A multi-agent safe operation mode and observer collaborative switching control method under DoS attack

Abstract

The application provides a multi-agent safe operation mode and observer cooperative switching control method under a DoS attack, and the method comprises the following steps: a network monitoring layer generates an attack event indicator and a communication graph connectivity indicator respectively, and controls the switching of an agent between a normal operation mode and a safe operation mode according to the attack event indicator; a full-order observer matched with a physical operation mode is used to reconstruct unmeasurable states; when the communication graph is connected, the relative information of neighbors is calculated by using the latest broadcasted observation state, and mode-related control input is applied; when the communication graph is disconnected, communication-related input is suspended. The triggering time is determined based on the sampling error, the relative information of neighbors and dynamic internal variables, the triggering is suspended and the internal variables are frozen during the disconnection. The application can maintain elastic consistency under the conditions of partial state measurability and multi-strategy denial of service (DoS) attack, improve the estimation performance of the safe mode and reduce the communication frequency.

Description

Technical Field

[0001] This invention relates to the fields of networked control, multi-agent cooperative control, and cyber-physical system security control technology, specifically to a method for switching control of multi-agent secure operation modes and observers under DoS attacks. Background Technology

[0002] Multi-agent systems (MAS) achieve collaboration among multiple agents through local communication, finding wide applications in fields such as unmanned aerial vehicle (UAV) swarming, mobile robot cooperation, intelligent transportation, distributed sensing, and power systems. Consistency control is fundamental to achieving this collaborative behavior. As MAS become increasingly reliant on communication networks, these links become vulnerable to denial-of-service (DoS) attacks. DoS attacks disrupt or interfere with information transmission, altering the communication topology or even causing connectivity loss, thus increasing consistency errors.

[0003] To mitigate the impact of denial-of-service (DoS) attacks, some existing methods switch agents to a pre-certified secure operating mode upon detecting an attack. This secure operating mode may employ a more conservative flight envelope, redundant actuator configurations, or an operating point with a lower open-loop divergence rate, thereby reducing the rate of consistency error growth during communication outages.

[0004] However, existing methods for maintaining consistency in safe operating modes typically rely on the direct measurement of the complete states of each agent. In practical systems, limitations in the number of sensors, hardware costs, and measurement channels often limit the acquisition of only partial outputs. While using a fixed observer gain may maintain stability in safe operating modes, it cannot guarantee that the estimated convergence speed after switching will meet the requirements for safe operation.

[0005] Furthermore, in multi-strategy Denial-of-Service (DoS) attacks, different attack strategies may switch within the same attack event. Some attack strategies disrupt the connectivity of the communication graph, while others cause link loss but maintain the connectivity of the communication graph. Equating the attack event state with the connectivity state of the communication graph would unnecessarily halt neighbor feedback and broadcasting during the still communicable period, reducing the efficiency of control and communication resource utilization.

[0006] Event-triggered control can update broadcast information only when trigger conditions are met, reducing periodic transmissions. However, in scenarios where only partial output can be measured, it is also necessary to simultaneously handle continuously evolving observation errors and sampling errors caused by resetting at the trigger moment; continuing to update event-triggered internal variables during communication graph disconnection may also compromise their non-negativity. Therefore, a dynamic event-triggered resilient consistency control scheme is needed that can distinguish between attack events, physical operating modes, and communication connectivity states, and is applicable to partial state measurements. Summary of the Invention

[0007] Purpose of the invention: The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a method for switching control of multi-agent secure operation mode and observer coordination under DoS attack. In cases where some states cannot be directly measured and there are multiple link disruption strategies within the attack event, the method improves the attack resilience, state estimation performance and communication efficiency of the system by separating the attack event state, physical operation mode and communication connectivity state.

[0008] The method includes the following steps:

[0009] Step S1: Obtain the measurable outputs of each agent, the start information of the Denial-of-Service (DoS) attack, the end information of the Denial-of-Service (DoS) attack, and the current communication topology information;

[0010] Step S2: Generate an attack event indicator based on the Denial-of-Service (DoS) attack start information and Denial-of-Service (DoS) attack end information. Generate connectivity status indicators based on the current communication topology information. And based on the attack event indication quantity Determine the physical operation mode of each intelligent agent The physical operating mode includes a nominal operating mode and a secure operating mode, and the attack event indication quantity... Connectivity status indicator and physical operation mode Determined independently of each other;

[0011] Step S3, based on the attack event indication quantity Control the physical operation mode of each intelligent agent After the attack is reported to have begun, each agent shall, within a specified time limit, Within a certain delay, each agent switches from the nominal operating mode to the secure operating mode and maintains the secure operating mode throughout the entire reported attack event; after the reported attack ends, each agent switches from the nominal operating mode to the secure operating mode within a certain timeframe. It returns to the nominal operating mode within a certain delay. The attack strategy switch within the attack event only changes... It does not generate additional physical mode switching;

[0012] Step S4: Reconstruct the unmeasurable state using a full-order observer that matches the current physical operating mode;

[0013] Step S5, when When, based on the state estimates of each agent's most recent broadcast and the state estimates of neighboring agents' most recent broadcast, the relative state information of neighbors is calculated, and the control input is generated according to the control gain corresponding to the current physical operating mode; when At this time, the communication-related control inputs will be set to zero;

[0014] Step S6: Calculate the event trigger function based on the sampling error between the current state estimate and the most recently broadcast state estimate, the relative state information of the neighbors, the current physical operation mode, and the dynamic internal variables;

[0015] Step S7, when And when the event triggering function meets the preset triggering conditions, it broadcasts the current state estimate and updates the most recently broadcast state estimate; when The broadcast is paused and the dynamic internal variables are frozen.

[0016] Step S2 includes: A Denial-of-Service (DoS) attack includes switching between two or more attack strategies within an attack event; Let be the Laplace matrix of the currently available communication topology, when season ,when season ; Effective attacks that disrupt the connectivity of the communication graph The parameters correspond to an invalid attack that is in an idle state or does not disrupt the connectivity of the communication graph. Used to describe whether a reported attack event is active. , ;otherwise Among them, algebraic connectivity The Laplace matrix represents the currently available communication topology. The second smallest eigenvalue; the attack event indicator d(t) = 1 indicates that the reported attack event is active, and d(t) = 0 indicates that the reported attack event is inactive; interval union symbol. This represents the union of all reported attack event intervals. This indicates the start time of the r-th attack event. The duration of the r-th attack event is represented by t, where t is the system runtime.

[0017] Step S3 includes: the dynamic model and measurable output of the i-th agent are as follows:

[0018] ,

[0019] ,

[0020] Where d represents the differential symbol. N is the number of agents participating in consensus control; Let be the true state vector of the i-th agent. To control the input, For measurable output, R represents the real number space. It can calm you down. Observable, Indicates the nominal operating mode. Indicates the safe operating mode; the state matrix under the current physical operating mode. The input matrix used to describe state evolution and the current physical operating mode. Used to describe the effect of control inputs on the state, the measurable output of the i-th agent. The output matrix C is used to map the state vector to a measurable output, which is the output quantity that the sensor can obtain. The state dimension n is the number of components contained in the state vector, and the output dimension m is the number of components contained in the measurable output. respectively Representation pattern The corresponding constant state matrix and constant input matrix, physical operation mode indicator Used to indicate the currently used operating mode.

[0021] Step S4 includes: The pattern-related full-order observer for the i-th agent is:

[0022] ,

[0023] The nominal operating mode uses observer gain L1, the safe operating mode uses observer gain L2, and makes... Here, Hurwitz matrix represents the observation error of the i-th agent. ,satisfy ; It is the state estimate of the i-th agent, which is the state reconstructed by the full-order observer; mode Corresponding observer gain Inject gain into the output error used in the current mode.

[0024] Step S5 includes: in At that time, the relative state information of the i-th agent's neighbors is calculated using the state estimate from the most recent broadcast. :

[0025] ,

[0026] in, and These are the most recent trigger times for the i-th agent and the j-th agent, respectively. The adjacency weights of the currently available communication topology; Let be the set of neighbors of the i-th agent at time t, representing the set of agents in the current available communication topology that can transmit information to the i-th agent. This indicates that the j-th agent was at the most recently triggered time. The broadcast state estimate;

[0027] The sampling error of the i-th agent at time t is , .

[0028] Step S5 further includes: the control input of the i-th agent is: when hour, ;when hour, ;in, c is the positive coupling coefficient. This is a positive definite matrix corresponding to the physical operation mode; It is the control gain corresponding to the current physical operating mode, used to map the relative state information of neighbors into control inputs; This indicates transpose.

[0029] Step S6 includes: the event triggering function is:

[0030] ,

[0031] in, , , , , The upper bound of the maximum Laplace eigenvalue for all connected and available communication topologies. For dynamic internal variables, the event triggering function of the i-th agent. Used to determine whether to broadcast; It is the positive trigger scale coefficient, used to adjust the trigger threshold; It is the sampling error weight, used to weight the sampling error term; It is the sampling error of the i-th agent, representing the difference between the most recently broadcast state estimate and the current state estimate; It is a mode-related weight matrix, which is a positive definite weighted matrix corresponding to the current physical operation mode; It is the relative information weight of neighbors, used to weight the relative state items of neighbors; It is the relative state vector of the neighbors.

[0032] In step S6, the dynamic internal variable satisfies: when hour, ;when hour, ;in, , , The next trigger time is and The first moment; It is the decay coefficient of the internal variable of the i-th agent, used to adjust the natural decay rate of the dynamic threshold. It is the initial value of the internal variable of the i-th agent, which is a positive initial value set at the start of control; It is the error feedback adjustment coefficient of the i-th agent, used to adjust the intensity of the influence of the error term on the dynamic internal variables.

[0033] Step S7 includes: the next triggering time for the i-th agent. Determined as:

[0034] ,

[0035] Where inf is the infimum operator, which represents the smallest lower bound in the set of times when a given triggering condition is met;

[0036] In the asynchronous implementation, the communication layer sets a non-zero minimum processing interval for timestamped broadcast events. Two or more broadcasts occurring simultaneously are treated as the same network event; updates are made after triggering. and will Reset to zero;

[0037] The controller and observer parameters are solved using linear matrix inequalities for each physical operating mode. ,make Please solve:

[0038] ,

[0039] ,

[0040] in, This is a lower bound on the algebraic connectivity of all available connected communication topologies. , , The solution is obtained and After that, I obtained and Among them, the pattern Corresponding inverse matrix decision variables Lyapunov matrix for controller The inverse matrix; This is the controller attenuation margin, a normal value to ensure the closed-loop convergence speed; mode The corresponding controller Lyapunov matrix It is a positive definite matrix; pattern The corresponding observation error Lyapunov matrix It is a positive definite matrix; pattern The corresponding observer-aided decision matrix Used to calculate observer gain; It is the observation error decay rate, a normal number used to ensure the convergence speed of the observation error;

[0041] For any The frequency of Denial-of-Service (DoS) attacks and the effective duration of attacks respectively satisfy the following conditions:

[0042] ,

[0043] ,

[0044] Among them, the starting time of the statistical interval The attack statistical interval is determined together with the termination time T of the statistical interval. [,T]; Number of attacks This interval represents [ The total number of reported attack events within [T]; upper bound of frequency jitter. For a finite number of permissible instantaneous deviations; average attack interval The lower bound of the average time between adjacent reported attack events; the effective attack time set. This interval represents [ The set measure of all time periods within [T] that cause communication graph disconnection. The effective attack cumulative duration; duration biased upper bound. For the allowable finite initial deviation, It is the sparsity parameter of effective attack duration, used to limit the proportion of the cumulative duration of effective attacks to the length of the statistical interval;

[0045] A multi-agent system can achieve resilient consistency under an allowed denial-of-service (DoS) attack when the following conditions are met:

[0046] ,

[0047] in, This is the upper bound of the Lyapunov function jump during physics mode switching. The convergence rate of the connected time interval. These are the upper bounds of the divergence growth rates for the safe operation mode and the nominal operation mode, respectively. It is the upper bound of the nominal operating mode divergence growth rate, representing the maximum growth rate of the nominal mode consistency error under adverse communication conditions; It is the upper bound of the divergence growth rate of the safe operation mode, representing the maximum growth rate of the consistency error of the safe mode under adverse communication conditions.

[0048] This invention also provides a multi-agent secure operation mode and observer cooperative switching control system under DoS attack, comprising the following modules:

[0049] The network monitoring module is used to output attack start information, attack end information, and communication topology connectivity information;

[0050] The mode switching module is used to generate attack event indicators and physical operating modes, and to control each agent to switch between the nominal operating mode and the secure operating mode.

[0051] The state observation module is used to obtain a state estimate based on the measurable output by employing the observer gain corresponding to the current physical operating mode.

[0052] The neighbor information module is used to calculate the relative state information of neighbors based on the state estimate of the most recent broadcast when the communication topology is connected.

[0053] The dynamic event triggering module is used to generate a broadcast trigger signal based on sampling error, relative status information of neighbors and dynamic internal variables, and to pause triggering and freeze dynamic internal variables when the communication topology is disconnected.

[0054] The control input generation module is used to generate control inputs corresponding to the current physical operating mode when the communication topology is connected, and to set the communication-related control inputs to zero when the communication topology is disconnected.

[0055] Compared with existing technologies, the present invention has the following advantages: First, it separates the attack event indicator, physical operation mode, and communication graph connectivity indicator, and continues to implement secure mode neighbor feedback during the period when communication is still connected during the attack event, avoiding unnecessary control deactivation; Second, it uses observer gain that matches the dynamics of the secure operation mode to improve state estimation performance when only part of the output can be measured; Third, it uses a dynamic event triggering mechanism based on the observation state to reduce the number of communications; Fourth, it pauses broadcasting and freezes dynamic internal variables during disconnection, keeping the internal variables positive and preventing Zeno behavior in the triggering process; Fifth, it can uniformly solve the controller and observer parameters under different physical modes through linear matrix inequalities. Attached Figure Description

[0056] Figure 1 This is the overall architecture diagram of the multi-agent dynamic event-triggered elastic consistency control system of the present invention.

[0057] Figure 2 This is a flowchart of the control method of the present invention.

[0058] Figure 3 This is a diagram illustrating the observation, event triggering, and control structure of a single intelligent agent in this invention.

[0059] Figure 4 This is a schematic diagram of the communication topology under a multi-strategy denial-of-service (DoS) attack in an embodiment of the present invention.

[0060] Figure 5 This is a timing diagram of the attack event indicator, physical mode indicator, and connectivity status indicator of the present invention.

[0061] Figure 6 This is a comparison chart of consistency errors between using the safe operation mode and not using the safe operation mode in the embodiments of the present invention.

[0062] Figure 7 This is a comparison chart of the observation errors of the mode-correlated observer and the fixed-gain observer in an embodiment of the present invention.

[0063] Figure 8 This is a comparison chart of the number of communications between dynamic event triggering and static event triggering in an embodiment of the present invention. Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0065] This invention provides a method for switching control of multi-agent secure operation modes and observer coordination under DoS attacks, comprising the following steps:

[0066] Step S1: Obtain the measurable outputs of each agent, the start information of the Denial-of-Service (DoS) attack, the end information of the Denial-of-Service (DoS) attack, and the current communication topology information. The network monitoring layer can generate timestamped monitoring results based on packet confirmation information, link status detection, and topology diagnosis, and send them to each agent via a protected low-speed management channel.

[0067] Step S2: Generate attack event indication based on the Denial-of-Service (DoS) attack start information and Denial-of-Service (DoS) attack end information. Generate connectivity state indicators based on the algebraic connectivity of the current communication topology. .

[0068] , ;otherwise ;

[0069] , ; , ;

[0070] in, This is the Laplace matrix of the currently available communication topology. This indicates that the current attack strategy disrupts the connectivity of the communication graph, corresponding to a valid attack; This indicates that the current communication graph remains connected, corresponding to an attack that is in an idle state or has not disrupted connectivity. Used to describe whether a reported attack event is active. Used to describe whether neighbor feedback is available; the two are not interchangeable.

[0071] Step S3, based on the attack event indication quantity Control the physical operation mode of each intelligent agent After the attack is reported to have begun, each agent shall, within a specified time limit... Within a certain delay, each agent switches from the nominal operating mode to the secure operating mode and maintains the secure operating mode throughout the entire reported attack event; after the reported attack ends, each agent switches from the nominal operating mode to the secure operating mode within a certain timeframe. It returns to the nominal operating mode within a certain delay. The attack strategy switch within the attack event only changes... It does not generate additional physical mode switching.

[0072] The i-th agent uses a continuous-time linear model:

[0073] , ,

[0074] in, ; For state vectors, To control the input, Measurable output; Indicates the nominal operating mode. Indicates a safe operating mode; It can calm you down. Observable. The safe operating mode uses a pre-certified dynamic matrix (A2, B2), whose open-loop divergence growth rate has an upper bound. Less than the upper limit of the nominal operating mode .

[0075] Step S4: Reconstruct the unmeasurable state using a full-order observer that matches the current physical operating mode:

[0076] ,

[0077] Where L1 is the observer gain in the nominal operating mode, and L2 is the observer gain in the safe operating mode. Observation error satisfy .choose make The Hurwitz matrix is ​​used; preferably, the spectral abscissa of the observation error matrix A2-L2C in the safe operation mode is smaller than the spectral abscissa of A2-L1C when using a fixed nominal gain, so as to improve the estimated attenuation rate in the safe operation mode.

[0078] Step S5, in At that time, the relative state information of the i-th agent's neighbors is calculated using the state estimate from the most recent broadcast:

[0079] ,

[0080] in, and These are the most recent trigger times for the i-th agent and the j-th agent, respectively; Let be the adjacency weights of the currently available communication topology. The sampling error of the i-th agent is defined as:

[0081] , ,

[0082] Observation error Continuous evolution and no reset at the trigger time; sampling error The value is reset to zero at the trigger moment. By distinguishing between two types of errors, the observation status feedback and broadcast triggering use the corresponding error information respectively.

[0083] The segmented control input for the i-th agent is:

[0084] , ;

[0085] , ,

[0086] ,

[0087] When an attack event is active but the current attack strategy does not disrupt the connectivity of the communication graph. and Each agent continues to use the safe operating mode to control gain K2 for neighbor feedback; only when Communication-related control inputs are only paused at certain times.

[0088] Step S6, construct a dynamic event triggering function based on the observed state:

[0089] ,

[0090] , , ,

[0091] in, ; The upper bound of the maximum Laplace eigenvalue for all connected and available communication topologies; For dynamic internal variables, initial value Its segmented update rules are as follows:

[0092] , ,

[0093] , ,

[0094] Parameters satisfy , Freezing dynamic internal variables during disconnection prevents them from being driven to negative values ​​when broadcasts are unavailable. Once the communication graph is restored, the triggering rules are reactivated using the current sampling error, relative neighbor status information, and dynamic internal variables.

[0095] Step S7, the next trigger time for the i-th agent is determined as follows:

[0096] ,

[0097] In the asynchronous implementation, the communication layer sets a non-zero minimum processing interval for timestamped broadcast events. Multiple broadcasts occurring simultaneously are treated as a single network event. Updates are performed after triggering. and will Reset to zero.

[0098] The controller and observer parameters can be solved using linear matrix inequalities. For each physical operating mode... ,make Please solve:

[0099] ,

[0100] ,

[0101] in, This is a lower bound on the algebraic connectivity of all available connected communication topologies. , , The solution is obtained. and Then, obtain according to the above relationship. and .

[0102] For any The frequency of Denial-of-Service (DoS) attacks and the effective duration of attacks respectively satisfy the following conditions:

[0103] ,

[0104] ,

[0105] A multi-agent system can achieve resilient consistency under an allowed denial-of-service (DoS) attack when the following conditions are met:

[0106] ,

[0107] in, This is the upper bound of the Lyapunov function jump during physics mode switching. The convergence rate of the connected time interval. These are the upper bounds of the divergence growth rates for the safe operating mode and the nominal operating mode, respectively.

[0108] like Figure 1 , Figure 2 and Figure 3 As shown, the network monitoring layer provides each agent with attack start, attack end, and communication topology connectivity information. The mode switching module, based on... Controlling physical modes The neighbor information module, dynamic event triggering module, and control input generation module are based on... Determine whether neighbor communication and feedback are available. This structure ensures that attack event status and communication availability status apply to different functional modules respectively.

[0109] This embodiment employs a leaderless formation system consisting of five aircraft agents. The state of each agent... ,in For the angle of attack, This refers to the pitch angular velocity; only the angle of attack is measured, therefore... The system matrices for nominal operating mode and safe operating mode are as follows:

[0110] , ,

[0111] , ,

[0112] Mode 2 corresponds to a pre-certified safe operating configuration, which has stronger aerodynamic damping, thus increasing the upper bound of its divergence growth rate. Less than mode 1 .

[0113] like Figure 4 As shown, the communication graphs corresponding to the nominal topology and attack strategies 2 and 3 remain connected, while attack strategy 1 disconnects the communication graph. The nominal topology, attack strategy 2, and attack strategy 3... The values ​​are (1,5), (1,5), and (0.519,4.170) respectively, therefore we take... , .

[0114] Solve the linear matrix inequality of the controller, taking... , ,get:

[0115] ,

[0116] ,

[0117] ,

[0118] ,

[0119] For partial output Select mode-dependent observer gain:

[0120] , ,

[0121] The eigenvalues ​​of A1-L1C are {-8, -6}, and the eigenvalues ​​of A2-L2C are {-12, -10}. If the safe operating mode still uses L1, then the eigenvalue of A2-L1C is -7.65 ± 2.175j. Both observers are stable in mode 2, but L2 has a larger asymptotic decay margin.

[0122] Event trigger parameters , , , , , , , , and .because Therefore, it satisfies .Pick , , and The left-hand side of the elastic consistency condition is -1.3 × 10⁻⁶. -2 , less than zero.

[0123] like Figure 5 As shown, [0.4, 7.4)s represents a reported attack event. Attack strategy 1 applies to [0.4, 2.4) and [3.4, 6.4), attack strategy 2 applies to [2.4, 3.4), and attack strategy 3 applies to [6.4, 7.4). The physical mode switches to the secure operating mode in 0.5s and returns to the nominal operating mode in 7.5s. The fact that the effective range of attack strategy 1 is zero only clearly demonstrates this. , and The separation.

[0124] The initial state and initial observation error of each agent are selected as follows:

[0125] ,

[0126] ,

[0127] make Using a step size of 5×10 -4 The fourth-order Runge-Kutta numerical integration method for s is used for numerical integration in the interval [0, 12]s. When And the observed state is updated and maintained when the event trigger condition is met; when No new events occur from time to time.

[0128] like Figure 6 As shown, after adopting the secure operation mode of this invention, the peak consistency error during the attack event decreased from 1184.222 when the secure operation mode was not adopted to 22.464. The final divergence error decreased from 0.433 to 0.00724; the peak total control input norm decreased from 7914.1 to 177.4, indicating that the safe operation mode can simultaneously suppress divergence growth and control input peak value.

[0129] like Figure 7 As shown, the observation error norm is 0.996 when entering the safe operation mode; after 0.5s, it drops to 0.0045 when using mode correlation gain L2, and is 0.0225 when using L1, indicating that the observer gain matched with the safe operation mode can improve the estimation convergence speed.

[0130] like Figure 8 As shown, when using static event triggering, the number of transmissions for the five agents are 601, 662, 556, 465 and 609 respectively, while when using the dynamic event triggering of this invention, they are reduced to 186, 205, 291, 214 and 205 respectively; the total number of transmissions is reduced from 2893 to 1101, a reduction of 61.9%, while both triggering schemes maintain comparable consistency recovery performance.

[0131] To illustrate that the dynamic internal variable maintains a positive value, let .exist Furthermore, between adjacent trigger times, the triggering rules have... ,and then:

[0132] ,

[0133] By the principle of comparison, if If it is positive at the beginning of a connected interval, it remains positive within any finite connected interval; Within the disconnection interval ,therefore Maintain a constant value. When triggered. Reset to zero and No jump, which can be obtained by induction. By combining the non-zero minimum processing interval of the communication layer, Zeno's behavior that is triggered an infinite number of times within a finite time can be eliminated.

[0134] This invention is not limited to aircraft formations, but can also be applied to mobile robots, unmanned ships, intelligent vehicles, distributed sensors, and networked power equipment. Safe operating modes can be achieved through conservative control envelopes, redundant actuators, derating operating points, or other certified configurations; as long as the attack event state, physical operating mode, and communication connectivity state participate in observation, triggering, and control according to the separation logic of this invention, they all fall under the technical concept of this invention.

[0135] This invention provides a method for controlling the coordinated switching of multi-agent secure operation modes and observers under DoS attacks. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A method for coordinating and switching control of multi-agent safe operation modes and observers under DoS attacks, characterized in that, Includes the following steps: Step S1: Obtain the measurable outputs of each agent, the start information of the denial-of-service (DoS) attack, the end information of the denial-of-service (DoS) attack, and the current communication topology information; Step S2: Generate an attack event indicator based on the Denial-of-Service (DoS) attack start information and Denial-of-Service (DoS) attack end information. Generate connectivity status indicators based on the current communication topology information. And based on the attack event indication quantity Determine the physical operation mode of each intelligent agent The physical operating mode includes a nominal operating mode and a secure operating mode, and the attack event indication quantity... Connectivity status indicator and physical operation mode They are determined independently of each other; Step S3, based on the attack event indication quantity Control the physical operation mode of each intelligent agent After the attack is reported to have begun, each agent shall, within a specified time limit, Within a certain delay, each agent switches from the nominal operating mode to the secure operating mode and maintains the secure operating mode throughout the entire reported attack event; after the reported attack ends, each agent switches from the nominal operating mode to the secure operating mode within a certain timeframe. Return to the nominal operating mode within the delay; Step S4: Reconstruct the unmeasurable state using a full-order observer that matches the current physical operating mode; Step S5, when When, based on the state estimates of each agent's most recent broadcast and the state estimates of neighboring agents' most recent broadcast, the relative state information of neighbors is calculated, and the control input is generated according to the control gain corresponding to the current physical operating mode; when At this time, the communication-related control inputs will be set to zero; Step S6: Calculate the event trigger function based on the sampling error between the current state estimate and the most recently broadcast state estimate, the relative state information of the neighbors, the current physical operation mode, and the dynamic internal variables; Step S7, when And when the event triggering function meets the preset triggering conditions, it broadcasts the current state estimate and updates the most recently broadcast state estimate; when The broadcast is paused and the dynamic internal variables are frozen.

2. The method according to claim 1, characterized in that, Step S2 includes: A Denial-of-Service (DoS) attack includes switching between two or more attack strategies within an attack event; Let be the Laplace matrix of the currently available communication topology, when season ,when season ; Effective attacks that disrupt the connectivity of the communication graph The parameters correspond to an invalid attack that is in an idle state or does not disrupt the connectivity of the communication graph. Used to describe whether a reported attack event is active. , ;otherwise Among them, algebraic connectivity The Laplace matrix represents the currently available communication topology. The second smallest eigenvalue; the attack event indicator d(t) = 1 indicates that the reported attack event is active, and d(t) = 0 indicates that the reported attack event is inactive; interval union symbol. This represents the union of all reported attack event intervals. This indicates the start time of the r-th attack event. The duration of the r-th attack event is represented by t, where t is the system runtime.

3. The control method according to claim 2, characterized in that, Step S3 includes: the dynamic model and measurable output of the i-th agent are as follows: ， ， Where d represents the differential symbol. N is the number of agents participating in consensus control; Let be the true state vector of the i-th agent. To control the input, For measurable output, R represents the real number space. It can calm you down. Observable, Indicates the nominal operating mode. Indicates the safe operating mode; the state matrix under the current physical operating mode. The input matrix used to describe state evolution and the current physical operating mode. Used to describe the effect of control inputs on the state, the measurable output of the i-th agent. The output matrix C is used to map the state vector to a measurable output, which is the output quantity that the sensor can obtain. The state dimension n is the number of components contained in the state vector, and the output dimension m is the number of components contained in the measurable output. respectively Representation pattern The corresponding constant state matrix and constant input matrix, physical operation mode indicator Used to indicate the currently used operating mode.

4. The control method according to claim 3, characterized in that, Step S4 includes: The pattern-related full-order observer for the i-th agent is: ， The nominal operating mode uses observer gain L1, the safe operating mode uses observer gain L2, and makes... Here, Hurwitz matrix represents the observation error of the i-th agent. ,satisfy ; It is the state estimate of the i-th agent; pattern Corresponding observer gain Inject gain into the output error used in the current mode.

5. The control method according to claim 4, characterized in that, Step S5 includes: in At that time, the relative state information of the i-th agent's neighbors is calculated using the state estimate from the most recent broadcast. : ， in, and These are the most recent trigger times for the i-th agent and the j-th agent, respectively. The adjacency weights of the currently available communication topology; It is the set of neighbors of the i-th agent at time t. This indicates that the j-th agent was at the most recently triggered time. Broadcast status estimate; The sampling error of the i-th agent at time t is , .

6. The control method according to claim 5, characterized in that, Step S5 further includes: the control input of the i-th agent is: when hour, ;when hour, ;in, c is the positive coupling coefficient. It is a positive definite matrix corresponding to the physical operation mode; It is the control gain corresponding to the current physical operating mode; This indicates transpose.

7. The control method according to claim 6, characterized in that, Step S6 includes: the event triggering function is: ， in, , , , , The upper bound of the maximum Laplace eigenvalue for all connected and available communication topologies. For dynamic internal variables, the event triggering function of the i-th agent. Used to determine whether to broadcast; It is the positive triggering scale coefficient; It is the sampling error weight; It is the sampling error of the i-th agent; It is a pattern-related weight matrix; It is the relative information weight of neighbors; It is the relative state vector of the neighbors.

8. The control method according to claim 7, characterized in that, In step S6, the dynamic internal variable satisfies: when hour, ;when hour, ;in, , , The next trigger time is and The first moment; It is the decay coefficient of the internal variable of the i-th agent. These are the initial values ​​of the internal variables of the i-th agent; It is the error feedback adjustment coefficient of the i-th agent.

9. The control method according to claim 8, characterized in that, Step S7 includes: the next triggering time of the i-th agent. Determined as: ， Here, inf is the underfum operator; In the asynchronous implementation, the communication layer sets a non-zero minimum processing interval for timestamped broadcast events. Two or more broadcasts occurring simultaneously are treated as the same network event; updates are made after triggering. and will Reset to zero; The controller and observer parameters are solved using linear matrix inequalities for each physical operating mode. ,make Please provide a solution: ， ， in, This is a lower bound on the algebraic connectivity of all available connected communication topologies. , , The solution is obtained and After that, I obtained and Among them, the pattern Corresponding inverse matrix decision variables Lyapunov matrix for controller The inverse matrix; It refers to the controller's attenuation margin; mode. The corresponding controller Lyapunov matrix It is a positive definite matrix; pattern The corresponding observation error Lyapunov matrix It is a positive definite matrix; pattern The corresponding observer-aided decision matrix Used to calculate observer gain; It is the observation error decay rate; For any The frequency of Denial-of-Service (DoS) attacks and the effective duration of attacks respectively satisfy the following conditions: ， ， Among them, the starting time of the statistical interval The attack statistical interval is determined together with the termination time T of the statistical interval. [,T]; Number of attacks This interval represents [ The total number of reported attack events within [T]; upper bound of frequency jitter. For a finite number of permissible instantaneous deviations; average attack interval The lower bound of the average time between adjacent reported attack events; the effective attack time set. This interval represents [ The set measure of all time periods within [T] that cause communication graph disconnection. The effective attack cumulative duration; duration biased upper bound. For the allowable finite initial deviation, It is a parameter for the sparsity of effective attack duration; A multi-agent system can achieve resilient consistency under an allowed denial-of-service (DoS) attack when the following conditions are met: ， in, This is the upper bound of the Lyapunov function jump during physics mode switching. The convergence rate of the connected time interval. These are the upper bounds of the divergence growth rates for the safe operating mode and the nominal operating mode, respectively. It is the upper bound of the nominal operating mode divergence growth rate; It is the upper limit of the growth rate of the divergence in the safe operation mode.

10. A method for controlling the cooperative switching of multi-agent secure operation modes and observers under DoS attacks to implement the method described in any one of claims 1 to 9, characterized in that, Includes the following modules: The network monitoring module is used to output attack start information, attack end information, and communication topology connectivity information; The mode switching module is used to generate attack event indicators and physical operating modes, and to control each agent to switch between the nominal operating mode and the secure operating mode. The state observation module is used to obtain a state estimate based on the measurable output by employing the observer gain corresponding to the current physical operating mode. The neighbor information module is used to calculate the relative state information of neighbors based on the state estimate of the most recent broadcast when the communication topology is connected. The dynamic event triggering module is used to generate a broadcast trigger signal based on sampling error, relative neighbor status information and dynamic internal variables, and to pause triggering and freeze dynamic internal variables when the communication topology is disconnected. The control input generation module is used to generate control inputs corresponding to the current physical operating mode when the communication topology is connected, and to set the communication-related control inputs to zero when the communication topology is disconnected.

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