Nonlinear multi-agent system safety generalized control method under DoS attack
By constructing a nonlinear multi-agent system and designing a control protocol and error compensation function, the stability and lag synchronization problems of the system under DoS attacks were solved, and stability and formation maintenance were achieved in the attack environment.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-08
- Publication Date
- 2026-04-03
AI Technical Summary
Existing technologies struggle to maintain the stability of nonlinear multi-agent systems and achieve more generalized lag synchronization under DoS attacks, especially in maintaining formation relationships in drone swarms.
By constructing a nonlinear multi-agent system that includes leaders and followers, designing control protocols and error compensation functions, defining the frequency and duration of DoS attacks, and satisfying specific stability conditions to achieve delayed synchronization.
Under DoS attacks, the system can remain stable and achieve delayed synchronization, demonstrating high security and robustness, and is suitable for a wider range of collaborative control problems.
Smart Images
Figure CN121792124A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of intelligent agent control technology, specifically relating to a secure generalized control method for nonlinear multi-agent systems under DoS attacks. Background Technology
[0002] Multi-agent systems (MAS) can accomplish complex tasks through the collaborative cooperation of multiple agents and are widely used in fields such as drone swarms, smart grids, and robot collaboration. Consistency control is the foundation of MAS collaboration, and its goal is to make the states or outputs of all agents tend to be consistent.
[0003] In practical applications, MAS typically interacts with other agents via wireless communication networks, making it vulnerable to network attacks. Denial-of-service attacks are a common and highly destructive type of attack. By blocking communication channels, they prevent agents from exchanging state information normally, leading to system performance degradation or even instability.
[0004] Existing research on MAS consensus control is mostly based on ideal communication environments or considers only simple linear system models. However, the dynamics of agents in real-world systems are often nonlinear, and DoS attacks can cause complex characteristics such as intermittent interruptions in system communication. Furthermore, traditional consensus control typically requires all agents to eventually reach the same state, which may be too stringent in practical applications. For example, in a drone swarm, we might want wingmen and the lead drone to maintain a fixed formation (i.e., a state transition relationship), rather than simply being in the same position.
[0005] Therefore, how to ensure that nonlinear multi-agent systems can not only remain stable under DoS attacks, but also achieve this more generalized consistency with specific mapping relationships (i.e., delayed synchronization) has become an urgent technical challenge. Summary of the Invention
[0006] The purpose of this invention is to provide a secure generalized control method for nonlinear multi-agent systems under DoS attacks, in order to solve the problems existing in the background technology.
[0007] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows: A method for secure generalized control of a nonlinear multi-agent system under DoS attack includes the following steps: Step S100: Construct a nonlinear multi-agent system containing one leader and N followers, and define a lag synchronization with the transformation matrix H as the core; The dynamic equation of the leader is expressed as: ; The dynamic equation of the i-th follower is expressed as: ; in For control protocols; Step S200: Design the control protocol for the nonlinear multi-agent system. The control protocol Includes control gain and error compensation function Define the DoS attack frequency and DoS attack duration; Step S300: Analyze the stability of the nonlinear multi-agent system under a DoS attack to obtain sufficient conditions to ensure the system achieves secure delayed synchronization, specifically including: ①Based on control protocol The gain matrix is obtained. The conditions that must be met; ②Based on the frequency of DoS attacks, the upper bound condition for the frequency of DoS attacks is obtained; ③ Based on the duration of the DoS attack, the upper bound condition for the duration of the DoS attack; Step S400: Apply the control protocol that satisfies the sufficient conditions to the multi-agent system, so that under a DoS attack that satisfies the upper bound condition, all followers can achieve delayed synchronization with the leader through the transformation matrix H.
[0008] As a further limitation of the technical solution of the present invention, in step S100, the nonlinear multi-agent system The following Lipschitz conditions must be met: ,in Preset positive numbers; Furthermore, in the aforementioned nonlinear multi-agent system, there is no communication channel for followers to transmit information to the leader.
[0009] As a further limitation of the technical solution of the present invention, in step S100, for any follower, the nonlinear multi-agent system achieves delayed synchronization when the transformation matrix H satisfies the following condition: .
[0010] As a further limitation of the technical solution of the present invention, in step S200, the control protocol Represented as: ; in, The error compensation function is expressed as: ; Indicates control gain; , indicating synchronization error; This indicates whether there is information exchange between the leader and the followers; if so, then... ,otherwise ; It is a diagonal matrix; This is a preset constant.
[0011] As a further limitation of the technical solution of the present invention, the definition of the DoS attack frequency in step S200 is specifically as follows: For any In the time period The total number of DoS attacks that occurred on the platform is expressed as follows: Then in the time period The frequency of DoS attacks is defined as follows: .
[0012] As a further limitation of the technical solution of the present invention, the duration of the DoS attack defined in step S200 is specifically as follows: For any In the time period The total duration of the DoS attack that occurred on the above is expressed as Then in the time period The duration of a DoS attack is defined as follows: ; in, , .
[0013] As a further limitation of the technical solution of the present invention, the gain matrix in step S300 The conditions to be met are: ; The upper bound condition for the frequency of DoS attacks is: ; in, is a constant and ; ; and ; The upper bound condition for the duration of a DoS attack is: .
[0014] Compared with the prior art, the present invention has the following advantages: Strong robustness: This invention explicitly considers the real-world network threat of DoS attacks and provides an upper limit on the attack strength that the system can maintain stability through theoretical analysis, making the control system highly secure and robust when facing bounded DoS attacks. High universality: By introducing a transformation matrix, this invention achieves a more generalized consistency of "lagging synchronization", breaking through the limitation that the state must be completely consistent in traditional control, and can describe and solve a wider range of cooperative control problems (such as formation maintenance). Handling nonlinearity: This invention is designed directly for nonlinear system models and introduces an error compensation function, which can effectively handle the challenges brought about by the inherent nonlinear dynamics of the system and has a wider range of applications. Attached Figure Description
[0015] The present invention can be further illustrated by the non-limiting embodiments given in the accompanying drawings.
[0016] Figure 1 This is a schematic diagram of the main process of the present invention; Figure 2 This is a schematic diagram of the topology of the intelligent agent system in the simulation experiment. Figure 3 This is a schematic diagram illustrating the time sequence of a DoS attack in a simulation experiment. Figure 4 The evolution trajectory of the state of the intelligent agent over time under the control method of the present invention is shown below. Figure 5 The second evolution trajectory of the state of the intelligent agent over time under the control method of the present invention; Figure 6 The third example illustrates the evolution trajectory of the agent's state over time under the control method of this invention. Figure 7 Under conventional consistency control, this is the trajectory of the agent's state evolving over time. Figure 8 The second part describes the evolution trajectory of the agent's state over time under conventional consistency control. Figure 9 Under the control method of the present invention, the error transformation trajectory of the follower and the leader with the transformation matrix is one; Figure 10 Under the control method of the present invention, the error transformation trajectory of the follower and the leader with the transformation matrix is two; Detailed Implementation
[0017] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.
[0018] I. The technical solution of this invention is as follows: A method for secure generalized control of a nonlinear multi-agent system under DoS attack includes the following steps: Step S100: Construct a nonlinear multi-agent system containing one leader and N followers, and define a lag synchronization with the transformation matrix H as the core; The dynamic equation of the leader is expressed as (Equation 1): ; The dynamic equation of the i-th follower is expressed as (Equation 2): ; in For control protocols; Specifically, Represents the state of follower i in a nonlinear multi-agent system. The following Lipschitz conditions must be met: ,in Preset positive numbers; In step S100, for any follower, the nonlinear multi-agent system achieves delayed synchronization when the transformation matrix H satisfies the following condition: .
[0019] Step S200: Design the control protocol for the nonlinear multi-agent system Control Protocol Includes control gain and error compensation function Define the DoS attack frequency and DoS attack duration; In step S200, the control protocol Represented as (Equation 3): ; in, The error compensation function is expressed as: ; Indicates control gain; , indicating synchronization error; This indicates whether there is information exchange between the leader and the followers; if so, then... ,otherwise ; It is a diagonal matrix; This is a preset constant.
[0020] The DoS attack frequency is defined in step S200 as follows: For any In the time period The total number of DoS attacks that occurred on the platform is expressed as follows: Then in the time period The frequency of DoS attacks is defined as follows: ; Step S200 defines the duration of the DoS attack as follows: For any In the time period The total duration of the DoS attack that occurred on the above is expressed as Then in the time period The duration of a DoS attack is defined as follows: ;in, , .
[0021] Step S300: Analyze the stability of the nonlinear multi-agent system under a DoS attack to obtain sufficient conditions to ensure the system achieves secure lag synchronization, specifically including: ①Based on control protocol The gain matrix is obtained. The conditions that must be met; Based on the foregoing ; make , ; right Differentiation yields (Equation 4): ; in, express Jacobian matrix; Combining equations 3 and 4, we get equation 5: ; Rewriting the above equation, we get (Equation 6): ; in, ; Gain matrix The condition to be met is (Equation 7): ; ②Based on the frequency of DoS attacks, the upper bound condition for the frequency of DoS attacks is obtained; The upper bound condition for the frequency of DoS attacks is (Equation 8): ; in, is a constant and ; ; and ; ③ Based on the duration of the DoS attack, the upper bound condition for the duration of the DoS attack; The upper bound condition for the duration of a DoS attack is (Equation 9): .
[0022] Step S400: Apply the control protocol that satisfies the sufficient conditions to the multi-agent system so that under a DoS attack that satisfies the upper bound condition, all followers can achieve delayed synchronization with the leader through the transformation matrix H.
[0023] II. Theoretical proof of the technical solution of this invention: After being subjected to a DoS attack, the agent can recover to a controllable state, but a certain recovery time is required. Therefore, the time of the m-th attack is defined as... Time range It is by and It consists of two sub-intervals, namely:
[0024] in ,
[0025] In the communication area, select the following Lyapunov function (Equation 10): ; Combining with formula 6, The derivative is obtained (Equation 11): ; From the aforementioned conditions, we can obtain (Equation 12): ; Combining Equations 11 and 12, we get (Equation 13): ; From the aforementioned conditions, we can conclude that: ; in: ; In the region where communication is interrupted, construct the Lyapunov function: ,right Differentiation has ; Define the following piecewise function: ; According to the Comparison lemma, we can obtain: ; if There is (Equation 14): ; if There is (Equation 15): ; From definition 4.2, we can obtain:
[0026] Therefore, for any Combining (4.14) and (4.15), we have (Equation 16): ; From the aforementioned conditions, we can conclude that: ; as well as: ; when hour, Converging to zero, i.e., the error... If the convergence reaches zero, then the nonlinear intelligent agent system has achieved safe lag synchronization.
[0027] III. Numerical Simulation: This study further verifies the correctness of the theory through numerical simulation experiments, considering a topology consisting of one leader and six followers, such as... Figure 2 As shown; From the above topology diagram, it is clear that the Laplacian matrix of the nonlinear intelligent agent system is:
[0028] The leader's initial value is The initial values of the pursuers are respectively , Consider the transformation matrix , Control gain , ; By substituting the relevant parameters into the system model and solving the differential equations using MATLAB, the state values of the nonlinear intelligent agent system can be obtained. Figure 3The time sequence of the DoS attacks is displayed, with the red areas indicating the time periods during which the attacks occurred.
[0029] like Figures 4 to 6 This illustrates the evolution of an agent's state over time across three dimensions. The horizontal axis represents time, and the vertical axis represents the agent's state value. Clearly, as time changes, all followers converge to the same value across all three dimensions. Furthermore, a certain relationship can be observed between the leader and the six followers in terms of their states. , , .
[0030] Figure 7 and Figure 8 The paper presents the time-varying motion trajectory of an agent under conventional consensus control. It shows that conventional control strategies can only achieve a single state mapping between the leader and followers across different dimensions. , , Therefore, the control strategy designed in this chapter is more universal than conventional control strategies.
[0031] To better demonstrate the effectiveness of the designed control protocol, Figure 9 and Figure 10 The above shows the error transformation trajectories of six followers and a leader with a transformation matrix. It is clear that the errors converge to zero in all three dimensions.
[0032] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.
Claims
1. A secure generalized control method for a nonlinear multi-agent system under DoS attack, characterized in that: Includes the following steps: Step S100: Construct a nonlinear multi-agent system containing one leader and N followers, and define a lag synchronization with the transformation matrix H as the core; The dynamic equation of the leader is expressed as: ; The dynamic equation of the i-th follower is expressed as: ; in For control protocols; Step S200: Design the control protocol for the nonlinear multi-agent system. The control protocol Includes control gain and error compensation function Define the DoS attack frequency and DoS attack duration; Step S300: Analyze the stability of the nonlinear multi-agent system under a DoS attack to obtain sufficient conditions to ensure the system achieves secure delayed synchronization, specifically including: ①Based on control protocol The gain matrix is obtained. The conditions that must be met; ②Based on the frequency of DoS attacks, the upper bound condition for the frequency of DoS attacks is obtained; ③ Based on the duration of the DoS attack, the upper bound condition for the duration of the DoS attack; Step S400: Apply the control protocol that satisfies the sufficient conditions to the multi-agent system, so that under a DoS attack that satisfies the upper bound condition, all followers can achieve delayed synchronization with the leader through the transformation matrix H.
2. The method for secure generalized control of a nonlinear multi-agent system under DoS attack as described in claim 1, characterized in that: In step S100, the nonlinear multi-agent system The following Lipschitz conditions must be met: ,in Preset positive numbers; Furthermore, in the aforementioned nonlinear multi-agent system, there is no communication channel for followers to transmit information to the leader.
3. The secure generalized control method for a nonlinear multi-agent system under DoS attack as described in claim 2, characterized in that: In step S100, for any follower, the nonlinear multi-agent system achieves delayed synchronization when the transformation matrix H satisfies the following condition: 。 4. The secure generalized control method for a nonlinear multi-agent system under DoS attack as described in claim 1, characterized in that: In step S200, the control protocol Represented as: ； in, The error compensation function is expressed as: ； Indicates control gain; , indicating synchronization error; This indicates whether there is information exchange between the leader and the followers; if so, then... ,otherwise ; It is a diagonal matrix; This is a preset constant.
5. A secure generalized control method for a nonlinear multi-agent system under DoS attack as described in claim 4, characterized in that: The DoS attack frequency defined in step S200 is as follows: For any In the time period The total number of DoS attacks that occurred on the platform is expressed as follows: Then in the time period The frequency of DoS attacks is defined as follows: 。 6. A secure generalized control method for a nonlinear multi-agent system under DoS attack as described in claim 5, characterized in that: The duration of the DoS attack defined in step S200 is as follows: For any In the time period The total duration of the DoS attack that occurred on the above is expressed as Then in the time period The duration of a DoS attack is defined as follows: ； in, , .
7. A method for secure generalized control of a nonlinear multi-agent system under DoS attack as described in claim 6, characterized in that: The gain matrix in step S300 The conditions to be met are: The upper bound condition for the frequency of DoS attacks is: ； in, is a constant and ; ； and ; The upper bound condition for the duration of a DoS attack is: 。