Resilient asynchronous sampling control method against denial-of-service attacks in networked systems

Abstract

The application belongs to the technical field of communication, and discloses a resilient asynchronous sampling control method for resisting denial of service attacks in a networked system, which adopts resilient asynchronous sampling data control to realize the rapid recovery and stability of the networked system after a DoS attack and the improvement of robustness. During normal operation of the system, the state data of the networked system is continuously monitored and recorded based on an asynchronous sampling strategy. After the DoS attack ends, a preset asynchronous sampling mechanism is triggered immediately, state information is updated rapidly, and control instructions are recalculated, so that the dynamic response and performance of the networked system are recovered. The method combines the asynchronous sampling mechanism, the discontinuous interval dependent functional analysis and the switching stability theory method organically, and cooperatively realizes the rapid communication recovery capability of the networked system after suffering from the DoS attack, and significantly enhances the stability and robustness of the system, and is especially suitable for application scenarios with high security requirements.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to a resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system. Background Technology

[0002] With the widespread application of networked systems in fields such as intelligent transportation, navigation and positioning, broadcasting and communication, and shipborne audiovisual information, the communication stability and security of networked systems are facing severe challenges.

[0003] In networked systems, the communication links between remote sensors and controllers are often highly vulnerable to network threats such as Denial of Service (DoS) attacks. DoS attacks consume large amounts of network resources or create communication congestion, preventing data from being transmitted in a timely manner, leading to information loss or delays, and in severe cases, even causing a complete system shutdown.

[0004] Currently, some traditional control methods have attempted to address the problem of DoS attacks, but they still have significant shortcomings: On the one hand, existing control schemes based on periodic sampling cannot be dynamically adjusted according to the actual network status. Once a DoS attack occurs, continuous packet loss is very likely to occur, causing system response lag and seriously affecting control accuracy and stability. On the other hand, although some event-triggered control methods can save communication resources to a certain extent, they usually ignore the real-time recovery of signal sampling and transmission during a DoS attack, resulting in the system being unable to recover to normal operation in a timely manner after the attack ends, thus prolonging the system recovery time.

[0005] Furthermore, existing methods often fail to adequately consider practical limitations such as limited network bandwidth and communication resources when resisting DoS attacks. Overly idealistic assumptions lead to poor actual deployment results and make it difficult to meet the high requirements for real-time communication and stability in practical application scenarios such as intelligent transportation and shipborne communication.

[0006] Therefore, how to design a control method with strong anti-attack performance, rapid real-time response, and fast recovery capability to effectively resist DoS attacks and ensure the stability and reliability of networked systems has become a key issue that urgently needs to be solved in the current technical field, in order to address the above-mentioned shortcomings of existing methods. Summary of the Invention

[0007] The purpose of this invention is to propose a resilient asynchronous sampling control method for resisting denial-of-service attacks in networked systems. This method can ensure the stability of networked systems even when data is lost due to DoS attacks.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A resilient asynchronous sampling control method for resisting denial-of-service attacks in networked systems includes the following steps:

[0010] Step 1. Deploy multiple asynchronous sampling sensors in the networked system, with each asynchronous sampling sensor using a different sampling period, to continuously monitor the status data of the networked system;

[0011] Step 2. Characterize and model the DoS attack signals to provide a mathematical basis for the subsequent design of a security controller with anti-attack capabilities;

[0012] Step 3. Design a security controller with anti-attack features. It adopts an elastic asynchronous sampling strategy. After the DoS attack is detected and ends, it immediately triggers the asynchronous sampling sensor to start data acquisition, collects the current status data of the networked system, and sends it to the control center.

[0013] Step 4. Perform stability analysis on the networked system under DoS attack controlled by a security controller with anti-attack characteristics, and design a security control gain based on asynchronous sampling secure communication based on the stability criteria of the networked system under DoS attack.

[0014] Step 5. Use a security controller with anti-attack capabilities to control the networked system to ensure its stability after a DoS attack.

[0015] The present invention has the following advantages:

[0016] As described above, this invention discloses a resilient asynchronous sampling control method for resisting denial-of-service attacks in networked systems. This method employs resilient asynchronous sampling data control to achieve rapid recovery and stability of the networked system after a DoS attack, as well as improved robustness. During normal system operation, based on a resilient asynchronous sampling strategy, each asynchronous sampling sensor uses a different sampling period to continuously monitor and record the state data of the networked system. After the DoS attack ends, the asynchronous sampling sensors are immediately triggered to collect the current state data of the networked system and send it to the control center to quickly update the state information and recalculate control commands, thereby restoring the dynamic response and performance of the networked system. This invention utilizes discontinuous interval dependency functionals and switching system stability analysis methods to ensure that the system maintains basic stability during the attack. Through a designed security controller with anti-attack characteristics, the control input is adjusted based on the latest sampled state to ensure rapid convergence of the system state. This invention organically combines asynchronous sampling mechanisms, discontinuous interval dependency functional analysis, and switching stability theory methods to synergistically achieve rapid communication recovery capability of networked systems after a DoS attack, and significantly enhances the stability and robustness of the system, making it particularly suitable for application scenarios with high security requirements. Attached Figure Description

[0017] Figure 1 This is a flowchart of a resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system, as described in an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of the control of the networked system under asynchronous sampling control in this embodiment.

[0019] Figure 3 This is a schematic diagram of the elastic asynchronous sampling scheme under DoS attack in this embodiment.

[0020] Figure 4 This is a schematic diagram of the state response of the networked system in this embodiment.

[0021] Figure 5 The sampling data in this embodiment The response diagram after holding at zero order.

[0022] Figure 6 This is a response diagram of the control input of the networked system in this embodiment.

[0023] Figure 7 This is a schematic diagram showing the sampling times of the two asynchronous sampling sensors in this embodiment. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0025] Example 1

[0026] The present invention proposes an elastic asynchronous sampling data control (RA-SDI) scheme for resisting denial-of-service attacks in networked systems. This scheme can ensure the stability of the networked system even when data is lost due to a denial-of-service (DoS) attack.

[0027] There are two reasons for proposing this invention: First, in practical applications, a multi-sensor-based sampling data control system that supports asynchronous arrival of packet data at the controller port is more practical and flexible. Second, DoS attacks can damage the integrity and availability of sampling data, making it difficult for networked systems to achieve stability.

[0028] For the reasons mentioned above, this invention designs a flexible asynchronous sampling data control scheme to overcome the negative impact of DoS attacks on the system. The method of this invention can send data immediately after a DoS attack, thereby mitigating the performance degradation caused by prolonged periods without input. This invention utilizes the stability analysis concept of switching systems to construct a discontinuous interval correlation function, which combines information from the flexible asynchronous sampling interval and the attack-active interval. Due to the analytical difficulties caused by the discontinuity of the functional, this invention uses discrete-time Lyapunov stability theory, convex combination techniques, and some estimation methods to derive sufficient conditions for mean-square asymptotic stability. This invention also provides a design algorithm for a safety controller based on stability criteria. Finally, this embodiment also provides a simulation example to demonstrate the effectiveness of the results obtained using the control method of this invention.

[0029] like Figure 1 As shown, the resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system includes the following steps:

[0030] Step 1. Deploy multiple asynchronous sampling sensors in the networked system. Each asynchronous sampling sensor uses a different sampling period to continuously monitor the status data of the networked system, so as to realize the asynchronous data perception and flexible adaptation capability of the networked system.

[0031] The networked system model with Markov jump parameters is established as follows:

[0032] .

[0033] in, The state vector representing a networked system is the system state. , to They represent The first to Nth components are the first to Nth state variables, where N represents the number of state variables and is a constant. and It is a constant matrix.

[0034] This indicates the need to design a security controller with attack resistance features. , to They represent The first to the qth components, where q is a constant.

[0035] definition It is a right-continuous continuous-time Markov process. Used to represent the transitions between different modes in a networked system. In a finite set Take the value from, where This indicates the number of system modes.

[0036] Define the transfer rate matrix as ,in Representing modes Transition to mode The transfer rate, , And satisfy , Representing modes Transition to mode The transfer rate.

[0037] The control diagram of a networked system under asynchronous sampling control is shown below. Figure 2 As shown, ZOH is a zero-order hold.

[0038] Suppose that p asynchronous sampling sensors are deployed in a networked system. ,in to Let represent the 1st to the pth asynchronous sampling sensors, where p is a constant. For the system state... Each asynchronous sampling sensor uses a different sampling period. Perform sampling. to Let represent the sampling periods of the 1st to pth asynchronous sampling sensors, respectively, and let the sampling periods satisfy . .

[0039] In other words, system state The group will be divided into p groups, and the number of components in each group will be denoted as follows: These p sets of system states will be assigned to p asynchronous sampling sensors for sampling. Definition Let i represent the state variable sampled by the i-th asynchronous sampling sensor, and have ,in , to These represent the continuous-time system states transmitted to the 1st to the pth asynchronous sampling sensors, respectively.

[0040] Step 2. Characterize and model DoS attack signals to provide a mathematical basis for the design of security controllers with anti-attack capabilities and for stability analysis of networked systems.

[0041] In step 2, the DoS attack signal is characterized and modeled to clarify the attack duration and intermittent characteristics, describe the DoS attack signal so that the subsequent communication system can establish a mathematical model, and provide an accurate mathematical basis for subsequent elastic asynchronous sampling data control.

[0042] DoS attack signals typically exhibit aperiodic characteristics and are energy-limited, introducing... Used to indicate whether a DoS attack has occurred, when This indicates that a DoS attack has occurred. This indicates that no DoS attack has occurred.

[0043] .

[0044] in, , Represents the set of positive integers. This refers to the g-th attack sleep interval, which is also the controller's working interval. Indicates the start time of the DoS attack. This represents the g-th active attack zone.

[0045] This indicates the g-th DoS attack cycle. This indicates the start time of the g-th DoS attack cycle. This indicates the end time of the g-th DoS attack cycle. This represents the control duration of the g-th DoS attack cycle, and satisfies the following condition: .

[0046] This represents the attack duration within the g-th DoS attack cycle. Defined as: .

[0047] definition , ,in This represents the maximum attack time within the g-th DoS attack cycle. This represents the minimum attack time within the g-th DoS attack cycle. It is a supremum function. It is the infimum function.

[0048] Define the minimum working time for the g-th DoS attack cycle. for: .

[0049] definition , , This represents the working range of the g-th controller. This represents the g-th active attack zone.

[0050] To measure the system's resistance to attacks, the maximum resistance ratio is given. for:

[0051] .

[0052] Step 3. Design a security controller with anti-attack features. It adopts a flexible asynchronous sampling strategy. After the DoS attack is detected and ends, it immediately triggers the asynchronous sampling sensor to start data acquisition, collects the current status data of the networked system, and sends it to the control center to quickly restore the communication performance of the networked system.

[0053] In step 3, immediately after the DoS attack is detected and confirmed to have ended, the preset asynchronous sampling sensor is triggered to quickly start data acquisition, collect the latest system status information and send it to the control center to quickly restore the communication performance of the networked system. The controller adopts a state feedback control law during normal periods, i.e., the controller's working interval, and the control input is zero during attack periods, i.e., the attack active interval.

[0054] Specifically, in an ideal communication environment without facing a DoS attack, assume that the i-th asynchronous sampling sensor is... Sampling at the location, , Represents the set of integers. Indicates the i-th asynchronous sampling sensor. The sampling time of the next sample , The state variable of the i-th asynchronous sampling sensor at time i is .

[0055] Design a secure communication controller for:

[0056] .

[0057] in, This represents the security control gain to be designed based on asynchronous sampling secure communication. Let represent the set of sampled states for all state variables, and have . .

[0058] However, when facing a DoS attack, in the active attack zone The sampling data transmission within the system will be interrupted. Therefore, to mitigate the adverse effects of DoS attacks, a resilient asynchronous sampling strategy is designed, as follows:

[0059] .

[0060] in, Indicates the i-th asynchronous sampling sensor The g-th controller operating range The initial sampling time, , Indicates the i-th asynchronous sampling sensor The g-th controller operating range The The sampling time of the next sample Indicates the i-th asynchronous sampling sensor The g-th controller operating range The The sampling time of the next sample.

[0061] To explain the elastic multi-rate sampling scheme more intuitively, assume there are two sensors. and .sensor and The sampling times are respectively as follows Figure 3 (a) and Figure 3 As shown in (b). Wherein, The sampling period is , The sampling period is A diagram illustrating the DoS attack cycle is shown below. Figure 3 As shown in (c).

[0062] To facilitate subsequent stability analysis, all sampling times of the asynchronous sampling sensor will be included. Integrating into a new time series, i.e., the fused time series middle, This represents the nth sampling moment after integration within the g-th DoS attack cycle.

[0063] in, , Integrated time series like Figure 3 As shown in (d), the closed-loop system in the interval will be analyzed within a unified framework. Internal stability.

[0064] Design a security controller with attack resistance to ensure the mean-square asymptotic stability of the system under DoS attack conditions. The attack-resistant security controller adopts a state feedback control law, in which the control input is zero during the active attack range. The state feedback control law is designed as follows:

[0065] .

[0066] in, The security control gain for the asynchronous sampling secure communication based design is determined by stability analysis. This represents the (n+1)th sampling moment after integration within the g-th DoS attack cycle.

[0067] Furthermore, based on the above description, in a DoS attack cycle The closed-loop system is modeled as follows:

[0068] .

[0069] in, This represents the (n+1)th sampling moment after integration within the g-th DoS attack cycle.

[0070] Step 4. Perform stability analysis on the networked system under DoS attack controlled by a security controller with anti-attack characteristics, and design a security control gain based on asynchronous sampling secure communication based on the stability criteria of the networked system under DoS attack.

[0071] for , , , , and security control gain based on asynchronous sampling secure communication ,in and For preset scalar, This is the minimum sampling period for the asynchronous sampling sensor.

[0072] If it exists 3D positive definite matrix , , , and any matrix , , , , , , , , .in, , , , , .

[0073] Make formulas (1) to (5) for and Established, among which Represents the merged time series If the time interval is specified, then the networked system controlled by the security controller with anti-attack characteristics is asymptotically stable.

[0074] Formulas (1) to (5) are expressed as follows:

[0075] (1)

[0076] (2)

[0077] (3)

[0078] (4)

[0079] (5)

[0080] in, Represented as:

[0081] .

[0082] Represented as:

[0083] .

[0084] Represented as:

[0085] .

[0086] Represented as:

[0087] .

[0088] in, Indicates a symmetric term. Represents the sum of symmetrical terms. Representing modes Transition to mode The transfer rate, express 3D positive definite matrix And there are:

[0089] .

[0090] .

[0091] , .

[0092] , .

[0093] , .

[0094] .

[0095] .

[0096] , , .

[0097] , , .

[0098] , , .

[0099] , , .

[0100] .

[0101] in, to They represent Weizhi 1D identity matrix Represents an N-dimensional identity matrix. , express A 2D matrix of all zeros. express A 2D matrix of all zeros. express A 2D matrix of all zeros. express A matrix consisting entirely of zeros.

[0102] Design a security controller with anti-attack features and provide a security control gain design scheme based on asynchronous sampling secure communication to ensure that the networked system can quickly stabilize after being subjected to a DoS attack.

[0103] Based on the established stability criteria for networked systems under DoS attacks, the security control gain based on asynchronous sampling secure communication is designed as follows:

[0104] .

[0105] in, This represents the controller gain after coupling. This represents the matrix to be solved.

[0106] Step 4 also includes performing stability analysis on the networked system controlled by the security controller with anti-attack characteristics, based on the idea of ​​switching system stability analysis, using the Lyapunov functional with discontinuous interval dependence.

[0107] The process of performing stability analysis on a networked system controlled by a security controller with attack resistance features is as follows:

[0108] For networked systems under DoS attacks, Lyapunov functionals with discontinuous interval dependencies are established on the attack dormancy interval and the attack activity interval, respectively.

[0109] Solve weak infinitesimal operators for the Lyapunov functional over the attack dormancy interval according to the system trajectory.

[0110] We solve weak infinitesimal operators for the Lyapunov functional over the active attack region according to the system trajectory.

[0111] By combining weak infinitesimal operators in both the dormant and active attack intervals, conclusions are drawn regarding the stability of the closed-loop system.

[0112] Specifically, the Lyapunov functional is a discontinuous form with interval dependence, reflecting information about the sampling period and the duration of the attack.

[0113] For networked systems under DoS attacks, the specific process of establishing Lyapunov functionals that depend on discontinuous intervals during the attack dormancy and attack activity intervals is as follows:

[0114] Lyapunov functionals for networked systems under DoS attacks Designed as follows:

[0115] .

[0116] in, This represents the (n+1)th sampling moment after integration within the g-th DoS attack cycle. This represents the last sampling time within the working interval of the g-th controller. This represents the first sampling time within the g-th active attack interval.

[0117] In the functional of the above design, and This represents the Lyapunov functional on the attack dormant interval. The Lyapunov functional is used to represent the active attack range, and the stability of the networked system is analyzed through the designed functional.

[0118] .

[0119] .

[0120] .

[0121] in:

[0122] .

[0123] in, Let represent the integration variable, and we have:

[0124] .

[0125] .

[0126] .

[0127] , .

[0128] in, express The system state value at time t. express The system state value at time t. express The system state value at a given time.

[0129] The specific process of solving the weak infinitesimal operator of the Lyapunov functional over the attack dormancy interval according to the system trajectory is as follows:

[0130] In the interval Within, calculate the infinitesimal operator along the system's trajectory. In this section, two cases are considered as follows.

[0131] Scenario 1: Consider In the case of, when hour:

[0132] .

[0133] To simplify the symbols, let's call it:

[0134] .

[0135] in, express The system state at any given moment.

[0136] Calculate along the system's trajectory ,get The estimate is:

[0137] .

[0138] in, Represents the mathematical expectation. express Infinitesimal operators.

[0139] According to formula (1), we have , , , Established, among which express hour The value, express hour The value, express hour The value, express hour The value of .

[0140] According to the convex combination technique, for any The following inequalities hold:

[0141] .

[0142] .

[0143] Therefore, based on the above analysis, we can conclude that:

[0144] .

[0145] in, .

[0146] It is worth noting that in the interval Internal, functional It is continuous and positive definite. Therefore, we obtain:

[0147] .

[0148] in, express exist The Lyapunov functional value at time t. This represents the initial sampling time after integration within the g-th DoS attack cycle. express exist The Lyapunov functional value at time t.

[0149] Scenario 2: Considering ,when When, the functional is chosen as:

[0150] .

[0151] Similar to case one, using convex combination techniques, for any... ,have and Established.

[0152] when and At that time, according to and ,get .

[0153] Therefore, the following inequality holds:

[0154] .

[0155] in, express At any moment The functional value, express At any moment The functional value of .

[0156] when At that time, that is ,have Established.

[0157] According to the convex combination inequality, the following relationship holds:

[0158] .

[0159] in, express exist Time-time functional value.

[0160] The specific process of solving the weak infinitesimal operator for the Lyapunov functional over the active attack region according to the system trajectory is as follows:

[0161] Considering the scenario where a networked system is subjected to a DoS attack, when hour:

[0162] .

[0163] To simplify the symbols, let's call it:

[0164] .

[0165] In the interval Trajectory calculation of the inner edge system ,get The estimates are as follows:

[0166] .

[0167] in, express Infinitesimal operators.

[0168] .

[0169] According to formula (2):

[0170] , .

[0171] have and Established, and obtained through Schur compensation technology. and .

[0172] in, Indicates when hour The value, Indicates when hour The value, Indicates when hour The value, Indicates when hour The value of .

[0173] against , , , ,in Indicates when hour The value, Indicates when hour The value, based on convex combination techniques, for any The following inequalities hold:

[0174] .

[0175] in, .

[0176] Furthermore, we obtain:

[0177] .

[0178] in, for exist The functional value at time , for exist The functional value at time.

[0179] The following steps demonstrate that the solution of the system is asymptotically stable in the mean-square sense. The specific process for deriving the stability conclusion of the closed-loop system by combining weak infinitesimal operators that attack both the dormant and active attack intervals is as follows:

[0180] according to and ,get:

[0181] .

[0182] .

[0183] in, express exist The functional value that approaches the left limit at any given time. for , express exist The functional value that approaches the right limit at any given time. express exist The functional value that approaches the left limit at any given time. express exist The functional value that approaches the right limit at any given time.

[0184] Furthermore, considering the discontinuity of the functional, then exist and The relationship between the moments is established as follows:

[0185] .

[0186] .

[0187] in, express exist The functional value that approaches the left limit at any given time.

[0188] According to the linear matrix inequality shown in formula (5), we have This is true. Therefore, it can be deduced that when... At that time, functional It is continuous and strictly decreasing, therefore, we get:

[0189] .

[0190] in, .

[0191] Due to functional In the interval Since the above is continuous, it can be deduced that:

[0192] .

[0193] It is noted that It is a constant. Therefore, using the squeeze-the-half rule, we obtain:

[0194] .

[0195] according to ,when At that time, we obtained:

[0196] .

[0197] when At that time, we obtained:

[0198] .

[0199] in, .

[0200] Therefore, under a DoS attack, the closed-loop system achieves global asymptotic stability in the mean square sense.

[0201] Step 5. Use a security controller with anti-attack capabilities to control the networked system to ensure its stability after a DoS attack.

[0202] In addition, to verify the effectiveness of the method proposed in this invention, the following specific experiments are also provided:

[0203] In this experiment Set the system parameters as follows:

[0204] , .

[0205] , , .

[0206] Assume there are two asynchronous sampling sensors, the first asynchronous sampling sensor The sampling period is The second asynchronous sampling sensor The sampling period is State variables , Assigned to asynchronous sampling sensor , Assigned to asynchronous sampling sensor .

[0207] Set the DoS parameter to , , Other parameters are set to , Then the resistance to attack is higher. It can be seen that the above parameters meet the conditions.

[0208] .

[0209] The controller gain, i.e., the security control gain based on asynchronous sampling secure communication, is set as follows:

[0210] , .

[0211] Based on the above parameters, let the initial conditions be... for The simulation results are as follows Figures 4 to 7 As shown.

[0212] When the system is under a DoS attack, the system state The time-domain response is as follows Figure 4 As shown, the gray area represents the duration of a DoS attack. Figure 4 It can be seen that the controlled system using the control method of the present invention can still achieve asymptotic stability under DoS attack, indicating that the system has good anti-interference ability.

[0213] Figure 5 The sampling data was displayed. The response plot after zero-order hold, where Represents state variables Passed by sensor Subsequent sampling data, Represents state variables Passed by sensor Subsequent sampling data, Represents state variables Passed by sensor Subsequent sampling data.

[0214] Figure 6 The control input is shown in the image. The response graph, in which Indicates entering the state variable The input signal, Indicates entering the state variable The input signal, Indicates entering the state variable The input signal can be used to determine when a DoS attack is present. The interruption and change to 0 reflects the direct impact of the attack on the system's control input.

[0215] Figure 7 Specifically demonstrating the asynchronous sampling sensor and The sampling time of successful transmission. (Within the time interval) Within this, it can be observed that, through the use of the flexible safety control scheme proposed by the method of this invention, asynchronous sampling sensors... 29 data packets were successfully transmitted from the asynchronous sampling sensor. Sixteen data packets were successfully transmitted. The simulation results not only demonstrate the behavior of the two asynchronous sampling sensors under a DoS attack environment, but also reflect the effectiveness of the method of this invention in dealing with DoS attacks.

[0216] Maximum attack resistance ratio (MAR) is used to evaluate the ability of a network control system to maintain normal operation when subjected to a DoS attack. Therefore, improving the MAR is of great significance for enhancing the robustness of network control systems.

[0217] according to By definition, we get:

[0218] .

[0219] When fixed parameters , , Adjustable parameters Compared to maximum resistance to attack The quantitative relationship, with The increase in the maximum resistance to attack ratio Gradually decrease.

[0220] This invention provides a resilient asynchronous sampling data control method for networked systems to resist Denial-of-Service (DoS) attacks. This method rapidly restores the data sampling and controller interaction process after a DoS attack, enabling timely updates of system state information and accurate application of control commands, thereby quickly restoring the system's communication performance. Specifically, this method designs a controller suitable for asynchronous sampling data. This controller can perform real-time calculations and adjustments based on the actually sampled system state data, effectively addressing communication interruptions and data loss caused by DoS attacks, significantly improving system stability and robustness. This invention comprehensively utilizes theoretical tools such as discontinuous interval dependency functionals and switched system stability analysis to guide the design of the asynchronous sampling data controller, ultimately realizing a practically feasible control algorithm. This invention can enhance the security of industrial control systems and is highly suitable for integration into modern power automation infrastructure to improve network physical resilience.

[0221] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A resilient asynchronous sampling control method for resisting denial-of-service attacks in networked systems, characterized in that, Includes the following steps: Step 1. Deploy multiple asynchronous sampling sensors in the networked system, with each asynchronous sampling sensor using a different sampling period, to continuously monitor the status data of the networked system; Step 2. Characterize and model the DoS attack signals to provide a mathematical basis for the subsequent design of a security controller with anti-attack capabilities; Step 3. Design a security controller with anti-attack features. It adopts an elastic asynchronous sampling strategy. After the DoS attack is detected and ends, it immediately triggers the asynchronous sampling sensor to start data acquisition, collects the current status data of the networked system, and sends it to the control center. Step 4. Perform stability analysis on the networked system under DoS attack controlled by a security controller with anti-attack characteristics, and design a security control gain based on asynchronous sampling secure communication based on the stability criteria of the networked system under DoS attack. Step 5. Use a security controller with anti-attack capabilities to control the networked system to ensure its stability after a DoS attack. Step 3 specifically involves: In an ideal communication environment without facing a DoS attack, assume that the i-th asynchronous sampling sensor is... Sampling was conducted at various locations, including p is a constant. , Represents the set of integers. to These represent the sampling periods of the 1st to the pth asynchronous sampling sensors, respectively. Indicates the i-th asynchronous sampling sensor. The sampling time of the next sample , The state variable sampled by the i-th asynchronous sampling sensor at time i is ; Design a secure communication controller for: ； in, This represents the security control gain to be designed based on asynchronous sampling secure communication. Let represent the set of sampled states for all state variables, and have . ; When facing a DoS attack, in the attack's active range The sampling data transmission within the system will be interrupted. To mitigate the adverse effects of a DoS attack, a resilient asynchronous sampling strategy is designed as follows: ； in, This indicates the start time of the g-th DoS attack cycle. This indicates the end time of the g-th DoS attack cycle. Indicates the i-th asynchronous sampling sensor The g-th controller operating range The initial sampling time, , Indicates the i-th asynchronous sampling sensor The g-th controller operating range The The sampling time of the next sample Indicates the i-th asynchronous sampling sensor The g-th controller operating range The The sampling time of the next sample; All sampling moments of the asynchronous sampling sensor Integrating into a new time series, i.e., the fused time series middle, This represents the nth sampling moment after integration within the g-th DoS attack cycle; in, , , This indicates the duration of control during the g-th DoS attack cycle; Design a security controller with attack resistance to ensure the mean-square asymptotic stability of the networked system under DoS attack conditions. The attack-resistant security controller adopts a state feedback control law, in which the control input is zero during the active attack range. The state feedback control law is designed as follows: ； in, This represents the (n+1)th sampling moment after integration within the g-th DoS attack cycle; During the g-th DoS attack cycle The closed-loop system is modeled as follows: ； in, The state vector representing a networked system is the system state. and It is a constant matrix.

2. The resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 1, characterized in that, Step 1 specifically involves: The networked system model with Markov jump parameters is established as follows: ； in, , to They represent The first to Nth components, where N is a constant; This indicates the need to design a security controller with attack resistance features. , to They represent The first to the qth components, where q is a constant; definition It is a right-continuous continuous-time Markov process. Used to represent the transitions between different modes in a networked system. In a finite set Take the value from, where Indicates the number of system modes; Define the transfer rate matrix as ,in Representing modes Transition to mode The transfer rate, , And satisfy , Representing modes Transition to mode The transfer rate; Suppose that p asynchronous sampling sensors are deployed in a networked system. ,in to These represent the 1st to the pth asynchronous sampling sensors, respectively. Regarding system status Each asynchronous sampling sensor uses a different sampling period. Sampling is performed, and the sampling period meets the requirements. ; System status The group is divided into p groups, and the number of components in each group is denoted as follows: The p groups of system states are assigned to p asynchronous sampling sensors for sampling; definition express If the state variable is sampled by the i-th asynchronous sampling sensor at time i, then: 。 3. The elastic asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 2, characterized in that, Step 2 specifically involves: Introduction Used to indicate whether a DoS attack has occurred, when This indicates that a DoS attack has occurred. This indicates that no DoS attack has occurred. ； in, , Represents the set of positive integers. This refers to the g-th attack sleep interval, which is also the controller's working interval. Indicates the start time of the DoS attack. This represents the g-th active attack zone; This indicates the g-th DoS attack cycle, and the following condition is met: ; This represents the attack duration within the g-th DoS attack cycle. Defined as: ; definition , ,in This represents the maximum attack time within the g-th DoS attack cycle. This represents the minimum attack time within the g-th DoS attack cycle. It is a supremum function. It is the infimum function; Define the minimum working time for the g-th DoS attack cycle. for: ; definition , , This represents the working range of the g-th controller. This represents the active attack zone of the g-th attack. Get the maximum resistance to attack ratio for: 。 4. The elastic asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 3, characterized in that, Step 4 specifically involves: for , , , , and security control gain based on asynchronous sampling secure communication ,in and For preset scalar, This is the minimum sampling period for the asynchronous sampling sensor; If it exists 3D positive definite matrix , , , and any matrix , , , , , , , , ; in, , , ; Make formulas (1) to (5) for and Established, among which Represents the merged time series The time interval indicates that the networked system controlled by the security controller with anti-attack characteristics is asymptotically stable. Formulas (1) to (5) are expressed as follows: (1) (2) (3) (4) (5) in, Represented as: ； Represented as: ； Represented as: ； Represented as: ； in, Indicates a symmetric term. Represents the sum of symmetrical terms. Representing modes Transition to mode The transfer rate, express 3D positive definite matrix And there are: ； ； ， ； ， ； ， ； ； ； ， ， ； ， ， ； ， ， ； ， ， ； ； in, to They represent Weizhi 1D identity matrix Represents an N-dimensional identity matrix. , express A 2D matrix of all zeros. express A 2D matrix of all zeros. express A 2D matrix of all zeros. express A matrix of all zeros; The security control gain based on asynchronous sampling secure communication is designed as follows: ； in, This represents the controller gain after coupling.

5. The elastic asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 4, characterized in that, Step 4 also includes performing stability analysis on a networked system controlled by a security controller with anti-attack characteristics, based on the idea of ​​switching system stability analysis, using a discontinuous interval-dependent Lyapunov functional. The process of performing stability analysis on a networked system controlled by a security controller with attack resistance features is as follows: For networked systems under DoS attacks, Lyapunov functionals that depend on discontinuous intervals on attack dormancy intervals and attack activity intervals are established respectively. Solve for infinitesimal operators of the Lyapunov functional over the attack dormancy interval according to the system trajectory; Solve for infinitesimal operators of the Lyapunov functional over the active attack region according to the system trajectory; By combining the infinitesimal operators of the attack dormant interval and the attack active interval, the stability of the closed-loop system is determined.

6. The resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 5, characterized in that, For networked systems under DoS attacks, the specific process of establishing Lyapunov functionals that depend on discontinuous intervals during the attack dormancy and attack activity intervals is as follows: Lyapunov functionals for networked systems under DoS attacks Designed as follows: ； in, This represents the last sampling time within the working interval of the g-th controller. This represents the first sampling time within the g-th active attack interval; and This represents the Lyapunov functional on the attack dormant interval. Represents the Lyapunov functional over the active attack region; ； ； ； in: ； And there are: ； ； ； ， ； in, express The system state value at time t. express The system state value at time t. express The system state value at a given time.

7. The resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 6, characterized in that, The specific process of solving for the infinitesimal operator of the Lyapunov functional over the attack dormancy interval according to the system trajectory is as follows: In the interval Within, calculate the infinitesimal operator along the system's trajectory. ; consider In the case of, when hour: ； To simplify the symbols, let's call it: ； in, express The system state at any given moment; Calculate along the system's trajectory ,get The estimate is: ； in, Represents the mathematical expectation. express Infinitesimal operators; According to formula (1), we have , , , Established, among which express hour The value, express hour The value, express hour The value, express hour The value; According to the convex combination technique, for any The following inequalities hold: ； ； get: ； in, ; In the interval Lyapunov functionals It is continuous and positive definite, so we get: ； in, express exist The Lyapunov functional value at time t. This represents the initial sampling time after integration within the g-th DoS attack cycle. express exist The Lyapunov functional value at time t; Considering ,when When choosing, the Lyapunov functional is: ； Using convex combination techniques, for any ,have and Established; when and At that time, according to and ,get ; The following inequalities hold: ； in, express At any moment The Lyapunov functional value, express At any moment The Lyapunov functional value; when At that time, that is ,have Established; According to the convex combination inequality, the following relationship holds: 。 8. The resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 7, characterized in that, The specific process of solving for the infinitesimal operator of the Lyapunov functional over the active attack region according to the system trajectory is as follows: Considering the scenario where a networked system is subjected to a DoS attack, when hour: ； To simplify the symbols, let's call it: ； In the interval Trajectory calculation of the inner edge system ,get The estimates are as follows: ； in, express Infinitesimal operators; ； According to formula (2): ， ； have and Established, and obtained through Schur compensation technology. and ; in, Indicates when hour The value, Indicates when hour The value, Indicates when hour The value, Indicates when hour The value; against , , , ,in Indicates when hour The value, Indicates when hour The value, based on convex combination techniques, for any The following inequalities hold: ； in, ; get: ； in, for exist The Lyapunov functional value at time t. for exist The Lyapunov functional value at time t.

9. The resilient asynchronous sampling control method for resisting denial-of-service attacks in a networked system according to claim 8, characterized in that, The process of deriving the stability conclusion of the closed-loop system by combining the infinitesimal operators of the attack dormancy interval and the attack activity interval is as follows: according to and ; get ; ； in, express exist The Lyapunov functional value that approaches the left limit at any given time. for , express exist The Lyapunov functional value that approaches the right limit at any time. express exist The Lyapunov functional value that approaches the left limit at any given time. express exist The Lyapunov functional value that approaches the right limit at any time; Considering the discontinuity of Lyapunov functionals, then exist and The relationship between the moments is established as follows: ； ； in, express exist The Lyapunov functional value that approaches the left limit at any time; According to formula (5), we have Established; Therefore when At that time, Lyapunov functionals It is continuous and strictly decreasing, resulting in: ； in, ; Due to Lyapunov functionals In the interval Since the above is continuous, we can deduce that: ； Assuming it is a constant, using the squeeze rule, we obtain: ； according to ,when At that time, we obtained: ； when At that time, we obtained: ； in, ; Under a DoS attack, the closed-loop system achieves global asymptotic stability in the mean square sense.

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