeno behavior, which is shown as follows:

[0017] A dynamic event-triggered mechanism is designed as follows:

[0018]

[0019] where, denotes the next triggering time of the ith agent; denotes the last triggering time of the ith agent; γ = 1 or γ = 0; α i is the adaptive variable to be designed; F is the feedback gain matrix; denotes the triggering error; denotes the consensus error; π i , β i is the constant to be designed; η i (t) denotes the internal dynamic variable; θ i ≥||F||; δ i = (ξ i σ i / θ i ) and 0 < σ i < 1.

[0020] Then, it is proved that there is no Zeno phenomenon:

[0021]

[0022] where,

[0023]

[0024] Since and α i , i = 1, …, n are bounded. That is, and are bounded and Z i exists.

[0025] Therefore:

[0026] Since:

[0027]

[0028] By solving the inequality, it can be obtained that:

[0029]

[0030] According to the analysis, By the triggering mechanism, it can be obtained that:

[0031]

[0032] Further:

[0033]

[0034] Therefore, when is true, it means that the designed dynamic event-triggered mechanism does not have Zeno behavior.

[0035] Then, based on Lyapunov stability theory analysis, a kind of event-triggered distributed adaptive controller is designed to solve the problem of multi-spacecraft formation consensus, the specific steps are as follows:

[0036] Consider the following adaptive event-triggered controller:

[0037]

[0038] In the formula, K and F are feedback gain matrix, and α1>0 represents the decay rate.

[0039] C001: First, consider the time region Select the following form of Lyapunov function:

[0040] V(t) = V1(t) + V2(t) + V3(t),

[0041] In the formula,

[0042] C002: Calculate the derivative of V1(t):

[0043]

[0044] C003: Further:

[0045]

[0046] C004: Finally:

[0047]

[0048] C005: Then consider the time region Select the similar Lyapunov function:

[0049]

[0050] C006: Derivation of V(t) is:

[0051]

[0052] C007: Let σ(t) ∈ {a, b} be a piecewise function, thus V(t) = V σ(t) (t), where V (t) when σ(t) = a a (t), and V (t) when σ(t) = b b (t).

[0053] B008: Thus:

[0054]

[0055] C009: Case 1, when σ(t) = a

[0056]

[0057] C0010: Case 2, when σ(t) = b

[0058]

[0059] C0011: According to N a (t0, t) = m when σ(t) = a Thus, for all t ≥ t0, there is

[0060]

[0061] C0012: Since

[0062] Therefore, there is

[0063]

[0064] C0013: Further:

[0065]

[0066] C0014: Let Finally, there is

[0067]

[0068] C0015: Therefore, the multi-agent spacecraft formation system is asymptotically stable under the adaptive event-triggered controller designed in the present application. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 is a flow chart of the method of the embodiments of the present application; ​​​​​

[0070] Figure 2 for DoS attack model;

[0071] Figure 3 for network communication topology of spacecrafts;

[0072] Figure 4 for velocity convergence of spacecrafts in x direction;

[0073] Figure 5 for position error e convergence of spacecrafts in x direction;

[0074] Figure 6 for event trigger graph under the method of the embodiment of the present application; DETAILED DESCRIPTION

[0075] The present application will be further illustrated below in conjunction with specific embodiments, which are only used to illustrate the present application and not used to limit the scope of the present application, and after reading the present application, various equivalent modifications of the present application by those skilled in the art all fall within the scope defined by the claims of the present application.

[0076] As shown in Figure 1 a kind of adaptive consensus control method of multi-spacecraft formation system based on dynamic event trigger under DoS attack,

[0077] comprising the following steps:

[0078] Step one, set the initial value of each parameter;

[0079] Step two, update internal dynamic variable η i (t);

[0080] Step three, using internal dynamic variable η i (t), adaptive parameter α i , trigger error e i (t), consensus error term q i (t) and some known parameters verify event trigger condition, update trigger state

[0081] Step four, use trigger output to update controller input

[0082] Step five, repeat step four until the end of running time.

[0083] An embodiment of the present application will be introduced below;

[0084] Consider a multi-spacecraft formation system in a reference [1], with corresponding dynamics model as:

[0085]

[0086]

[0087]

[0088] ω0= 0.001 is the angular velocity of the spacecraft.

[0089] Figure 1 is the flow chart of the method of the embodiment of the application; Figure 2 is the DoS attack model; Figure 3 is the network communication topology of the spacecraft; the speed of the multi-spacecraft system under the state feedback control condition using the proposed method is as shown in Figure 4 is the position error of the spacecraft in the x direction, and Figure 5 is the event-triggered graph. As can be seen from it, the proposed event-triggered mechanism effectively reduces the communication transmission. Figure 6

[0090] References

[0091] [1] Hu W, Yang C, Huang T, et al. A distributed dynamic event-triggered control approach to consensus of linear multiagent systems with directed networks [J]. IEEE Transactions on Cybernetics, 2018, 50(2): 869-874.

[0092] [2] Zhao G, Wei H, Fu X. Distributed dynamic event-triggered control approach to multi-agent systems via adaptive consensus protocols [J]. Asian Journal of Control, 2022, 24(3): 1486-1496.​

Claims

1. An adaptive consistency control method for a multi-spacecraft formation system based on dynamic event triggering under DoS attacks, characterized in that, Includes the following steps: Based on the theory of multi-agent consensus model, a multi-agent system model of multi-spacecraft formation system is established. Considering time-series-based DoS attacks, this paper analyzes and studies the frequency and duration of DoS attacks to address the consistency problem of multi-spacecraft formations under DoS attacks. A dynamic event triggering mechanism was designed to reduce the communication transmission frequency, and it was proven that no Zeno behavior exists. Based on Lyapunov stability theory analysis, an event-triggered distributed adaptive controller is designed to solve the consistency problem of multi-spacecraft formation; The multi-agent system model for a multi-spacecraft formation system, based on the multi-agent consensus model theory, is established through the following specific steps: Based on the multi-agent consensus theory, the following dynamic model is established for spacecraft formation systems: In the formula, It is the system state, where It is the expected deviation distance on the X, Y, and Z axes; It refers to the velocity in three directions, and w0 = 0.001 is the angular velocity of the aircraft; Design the following dynamic event triggering mechanism: In the formula, Indicates the next trigger time for the i-th agent; Indicates the previous triggering time of the i-th agent; γ = 1 or γ = 0; α i Here are the adaptive variables to be designed; F is the feedback gain matrix. Indicates triggering error; Indicates consistency error; π i ,β i η is a constant to be designed. i (t) represents the internal dynamic variable; θ i ≥||F||;δ i =(ξ i σ i / θ i ) and 0 < σ i <1; Consider the following adaptive event-triggered controller: In the formula, K and F are the feedback gain matrices, and α1 > 0 represents the decay rate.

2. Based on the adaptive consistency control method for a multi-spacecraft formation system triggered by dynamic events under a DoS attack as described in claim 1, this method considers time-series-based DoS attacks and analyzes and studies the frequency and duration of DoS attacks to solve the consistency problem of multi-spacecraft formations under DoS attacks. The specific steps are as follows: During a DoS attack, although the agents still maintain communication capabilities, data availability is affected. For a more comprehensive understanding, assume that the attacker can launch attacks on the communication network at different active periods. After attacking for a period of time, the attacker must stop attacking, conserve energy, and prepare for the next attack. Indicates during a DoS attack An attack sequence initiated at any given time, considering a time interval. Let represent the duration of the nth attack. Then, over the interval [τ, t], the total DoS attack duration is: This means that the allowed communication time is Regarding the frequency of DoS attacks Where N a (T1, T2) represents the number of attacks within the time range [T1, T2), followed by the attack duration satisfying the condition.

3. Based on the adaptive consistency control method for a multi-spacecraft formation system under DoS attack based on dynamic event triggering as described in claim 1, a dynamic event triggering mechanism is designed to reduce the communication transmission frequency, and it is proven that no Zeno behavior exists. The specific steps are as follows: Proof that there is no Zeno phenomenon: In the formula, And because and α i The numbers i = 1, ..., n are all bounded, meaning that... and Both are bounded and Z i It exists; therefore: And because: By solving the inequalities, we can conclude that: According to the analysis, Based on the triggering mechanism, we can conclude that: further: Therefore, as k→∞, This is true, meaning that the designed dynamic event triggering mechanism does not contain Zeno behavior.

4. Based on the adaptive consistency control method for a multi-spacecraft formation system triggered by dynamic events under DoS attacks as described in claim 1, and based on Lyapunov stability theory analysis, an event-triggered distributed adaptive controller is designed to solve the consistency problem of multi-spacecraft formations. The specific steps are as follows: B001: First, consider Choose a Lyapunov function of the following form: V(t) = V1(t) + V2(t) + V3(t), In the formula, B002: Calculate the derivative of V1(t): B003: Further: B004: Finally: B005: Next, consider the time zone. Choose similar Lyapunov functions: B006: Differentiating V(t) yields: B007: Let σ(t)∈{a, b} be a piecewise function, therefore V(t)=V σ(t) (t), hit the mark At that time, V(t) = V a (t), when At that time, V(t) = V b (t); B008: Therefore: B009: Case 1, when hour B0010: Case 2, when At the same time, there are B0011: According to N a (t0, t) = m, And when hour, Therefore, for all t ≥ t0, we have B0012: And because as well as have B0013: Going a step further: B0014: Order Ultimately there are B0015: Therefore, the multi-agent spacecraft formation system is asymptotically stable under an adaptive event-triggered controller.

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