A Safety Cooperative Control Method for Multi-Agent Systems Based on High-Order All-Drive Method

Abstract

This invention provides a secure collaborative control method for multi-agent systems based on a high-order all-drive approach, belonging to the technical field of networked multi-agent control strategies based on computer data processing. It constructs a dynamic mathematical model of a high-order all-drive nonlinear multi-agent system and establishes a unified description of multiplicative and additive actuator faults. An extended state observer is designed to estimate fault values ​​in real time. A timing model of denial-of-service attacks is established, dividing the system timeline into secure communication intervals and paralyzed communication intervals. A distributed event-triggered fault-tolerant formation control protocol is designed, providing constraints on controller parameters and attack intensity, as well as event triggering threshold parameters, ensuring that the formation tracking error is eventually uniformly bounded under conditions of intermittent communication link paralysis and actuator failures. This invention is applicable to practical physical systems such as UAV swarms, achieving secure collaborative control under simultaneous actuator failures and denial-of-service attacks.

Description

Technical Field

[0001] This invention belongs to the field of networked multi-agent control strategy technology based on computer data processing, and particularly relates to a safe and cooperative control method for multi-agent systems based on a high-order all-drive method. Background Technology

[0002] With the rapid development of industrial internet and artificial intelligence technologies, multi-agent systems are increasingly being used in fields such as drone swarms, autonomous driving, and intelligent manufacturing. Cooperative control, especially leader-follower consistency and formation control, is the core technology for realizing these applications. However, real-world systems face two major challenges: first, the high-order nonlinear characteristics of the system itself and actuator failures (such as performance degradation, jamming / biasing) can seriously affect control performance; second, the open communication network on which agents rely is highly vulnerable to denial-of-service attacks, leading to information transmission interruptions and compromising system stability. Traditional state-space methods present complex controller designs when dealing with strongly nonlinear, high-order systems, and struggle to uniformly handle faults and network attacks. In recent years, high-order all-drive system methods have provided a novel approach to nonlinear control, but research on their extension to the field of secure collaborative control where actuator faults and denial-of-service attacks coexist is still insufficient. Therefore, there is an urgent need for a secure collaborative control method that can uniformly handle system nonlinearity, actuator faults, and network attacks, and is simple in design and easy to implement in engineering. Summary of the Invention

[0003] This invention addresses the shortcomings of existing technologies by providing a secure cooperative control method for multi-agent systems based on a high-order all-drive approach. This method ensures that the multi-agent system can still complete its intended cooperative formation task even when the communication network is subjected to a denial-of-service attack and some agents experience actuator failures.

[0004] This invention provides a method for safe cooperative control of a multi-agent system based on a high-order all-drive method, comprising the following processes: S1, Construct a dynamic mathematical model of a high-order, all-driven, nonlinear multi-agent system. This dynamic mathematical model includes a virtual leader model. A follower model and an actuator failure model in each agent; S2, Design an extended state fault observer to perform real-time estimation of the actuator fault model and obtain fault estimates; S3, Establish a timing model for a denial-of-service attack, wherein the timing model divides the system's operating timeline into a secure communication interval and a paralyzed communication interval; S4. Based on the obtained timing model, perform event-triggered state updates in the safe communication interval, use open-loop predictive state for control calculation in the paralyzed communication interval, and design an event-triggered safe formation control protocol in combination with fault estimates. S5. Based on the designed event-triggered secure formation control protocol, calculate and output the actual control commands for N follower models; set controller parameters and attack strength constraints, as well as event trigger threshold parameters, so that the system formation tracking error is eventually consistent and bounded under the action of the actual control commands; at the same time, set an anti-Zeno constant in the event trigger conditions to ensure that the time interval between adjacent triggers is greater than zero.

[0005] Preferably, the dynamic mathematical model of the high-order all-drive nonlinear multi-agent system in S1 is as follows: The nth-order dynamic equation of the virtual leader model: ; in , These are the virtual leader states. The first derivative and the control input of the virtual leader, Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition ; Indicates virtual leader 0 to A stacked vector of states of order; The derivatives of the virtual leader state and Derivative order; No. The nth-order dynamic equations of a follower model: ; in , The first The nth derivative of the follower state and the th... The actual control input of a follower External disturbances Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition ; Indicates the first 0 followers Stacked vector of order states; The first The derivatives of each follower state and The first derivative.

[0006] Preferably, the unified description model of the actuator fault model in S1 is specifically as follows: ; in For the first The actual control input of a follower For the first The controller output of a follower This is a diagonal matrix of energy efficiency loss coefficients. For the first The first follower The efficiency coefficient of each controller, For additive fault terms; define equivalent multiplicative faults. Then the fault model is equivalent to .

[0007] Preferably, the extended state fault observer described in S2 is designed as follows: ; in For virtual control input, For the output value, For the internal state of the observer, The derivative of the observer's internal state is given. For extended state The estimated value, For observer gain; by selecting such that The denoted matrix is ​​the Herwitz matrix, thus the observation error converges asymptotically.

[0008] Preferably, the timing model of the denial-of-service attack described in S3 is as follows: Definition of the first Secondary Denial-of-Service Attack Range Define the set of failure trigger attempts. System uptime Divided into secure communication zones and paralyzed communication interval And impose constraints on attack frequency and duration: ; in For the first The start time of the denial-of-service attack. For the first Duration of the denial-of-service attack. Indicates follower In the The trigger time corresponds to one controller update. For followers The sequence of event trigger times, For any time interval, For the number of attacks, Total attack duration; , , Constant parameters related to denial-of-service attacks.

[0009] Preferably, the event-triggered fault-tolerant grouping control protocol described in S4 includes: Local formation error based on open-loop prediction model: ; Condition measurement deviation: ; in These are the elements of the communication topology adjacency matrix. For followers The neighborhood group, Indicates the first 0 followers Stacked vectors of order states To estimate neighbor states using an open-loop prediction model; For desired formation offset; Event triggering conditions: ; in For followers The sequence of event trigger times, For trigger coefficient, To prevent the dead zone constant of Zeno's behavior, Represents the norm, Indicates the infimum; Virtual Control Protocol: ; Final controller output: ; in For coupling gain, For the feedback gain matrix, Real-time estimates provided for the fault observer Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition , This is the linearized parameter matrix obtained using the pole placement method. This is a feedforward compensation term for formation feasibility.

[0010] Preferably, the controller parameters and attack strength constraints in S5 are specifically as follows: There exists a positive definite symmetric matrix , This makes the algebraic Riccati equation hold: ; in , The system matrix is ​​in the form of a friend matrix; for A zero-order matrix, for An identity matrix of order 1; Event trigger threshold satisfied ,in For the first The event trigger threshold coefficient for each follower The largest eigenvalue of the communication topology matrix; Feedback gain design is and coupling gain ,in It is the smallest non-zero eigenvalue of the information exchange matrix; Denial-of-Service Attack Parameters System attenuation rate within the normal communication range and divergence rate within the paralysis interval satisfy ; Dead time constant in event triggering conditions Make the adjacent trigger time interval satisfy This eliminates the possibility of Zeno's behavior; in For any follower The adjacent trigger time interval, It is a globally bounded constant related to the system state, disturbance extrema, and control gain. For the system matrix Norm form.

[0011] Compared with the prior art, the present invention has the following beneficial effects: This invention proposes a safe cooperative control method for multi-agent systems based on a high-order full-drive approach. Compared with traditional state-space methods, the controller designed by this method is simple and practical, and can simultaneously handle system nonlinearity, actuator failures, and network attacks within a unified framework. Specifically, online estimation and proactive compensation for multiplicative and additive faults are achieved based on an extended state observer; by establishing a communication time partitioning model under denial-of-service attacks, the event triggering mechanism and anti-attack control are deeply integrated, ensuring system stability under communication-constrained conditions; simultaneously, by incorporating high-order full-drive theory and obtaining the controller linearization parameter terms based on the pole placement method, control performance is optimized. Notably, the control scheme designed in this invention is applicable to general directed communication topologies and has broad application prospects in practical fields such as UAV swarms, unmanned vehicle platooning, and intelligent manufacturing.

[0012] Integrated proactive fault tolerance and attack defense: By extending the online approximation of the state observer and the feedforward compensation of multiplicative / additive faults of the actuator, and combining the timing model and event triggering mechanism of denial-of-service attacks, dual defense against physical faults and network attacks is achieved in the same controller, and the system robustness is significantly enhanced. Significant savings in communication resources: The distributed event-triggered communication mechanism only transmits information when the state measurement deviation exceeds the threshold. Compared with the traditional periodic sampling method, this greatly reduces the number of communications between agents, reduces network bandwidth and energy consumption, and strictly avoids the infinite triggering problem by setting an anti-Zeno constant. The controller design is simple and practical: based on high-order all-drive theory, the complex nonlinear control problem is transformed into a linear control problem, making the design of the corresponding safety cooperative controller simpler and more practical. Controller parameters can be uniformly obtained by solving linear matrix inequalities and Riccati equations, facilitating direct debugging and deployment by engineering technicians. Wide range of applications: This invention does not depend on the specific system order and degrees of freedom, and is applicable to any high-order nonlinear multi-agent system that meets the all-drive condition. It can also be effectively extended to actual physical systems such as quadcopter drones, mobile robots, and robotic arms. Attached Figure Description

[0013] Figure 1 This is a flowchart of the overall process of the present invention.

[0014] Figure 2 This is a directed topological graph of a multi-agent system.

[0015] Figure 3 Here is the trajectory diagram of a multi-agent system, where: (a) is (a) Initial position distribution map of the multi-agent system; (b) is (c) is the formation motion trajectory diagram of a multi-agent system; Formation-keeping trajectory diagram of a multi-agent system; (d) is (e) is the formation migration trajectory diagram of a multi-agent system; (f) is the formation tracking trajectory diagram of a multi-agent system; The final formation trajectory diagram of the multi-agent system.

[0016] Figure 4 The following are the trigger times and formation error diagrams for a multi-agent system, where: (a) is the event trigger time distribution diagram for each follower; and (b) is the formation error variation curve for each follower.

[0017] Figure 5 The diagram shows the control inputs for a multi-agent system, where: (a) represents the first-dimensional control inputs for each follower. (a) The change curve; (b) The second-dimensional control input of each follower. The change curve.

[0018] Figure 6 This is a diagram of the observation error of a multi-agent system.

[0019] Figure 7 This is a graph showing the first-dimensional state values ​​and observations of a multi-agent system.

[0020] Figure 8 This is a graph showing the second-dimensional state values ​​and observations of a multi-agent system. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0022] Example 1: This embodiment provides a multi-agent system safety cooperative control method based on a high-order all-drive approach. The overall process is as follows: Figure 1 As shown, it includes the following steps: Step S1: Establish a dynamic mathematical model and actuator fault model for a high-order all-drive nonlinear multi-agent system; This step first constructs a high-order full-drive model of a multi-agent system consisting of one virtual leader and N followers. The nth-order dynamic equation of the virtual leader is expressed as: ; in , Let n be the nth derivative of the virtual leader's state and the control input of the virtual leader, respectively. Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition ; Indicates virtual leader 0 to A stacked vector of states of order; The derivatives of the virtual leader state and Derivative order; No. The dynamic equations and output equations of the nth order for each follower are: ; in , The first The nth derivative of the follower state and the th... A follower's control input, For system output, External disturbances Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition ; Indicates the first 0 followers A stacked vector of states of order; The first The derivatives of each follower state and Derivative order; The unified descriptive model for actuator failure is as follows: Let the output calculated by the controller be... The actual control input acting on the system is: ; in For the first The actual control input of a follower For the first The controller output of a follower This is a diagonal matrix of energy efficiency loss coefficients. For the first The first follower The efficiency coefficient of each controller (1 indicates normal operation, 0 indicates complete failure). For additive fault terms (such as stuck bias); define equivalent multiplicative faults. Then the fault model is equivalent to ; The above equivalent transformation unifies multiplicative and additive faults into additive unknowns that enter the control channel, facilitating subsequent observer design.

[0023] To eliminate system nonlinearity and facilitate the design of a co-controller, a virtual control input is introduced. The following high-order all-wheel drive control law is designed: ; in Let be the linearization parameter matrix to be designed. Substituting the above equation into the original system, we obtain the linear closed-loop system with respect to the virtual input: ; in , The system matrix is ​​in the form of a friend matrix; for A zero-order matrix, for An identity matrix of order 1; The system state and fault state are augmented to define an extended state vector. Then we obtain the augmented linear system: ; in To expand the state vector The derivative form, The derivative includes external disturbances and faults. It is a constant matrix of appropriate dimension.

[0024] Step S2: Design an extended state fault observer; For the augmented system obtained in step S1, the following extended state observer is designed: ; in For virtual control input, For the output value, For the internal state of the observer, The derivative of the observer's internal state is given. For extended state The estimated value, For observer gain; Define observation error By appropriately selecting the gain matrix, the following conditions can be met: ; in It is the identity matrix. To augment the system's output matrix; select a gain such that the matrix... All eigenvalues ​​have negative real parts (i.e. If is the Herwitz matrix, then the observation error asymptotically converges to zero, i.e. Thus, the multiplicative fault is obtained. Additive faults Real-time estimates and .

[0025] Step S3: Establish a timing model for denial-of-service attacks. Define the activation interval of the m-th denial-of-service attack as follows: ,in The moment the attack begins. Let the duration of the attack be denoted as ; let the sequence of event trigger times be . If an event occurs within the attack zone, the state update will fail to transmit successfully. Define the set of failed trigger attempts: ; Indicates follower In the One controller update corresponding to each trigger moment; To accurately describe the impact of communication interruptions on the system, the timeline is redefined: system runtime is recalculated. Divided into non-overlapping secure communication zones and paralyzed communication interval Within the secure communication range, the event triggering mechanism operates normally, and the agent can obtain the neighbor's state in a timely manner; within the paralyzed communication range, communication is completely interrupted, and the agent can only rely on the open-loop prediction model to estimate the neighbor's state.

[0026] The following two reasonable constraints should be imposed on denial-of-service attacks: Attack frequency constraint: There exists a constant. and , such that for any interval Number of attacks satisfy ; Attack duration constraint: There exists a constant. and This makes the total attack duration satisfy ; The above constraints ensure that the communication availability interval is long enough on average, which forms the basis for subsequent stability analysis.

[0027] Step S4: Design an event-triggered fault-tolerant formation control protocol that includes fault feedforward compensation; Definition of the first The expected grouping bias of each follower is The local tracking state is ; Under the event-triggered mechanism, followers cannot obtain the real state of their neighbors in real time. Therefore, an open-loop prediction model is designed based on the time-series model in S3: between two triggers, each follower predicts its own state based on its own linear dynamics model and sends the predicted value to its neighbors; the prediction model is as follows: ; in To estimate follower states using an open-loop prediction model At the trigger time The predicted state is reset to the actual state: ; Define local formation error based on predicted state: ; in These are the elements of the communication topology adjacency matrix. For followers The neighborhood group, To estimate neighbor states using an open-loop prediction model.

[0028] Define the state measurement deviation: ; This bias reflects the difference between the follower's true state and the estimates held by its neighbors. The sequence of event triggers is determined by the following conditions: ; in This is the trigger coefficient, used to adjust the trigger sensitivity; To prevent the dead-time constant of Zeno behavior, a lower bound is guaranteed for the adjacent trigger interval; Represents the norm, Indicates the infimum; Based on the fault estimate obtained in step S2, the virtual control input is designed as follows: ; in For coupling gain, The feedback gain matrix to be designed, To satisfy the feedforward compensation term for formation feasibility conditions, its design must meet the following requirements: ; This condition ensures that the system can accurately track the desired formation trajectory when the formation error is zero.

[0029] Finally, the controller output is: .

[0030] Step S5: Controller parameter settings and stability conditions To ensure that the global formation tracking error of the system is eventually consistent and bounded under denial-of-service attacks and actuator failures, and to eliminate Zeno behavior, the controller parameters need to be set as follows.

[0031] (1) Linearization of the parameter matrix The pole placement method is used to determine the desired set of closed-loop poles. Based on the parameterized design formula for high-order all-drive systems, the generalized Vandermonde matrix and the free parameter matrix are used. Calculated.

[0032] (2) Solve the algebraic Riccati equation: Choose a positive definite symmetric matrix and input weight matrix Solve the following Riccati equation to obtain the positive definite symmetric matrix. : ; (3) The feedback gain matrix is ​​taken as The coupling gain Must meet , For information exchange matrix The smallest non-zero eigenvalue (determined by the communication topology); where For the graph Laplace matrix, It is an adjacency matrix.

[0033] (4) Event trigger threshold parameter Must meet ,in for The largest eigenvalue.

[0034] (5) Parameters of a Denial-of-Service Attack (Determined by attack frequency and duration) must meet the following requirements ,in This represents the error attenuation rate within the normal communication range. The error divergence rate within the paralyzed communication interval can be calculated from the system matrix and the observer gain.

[0035] (6) Dead-time constant in event triggering conditions A small positive number should be chosen to ensure that the lower bound of the adjacent triggering interval is positive; specifically, the adjacent triggering interval satisfies: ; in Let be a constant related to the system state, the upper bound of the disturbance, and the control gain. This inequality shows that as long as... The system will not exhibit Zeno's behavior; After setting the parameters according to the above steps, the system's global formation tracking error It is eventually uniformly bounded, and communication resources are significantly saved.

[0036] Example 2: The invention will be further explained in detail below with a specific numerical simulation example. This embodiment uses a second-order nonlinear multi-agent system model to verify the effectiveness of the control method described in steps S1 to S5 of the invention; the interaction topology diagram is as follows. Figure 2 As shown; System Model: Consider a multi-agent system consisting of one virtual leader and four followers; the communication topology between the agents is a directed graph, and its corresponding Laplace matrix is... Adjacency matrix of leaders They are respectively: ; Only agent 1 can receive information from the leader; the order of the system is taken as... The state dimension of each agent The dynamic model of a leader is: ; No. The dynamic model of a follower is: ; Where the nonlinear function is taken as Control gain External disturbances The leader's reference trajectory is set as follows: The control objective is to enable all followers to asymptotically track the leader, that is... .

[0037] Actuator fault settings: Suppose that at the 20th second, the actuator of agent 3 fails: the efficiency loss is 50% (i.e., the multiplicative failure coefficient). Simultaneously, a jamming bias with an amplitude of 0.5 is applied (additive fault). The fault persists until the simulation ends (50 seconds).

[0038] Denial-of-Service Attack Settings: Within a 50-second simulation period, a non-periodic denial-of-service attack interval is set, with the specific time periods as follows (the first line is the start time, and the second line is the end time): ; Within these intervals, communication between agents is completely interrupted, and state information cannot be transmitted. Controller design and parameter selection: First, based on the high-order all-wheel drive method, the desired closed-loop pole is set as... The linearization parameters are calculated. , ; Then, an extended state observer is designed. The augmented system state includes position, velocity, multiplicative faults, and additive faults; the observer gain matrix... The selected eigenvalues ​​are all in The left and right Hurwitz matrices are as follows: ; Other observer gains Obtained by solving the observer constraint equations; Event triggering parameter selection: trigger coefficient Zeno constant ; In distributed control protocols, the communication topology matrix Its smallest non-zero eigenvalue The largest eigenvalue Take the coupling gain ,satisfy Solving the algebraic Riccati equation: Selecting , Solving for This leads to feedback gain. .

[0039] Simulation results: Numerical simulations were performed with the above parameter settings, a simulation step size of 0.01 seconds, and a total duration of 50 seconds; the results are as follows: Tracking performance: In the absence of faults and attacks (0-1 second, 2.5-4 seconds, etc.), each follower can quickly track the leader's trajectory with tracking error approaching zero; Fault tolerance capability: After an actuator failure occurs at 20 seconds, due to the rapid estimation and feedforward compensation of the extended state observer, the system only experiences a brief fluctuation at the moment of the failure (maximum error of about 0.3), and then resumes stable tracking within 1 second; the observer's estimation error for multiplicative and additive faults quickly converges to zero.

[0040] Anti-attack capability: During the denial-of-service attack period, communication interruption prevents the agent from acquiring neighbor states, causing a temporary increase in tracking error (maximum error of approximately 0.5); however, after the attack ends, the system quickly reconverges, and the error returns to zero. Throughout the simulation, the system remains stable without exhibiting any divergence.

[0041] Communication resource conservation: The event-triggered mechanism effectively reduced the number of communications. The number of triggers for the four agents were 1072, 1569, 1756, and 1262, respectively; compared with periodic sampling (5000 times), the average communication volume was saved by about 70%; the time interval between adjacent triggers was greater than 0.01 seconds, and no Zeno behavior was observed.

[0042] like Figure 3 As shown, the four followers start from the initial position and gradually form and maintain a preset formation under the control protocol, demonstrating that the proposed method can realize formation tracking control of multi-agent systems.

[0043] like Figure 4 As shown, Figure 4 Figure (a) shows the event triggering time distribution for each follower. Figure 4 Figure (b) shows the formation error variation curve. It can be seen that the event triggering mechanism effectively reduces the number of communication updates; during the denial-of-service attack range, the formation error will increase briefly, but after the attack ends, the error can converge back to the bounded range, verifying the anti-attack capability of the proposed method.

[0044] like Figure 5 As shown, Figure 5Figures (a) and (b) show the changes in the first and second dimensions of the control input for each follower, respectively. It can be seen that the control input remains bounded under actuator failure and denial-of-service attacks, indicating that the designed control law can function normally under conditions of both failure and attack.

[0045] like Figure 6 As shown, the observation errors of each follower decrease rapidly in the early stages of the simulation and remain within a small range after the fault occurs, indicating that the extended state fault observer can effectively estimate the system fault state. Figure 7 As shown, the actual values ​​of the first-dimensional state of each follower are basically consistent with the estimated values, indicating that the observer has a good estimation effect on the first-dimensional state.

[0046] like Figure 8 As shown, the actual values ​​of the second-dimensional states of each follower are basically consistent with the estimated values, further demonstrating that the designed extended state fault observer can accurately track system state changes.

[0047] This embodiment fully demonstrates the effectiveness of the security collaborative control method proposed in this invention in the case of simultaneous actuator failure and denial-of-service attack.

[0048] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0049] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for safe cooperative control of a multi-agent system based on a high-order all-drive method, characterized in that, The process includes the following: S1, Construct a dynamic mathematical model of a high-order, all-driven, nonlinear multi-agent system. This dynamic mathematical model includes a virtual leader model. A follower model and an actuator failure model in each agent; S2, Design an extended state fault observer to perform real-time estimation of the actuator fault model and obtain fault estimates; S3, Establish a timing model for a denial-of-service attack, wherein the timing model divides the system's operating timeline into a secure communication interval and a paralyzed communication interval; S4. Based on the obtained timing model, perform event-triggered state updates in the safe communication interval, use open-loop predictive state for control calculation in the paralyzed communication interval, and design an event-triggered safe formation control protocol in combination with fault estimates. S5 calculates and outputs the actual control commands for N follower models based on the designed event-triggered safety formation control protocol. The controller parameters and attack strength constraints, as well as the event trigger threshold parameters, are set to ensure that the system formation tracking error is eventually consistent and bounded under the actual control command. At the same time, an anti-Zeno constant is set in the event trigger conditions to ensure that the time interval between adjacent triggers is greater than zero.

2. The multi-agent system safety cooperative control method based on a high-order all-drive method as described in claim 1, characterized in that: The dynamic mathematical model of the high-order all-drive nonlinear multi-agent system in S1 is as follows: The nth-order dynamic equation of the virtual leader model: ； in , Let n be the nth derivative of the virtual leader's state and the control input of the virtual leader, respectively. Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition ; Indicates virtual leader 0 to A stacked vector of states of order; The derivatives of the virtual leader state and Derivative order; No. The nth-order dynamic equations of a follower model: ； in , The first The nth derivative of the follower state and the th... The actual control input of a follower External disturbances Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition ; Indicates the first 0 followers A stacked vector of states of order; The first The derivatives of each follower state and The first derivative.

3. The multi-agent system safety cooperative control method based on a high-order all-drive method as described in claim 1, characterized in that: The unified description model of the actuator fault model described in S1 is as follows: ； in For the first The actual control input of a follower For the first The controller output of a follower This is a diagonal matrix of energy efficiency loss coefficients. For the first The first follower The efficiency coefficient of each controller, For additive fault terms; define equivalent multiplicative faults. Then the fault model is equivalent to .

4. The multi-agent system safety cooperative control method based on a high-order all-drive method as described in claim 1, characterized in that: The extended state fault observer described in S2 is designed as follows: ； in For virtual control input, For the output value, For the internal state of the observer, The derivative of the observer's internal state is given. For extended state The estimated value, For observer gain; by selecting such that The denoted matrix is ​​the Herwitz matrix, thus the observation error converges asymptotically.

5. The multi-agent system safety cooperative control method based on a high-order all-drive method as described in claim 1, characterized in that: The specific time-series model of the denial-of-service attack described in S3 is as follows: Definition of the first Secondary Denial-of-Service Attack Range Define the set of failure trigger attempts. System uptime Divided into secure communication zones and paralyzed communication interval And impose constraints on attack frequency and duration: ； in For the first The start time of the denial-of-service attack. For the first Duration of the denial-of-service attack. Indicates follower In the The controller update corresponds to each trigger moment. For followers The sequence of event trigger times, For any time interval, For the number of attacks, Total attack duration; , , Constant parameters related to denial-of-service attacks.

6. The multi-agent system safety cooperative control method based on a high-order all-drive method as described in claim 1, characterized in that: The event-triggered fault-tolerant grouping control protocol described in S4 includes: Local formation error based on open-loop prediction model: ； Condition measurement deviation: ； in These are the elements of the communication topology adjacency matrix. For followers The neighborhood group, Indicates the first 0 followers Stacked vectors of order states To estimate neighbor states using an open-loop prediction model; For desired formation offset; Event triggering conditions: ; in For followers The sequence of event trigger times, For trigger coefficient, To prevent the dead zone constant of Zeno's behavior, Represents the norm, Indicates the infimum; Virtual Control Protocol: ; Final controller output: ； in For coupling gain, For the feedback gain matrix, Real-time estimates provided for the fault observer Given a known nonlinear function of the system, It is a control gain matrix and satisfies the condition , This is the linearized parameter matrix obtained using the pole placement method. This is a feedforward compensation term for formation feasibility.

7. The multi-agent system safety cooperative control method based on a high-order all-drive method as described in claim 6, characterized in that: The controller parameters and attack strength constraints described in S5 are as follows: There exists a positive definite symmetric matrix , This makes the algebraic Riccati equation hold: ； in , The system matrix is ​​in the form of a friend matrix; for A zero-order matrix, for An identity matrix of order 1; Event trigger threshold satisfied ,in For the first The event trigger threshold coefficient for each follower The largest eigenvalue of the communication topology matrix; Feedback gain design is And coupling gain ,in It is the smallest non-zero eigenvalue of the information exchange matrix; Denial-of-Service Attack Parameters System attenuation rate within the normal communication range and divergence rate within the paralysis interval satisfy ; Dead time constant in event triggering conditions Make the adjacent trigger time interval satisfy This eliminates the possibility of Zeno's behavior; in For any follower The adjacent trigger time interval, It is a globally bounded constant related to the system state, disturbance extrema, and control gain. For the system matrix Norm form.

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