Elastic asynchronous sampling control method for resisting denial of service attack in networked system

Abstract

The invention belongs to the technical field of communication, and discloses an elastic asynchronous sampling control method for resisting denial of service attack in a networked system, which adopts elastic asynchronous sampling data control to realize quick recovery and stability of the networked system after DoS attack and improvement of robustness. And during normal operation of the system, continuously monitoring and recording state data of the networked system based on an asynchronous sampling strategy. And after the DoS attack is finished, a preset asynchronous sampling mechanism is triggered immediately, state information is updated quickly, and a control instruction is calculated again, so that the dynamic response and performance of the networked system are recovered. According to the method, an asynchronous sampling mechanism, discontinuous interval dependency functional analysis and a switching stability theory method are organically combined, the rapid communication recovery capability of a networked system after the networked system is attacked by DoS is cooperatively realized, the stability and robustness of the system are remarkably enhanced, and the method is particularly suitable for application scenes with high security requirements.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a resilient asynchronous sampling control method for resisting denial of service attacks in a networked system. Background Art

[0002] With the widespread application of networked systems in intelligent transportation, navigation and positioning, broadcast communications, shipborne audio-visual information and other fields, the communication stability and security of networked systems face severe challenges.

[0003] In networked systems, the communication links between remote sensors and controllers are often vulnerable to network threats such as denial of service (DoS) attacks. DoS attacks occupy a large amount of network resources or cause communication congestion, preventing timely data transmission, leading to information loss or delays, and in severe cases, even complete system failure.

[0004] At present, some traditional control methods have attempted to solve the problem of DoS attacks, but there are still significant shortcomings: on the one hand, the existing control schemes based on periodic sampling cannot be dynamically adjusted according to the actual network status. Once a DoS attack occurs, continuous data packet loss is very likely to occur, causing system response lag, 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 problem of signal sampling and transmission during the DoS attack, resulting in the system being unable to return to normal operation in time after the attack, which prolongs the system recovery time.

[0005] In addition, existing methods often fail to fully 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 communication real-time and stability in actual application scenarios such as intelligent transportation and shipboard communications.

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

[0007] The purpose of the present invention is to propose a resilient asynchronous sampling control method for networked systems to resist denial of service attacks, which can ensure the stability of the networked system when data is lost due to DoS attacks.

[0008] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions: A resilient asynchronous sampling control method for resisting denial of service attacks in a networked system includes the following steps: 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. Step 2. Characterize and model the DoS attack signal to provide a mathematical foundation for the subsequent design of a security controller with anti-attack features. Step 3. Design a security controller with attack resistance. This controller uses a flexible asynchronous sampling strategy. Once a DoS attack is detected, it immediately triggers asynchronous sampling sensors to start data collection. This controller collects the current networked system status data and sends it to the control center. Step 4. Perform stability analysis on the networked system controlled by the security controller with anti-attack characteristics under DoS attacks, and design a security control gain based on asynchronous sampling secure communication based on the stability criterion of the networked system under DoS attacks. Step 5. Use a security controller with anti-attack features to control the networked system to ensure that the networked system remains stable after a DoS attack.

[0009] The present invention has the following advantages: As described above, the present invention describes a resilient asynchronous sampling control method for networked systems to resist denial of service attacks. This method uses 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 the control instructions, thereby restoring the dynamic response and performance of the networked system. The present invention utilizes discontinuous interval dependence functionals and switching system stability analysis methods to ensure that the system remains basically stable during the attack. A designed security controller with anti-attack characteristics adjusts the control input based on the latest sampled state to ensure rapid convergence of the system state. The present method organically combines the asynchronous sampling mechanism, discontinuous interval dependence functional analysis, and switching stability theory methods to collaboratively achieve the rapid communication recovery capability of the networked system after a DoS attack, and significantly enhance the stability and robustness of the system. It is particularly suitable for application scenarios with high security requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 This is a flow chart of a flexible asynchronous sampling control method for resisting denial of service attacks in a networked system according to an embodiment of the present invention.

[0011] Figure 2 Schematic diagram of the control of the networked system under asynchronous sampling control in the embodiment of the present invention.

[0012] Figure 3 Schematic diagram of the elastic asynchronous sampling scheme under DoS attack in the embodiment of the present invention.

[0013] Figure 4 Schematic diagram of the state response of the networked system in the embodiment of the present invention.

[0014] Figure 5 For the sampling data in this embodiment Response plot after zero-order hold.

[0015] Figure 6 This is a response diagram of the control input of the networked system in the embodiment of the present invention.

[0016] Figure 7 Schematic diagram of the sampling timing of two asynchronous sampling sensors in the embodiment of the present invention. DETAILED DESCRIPTION

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 The present invention provides a resilient asynchronous sampling control method for resisting denial of service attacks in a networked system, and proposes a resilient asynchronous sampling data control RA-SDI scheme, which can ensure the stability of the networked system even when data is lost due to a denial of service (DoS) attack.

[0018] The method proposed in this paper is based on two reasons: First, in practical applications, a multi-sensor sampled data control system that supports asynchronous arrival of packet data at the controller port is more practical and flexible. Second, DoS attacks can destroy the integrity and availability of sampled data, making it difficult for networked systems to achieve stability.

[0019] In view of the above reasons, the present invention designs a flexible asynchronous sampling data control scheme to overcome the negative impact of DoS attacks on the system. The method of the present invention can send data once immediately after a DoS attack, thereby alleviating the performance degradation caused by long-term no input. The method of the present invention utilizes the stability analysis idea of ​​the switching system to construct a discontinuous interval correlation function, which combines the information of the flexible asynchronous sampling interval and the attack active interval. Due to the analysis difficulties caused by the discontinuity of the functional, the present invention uses discrete-time Lyapunov stability theory, convex combination technology and some estimation methods to derive sufficient conditions for mean square asymptotic stability. The method of the present invention also provides a design algorithm for a safety controller based on the stability criterion. Finally, a simulation example is also provided in this embodiment to demonstrate the effectiveness of the results obtained using the control method of the present invention.

[0020] like Figure 1 As shown, the elastic asynchronous sampling control method for resisting denial of service attacks in a networked system includes the following steps: 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 to achieve asynchronous data perception and elastic adaptability of the networked system.

[0021] The networked system model with Markov jump parameters is established as: .

[0022] in, The state vector representing the networked system is the system state, , to Respectively The 1st to Nth components of are the 1st to Nth state variables, where N represents the number of state variables and is a constant. and is a constant matrix.

[0023] It means that a security controller with anti-attack characteristics needs to be designed. , to Respectively The 1st to qth components of , where q is a constant.

[0024] definition is a right-continuous continuous-time Markov process, Used to represent the transition between different modes of a networked system. In a finite set The value in Indicates the number of system modes.

[0025] Define the transfer rate matrix as ,in Indicates modality Transfer to modal The transfer rate, , , and satisfies , Indicates modality Transfer to modal transfer rate.

[0026] The control diagram of the networked system under asynchronous sampling control is as follows: Figure 2 As shown, where ZOH is the zero-order holder.

[0027] Assume that there are p asynchronous sampling sensors deployed in the networked system ,in to Represent the 1st to pth asynchronous sampling sensors respectively, and p is a constant. , each asynchronous sampling sensor has a different sampling period Take samples, to Respectively represent the sampling periods of the 1st to pth asynchronous sampling sensors, and the sampling periods satisfy .

[0028] That is, the system status Will be divided into p groups, and the number of components in each group is recorded as , these p groups of system states will be assigned to p asynchronous sampling sensors for sampling. Definition Represents the state variable sampled by the i-th asynchronous sampling sensor, ,in , to are the continuous-time system states transmitted to the 1st to pth asynchronous sampling sensors respectively.

[0029] Step 2. Characterize and model the DoS attack signal to provide a mathematical foundation for the subsequent design of a security controller with anti-attack characteristics and stability analysis of networked systems.

[0030] In step 2, the DoS attack signal is characterized and a model is constructed to clarify the attack duration and intermittent characteristics. The DoS attack signal is described to facilitate the establishment of a mathematical model for the subsequent communication system and provide an accurate mathematical basis for subsequent elastic asynchronous sampling data control.

[0031] DoS attack signals usually exhibit non-periodic characteristics and are energy-limited. Used to indicate whether a DoS attack occurs. It indicates a DoS attack. When , it means that no DoS attack has occurred, that is: .

[0032] in, , represents the set of positive integers, is the g-th attack sleep interval, i.e., the controller working interval, Indicates the time when the DoS attack starts. is the gth attack active interval.

[0033] Indicates the g-th DoS attack cycle, Indicates the start time of the g-th DoS attack cycle, Indicates the end time of the g-th DoS attack cycle, Indicates the control duration of the g-th DoS attack cycle, and meets the following conditions: .

[0034] Indicates the attack time in the gth DoS attack cycle, Defined as: .

[0035] definition , ,in Indicates the maximum attack time in the g-th DoS attack cycle, Indicates the minimum attack time in the g-th DoS attack cycle, is the supremum function, is the infimum function.

[0036] Define the minimum working time of the gth DoS attack cycle for: .

[0037] definition , , represents the g-th controller working range, Indicates the gth attack active interval.

[0038] In order to measure the system's anti-attack capability, the maximum anti-attack ratio is given. for: .

[0039] Step 3. Design a security controller with attack resistance. This controller uses a flexible asynchronous sampling strategy. After detecting the end of the DoS attack, it immediately triggers the asynchronous sampling sensor to start data collection. The controller collects the current networked system status data and sends it to the control center to quickly restore the networked system's communication performance.

[0040] In step 3, immediately after the DoS attack is detected and confirmed to be over, the preset asynchronous sampling sensor is triggered to quickly start data collection, 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 the state feedback control law during the normal period, that is, the controller working range, and the control input is zero during the attack period, that is, the attack active range.

[0041] Specifically, in an ideal communication environment without DoS attacks, assuming that the i-th asynchronous sampling sensor is Sampling at , represents a set of integers, Indicates the i-th asynchronous sampling sensor The sampling time of the sub-sampling, , The state variable of the i-th asynchronous sampling sensor at time is .

[0042] Designing a secure communications controller for: .

[0043] in, represents the safety control gain to be designed based on asynchronous sampling safety communication, represents the sampling state set of all state variables, and there is .

[0044] However, when facing a DoS attack, during the active attack period The sampling data transmission within will be interrupted. Therefore, in order to cope with the adverse effects of DoS attacks, a resilient asynchronous sampling strategy is designed as follows: .

[0045] in, Represents the i-th asynchronous sampling sensor In the gth controller working range The initial sampling time, , Represents the i-th asynchronous sampling sensor In the gth controller working range No. The sampling time of the sub-sampling, Represents the i-th asynchronous sampling sensor In the gth controller working range No. The sampling time of the subsampling.

[0046] To explain the elastic multi-rate sampling scheme more intuitively, assume that there are two sensors and .sensor and The sampling times are as follows: Figure 3 (a) and Figure 3 (b). Among them, The sampling period is , The sampling period is The schematic diagram of the DoS attack cycle is as follows: Figure 3 (c) shown.

[0047] In order to facilitate the subsequent stability analysis, all sampling moments of the asynchronous sampling sensor are Integrate into a new time series, namely the fused time series middle, Indicates the nth sampling time after integration in the gth DoS attack cycle.

[0048] in, , The integrated time series like Figure 3 (d) is shown. The closed-loop system in the interval Internal stability.

[0049] A security controller with anti-attack characteristics is designed to ensure the mean square asymptotic stability of the system under DoS attacks. The security controller with anti-attack characteristics adopts a state feedback control law, whose control input is zero in the active attack interval. The state feedback control law is designed as follows: .

[0050] in, is the safety control gain based on asynchronous sampling safety communication to be designed, which is determined by stability analysis. It represents the n+1th sampling time after integration in the gth DoS attack cycle.

[0051] Furthermore, according to the above description, in a DoS attack cycle Internally, the closed-loop system is modeled as: .

[0052] in, It represents the n+1th sampling time after integration in the gth DoS attack cycle.

[0053] Step 4. Perform stability analysis on the networked system under DoS attack controlled by the security controller with anti-attack characteristics, and design a security control gain based on asynchronous sampling secure communication based on the stability criterion of the networked system under DoS attack.

[0054] for 、 、 、 、 and safety control gain based on asynchronous sampling safety communication ,in and is the preset scalar, The minimum sampling period of the asynchronous sampling sensor.

[0055] If exists -dimensional positive definite matrix 、 、 、 and any matrix 、 、 、 、 、 、 、 、 .in, , , , , .

[0056] So that formula (1) to formula (5) are and Established, of which Represents the fused time series If the time interval is , the networked system controlled by the security controller with anti-attack characteristics is mean square asymptotically stable.

[0057] Formula (1) to Formula (5) are expressed as: (1) (2) (3) (4) (5) in, Expressed as: .

[0058] Expressed as: .

[0059] Expressed as: .

[0060] Expressed as: .

[0061] in, represents the symmetric term, represents the sum of symmetric terms, Indicates modality Transfer to modal The transfer rate, express -dimensional positive definite matrix, , and there is: .

[0062] .

[0063] , .

[0064] , .

[0065] , .

[0066] .

[0067] .

[0068] , , .

[0069] , , .

[0070] , , .

[0071] , , .

[0072] .

[0073] in, to Respectively Weizhi dimensional unit matrix, represents the N-dimensional unit matrix, , express dimensional all-zero matrix, express dimensional all-zero matrix, express dimensional all-zero matrix, express dimensional all-zero matrix.

[0074] A security controller with anti-attack characteristics is designed, and a security control gain design scheme based on asynchronous sampling secure communication is given to ensure that the networked system can quickly stabilize after suffering a DoS attack.

[0075] According to the established stability criterion for networked systems under DoS attacks, the security control gain based on asynchronous sampling secure communication is designed as: .

[0076] in, represents the controller gain after coupling, Represents the matrix to be solved.

[0077] Step 4 also includes stability analysis of the networked system controlled by the security controller with anti-attack characteristics based on the idea of ​​switching system stability analysis and the use of discontinuous interval dependent Lyapunov functional.

[0078] The process of stability analysis of a networked system controlled by a security controller with anti-attack characteristics is as follows: For the networked system under DoS attack, a discontinuous interval-dependent Lyapunov functional is established on the attack dormant interval and the attack active interval respectively.

[0079] The weak infinitesimal operator is solved for the Lyapunov functional on the attack dormant interval according to the system trajectory.

[0080] The weak infinitesimal operator is solved for the Lyapunov functional on the attack active interval according to the system trajectory.

[0081] By synthesizing the weak infinitesimal operators of the attack dormant interval and the attack active interval, the stability conclusion of the closed-loop system is obtained.

[0082] Specifically, the Lyapunov functional is an interval-dependent discontinuous form that reflects the information of the sampling period and the attack duration.

[0083] For a networked system under DoS attack, the process of establishing the discontinuous interval-dependent Lyapunov functional on the attack dormant interval and the attack active interval is as follows: For networked systems under DoS attacks, Lyapunov functional Designed to: .

[0084] in, represents the n+1th sampling time after integration in the gth DoS attack cycle, represents the last sampling moment in the working interval of the g-th controller, Indicates the first sampling time in the gth attack active interval.

[0085] In the functional designed above, and represents the Lyapunov functional on the attack dormant interval, It represents the Lyapunov functional on the attack active interval, and the stability of the networked system is analyzed through the designed functional.

[0086] .

[0087] .

[0088] .

[0089] in: .

[0090] in, represents the integration variable, and we have: .

[0091] .

[0092] .

[0093] , .

[0094] in, express The system status value at the moment, express The system status value at the moment, express The system status value at a certain moment.

[0095] The specific process of solving the weak infinitesimal operator for the Lyapunov functional on the attack dormant interval according to the system trajectory is as follows: In the interval Inside, compute the infinitesimal operator along the trajectory of the system In this section, two cases are considered as follows.

[0096] Case 1: Consider In the case of hour: .

[0097] To simplify the notation, let: .

[0098] in, express The system status at a moment.

[0099] Calculate along the trajectory of the system ,get The estimate is: .

[0100] in, represents the mathematical expectation, express Infinitesimal operator.

[0101] According to formula (1), we have 、 、 、 Established, of which express hour The value of express hour The value of express hour The value of express hour The value of .

[0102] According to the convex combination technique, for any , the following inequality holds: .

[0103] .

[0104] Therefore, according to the above analysis, we can get: .

[0105] in, .

[0106] It is worth noting that in the interval Internal functional is continuous and positive definite. Therefore, we have: .

[0107] in, express exist The Lyapunov functional value at time , represents the initial sampling time after integration in the g-th DoS attack cycle, express exist The Lyapunov functional value at time .

[0108] Case 2: Considering ,when When , the functional is selected as: .

[0109] Similar to case 1, using convex combination technology, for any ,have and Established.

[0110] when and When, according to and ,get .

[0111] Therefore, the following inequality holds: .

[0112] in, express At the moment The functional value of express At the moment Functional value of .

[0113] when When ,have Established.

[0114] According to the convex combination inequality, the following relationship holds: .

[0115] in, express exist Time functional value.

[0116] The specific process of solving the weak infinitesimal operator for the Lyapunov functional on the attack active interval according to the system trajectory is as follows: Consider the case where a networked system is attacked by DoS. hour: .

[0117] To simplify the notation, let: .

[0118] In the interval Trajectory calculation of inner edge system ,get The estimates are as follows: .

[0119] in, express Infinitesimal operator.

[0120] .

[0121] According to formula (2), we can get: , .

[0122] have and Established, with the help of Schur complement technology, we get and .

[0123] in, Indicates when hour The value of Indicates when hour The value of Indicates when hour The value of Indicates when hour The value of .

[0124] against 、 、 、 ,in Indicates when hour The value of Indicates when hour The value of , based on the convex combination technique, for any The following inequality holds: .

[0125] in, .

[0126] Further, we get: .

[0127] in, for exist Functional value at time, for exist Functional value at time.

[0128] The following steps prove that the solution of the system is asymptotically stable in the mean square sense. The weak infinitesimal operators of the attack dormant interval and the attack active interval are synthesized to draw the conclusion on the stability of the closed-loop system: according to and ,get: .

[0129] .

[0130] in, express exist The functional value that always approaches the left limit, for , express exist The functional value that always approaches the right limit, express exist The functional value that always approaches the left limit, express exist The functional value always approaches the right limit.

[0131] In addition, considering the discontinuity of the functional, exist and The relationship between the moments is established as follows: .

[0132] .

[0133] in, express exist The functional value tends to the left limit at all times.

[0134] According to the linear matrix inequality shown in formula (5), we have Therefore, it can be deduced that When the functional is continuous and strictly decreasing, so we get: .

[0135] in, .

[0136] Because the functional In the interval is continuous, so we can deduce that: .

[0137] Notice that is a constant. Therefore, using the two-sides rule we get: .

[0138] according to ,when When , we get: .

[0139] when When , we get: .

[0140] in, .

[0141] Therefore, under DoS attacks, the closed-loop system achieves global asymptotic stability in the mean square sense.

[0142] Step 5. Use a security controller with anti-attack features to control the networked system to ensure that the networked system remains stable after a DoS attack.

[0143] In addition, in order to verify the effectiveness of the method proposed in the present invention, the following specific experiments are given: In this experiment , set the system parameters as follows: , .

[0144] , , .

[0145] 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 sensors , Assigned to asynchronous sampling sensors .

[0146] Set the DoS parameter to , , , and other parameters are set to , . Then the anti-attack ratio , it can be seen that the above parameters meet the conditions.

[0147] .

[0148] The controller gain, i.e., the safety control gain based on asynchronous sampling safety communication, is set as: , .

[0149] According to the above parameters, the initial conditions are for , the simulation results are as follows Figures 4 to 7 shown.

[0150] When the system is under DoS attack, the system status The time domain response of Figure 4 As shown in the figure, the gray area represents the duration of the 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 attacks, indicating that the system has good anti-interference ability.

[0151] Figure 5 Shows sample data Response diagram after zero-order hold, where Represents state variables Passing sensor After the sampling data, Represents state variables Passing sensor After the sampling data, Represents state variables Passing sensor The sampled data after .

[0152] Figure 6 The control input is shown in Response plot of Indicates entry into state variables The input signal, Indicates entry into state variables The input signal, Indicates entry into state variables The input signal shows that when there is a DoS attack, is interrupted and becomes 0, reflecting the direct impact of the attack on the system control input.

[0153] Figure 7 Specifically demonstrates the asynchronous sampling sensor and The sampling moment of successful transmission. It can be observed that by using the elastic safety control scheme proposed by the method of the present invention, the asynchronous sampling sensor 29 packets transmitted successfully, asynchronous sampling sensor 16 data packets were successfully transmitted. The simulation results not only show the operation of two asynchronous sampling sensors under DoS attack environment, but also reflect the effectiveness of the proposed method in dealing with DoS attacks.

[0154] The maximum attack resistance ratio is used to evaluate the ability of a network control system to maintain normal operation when subjected to a DoS attack. Therefore, improving the maximum attack resistance ratio is of great significance to enhancing the robustness of the network control system.

[0155] according to The definition of , we get: .

[0156] When fixed parameters 、 、 When the adjustable parameters Ratio to maximum anti-attack The quantitative relationship between The increase of the maximum anti-attack ratio Gradually decrease.

[0157] The present invention provides a resilient asynchronous sampling data control method suitable for networked systems that is resistant to denial of service (DoS) attacks. The method quickly restores the data interaction process between data sampling and the controller after the DoS attack ends, thereby achieving timely updating of system status information and accurate application of control instructions, thereby quickly restoring the communication performance of the system. Specifically, the present method designs a controller suitable for asynchronous sampling data, which can perform real-time calculations and adjustments based on the actual sampled system status data, thereby effectively dealing with communication interruptions and data loss problems caused by DoS attacks, and significantly improving the stability and robustness of the system. The method of the present invention comprehensively utilizes theoretical tools such as discontinuous interval dependence functionals and switching system stability analysis to guide the design of asynchronous sampling data controllers, and ultimately realizes a control algorithm with practical feasibility. The method of the present invention can be used to enhance the security of industrial control systems and is very suitable for integration into modern power automation infrastructure to improve network physical resilience.

[0158] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above-mentioned embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with this field under the guidance of this specification fall within the substantive 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: The steps include: 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. Step 2. Characterize and model the DoS attack signal to provide a mathematical foundation for the subsequent design of a security controller with anti-attack features. Step 3. Design a security controller with attack resistance. This controller uses a flexible asynchronous sampling strategy. Once a DoS attack is detected, it immediately triggers asynchronous sampling sensors to start data collection. This controller collects the current networked system status data and sends it to the control center. Step 4. Perform stability analysis on the networked system controlled by the security controller with anti-attack characteristics under DoS attacks, and design a security control gain based on asynchronous sampling secure communication based on the stability criterion of the networked system under DoS attacks. Step 5. Use a security controller with anti-attack features to control the networked system to ensure that the networked system remains stable after a DoS attack.

2. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 1, characterized in that: The step 1 is specifically as follows: The networked system model with Markov jump parameters is established as: ； in, The state vector representing the networked system is the system state, , to Respectively The 1st to Nth components of , where N is a constant; and is a constant matrix; It means that a security controller with anti-attack characteristics needs to be designed. , to Respectively The 1st to qth components of , q is a constant; definition is a right-continuous continuous-time Markov process, Used to represent the transition between different modes of a networked system. In a finite set The value in Indicates the number of system modes; Define the transfer rate matrix as ,in Indicates modality Transfer to modal The transfer rate, , , and satisfies , Indicates modality Transfer to modal The transfer rate; Assume that there are p asynchronous sampling sensors deployed in the networked system ,in to They represent the 1st to pth asynchronous sampling sensors respectively, and p is a constant; System status , each asynchronous sampling sensor has a different sampling period Take samples, to Respectively represent the sampling periods of the 1st to pth asynchronous sampling sensors, and the sampling periods satisfy ; System Status It is divided into p groups, and the number of components in each group is recorded as , assign p groups of system states to p asynchronous sampling sensors for sampling; definition express The state variable sampled by the i-th asynchronous sampling sensor at time , then: 。 3. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 2, wherein: The step 2 is specifically as follows: Introduction Used to indicate whether a DoS attack occurs. It indicates a DoS attack. When , it means that no DoS attack has occurred, that is: ； in, , represents the set of positive integers, is the g-th attack sleep interval, i.e., the controller working interval, Indicates the time when the DoS attack starts. is the gth attack active interval; Indicates the g-th DoS attack cycle, Indicates the start time of the g-th DoS attack cycle, Indicates the end time of the g-th DoS attack cycle, Indicates the control duration of the g-th DoS attack cycle, and meets the following conditions: ; Indicates the attack time in the gth DoS attack cycle, Defined as: ; definition , ,in Indicates the maximum attack time in the g-th DoS attack cycle, Indicates the minimum attack time in the g-th DoS attack cycle, is the supremum function, is the infimum function; Define the minimum working time of the gth DoS attack cycle for: ; definition , , represents the g-th controller working range, represents the gth attack active interval; Get the maximum anti-attack ratio for: 。 4. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 3, wherein: The step 3 is specifically as follows: In an ideal communication environment without DoS attacks, it is assumed that the i-th asynchronous sampling sensor is Sampling at , represents a set of integers, Indicates the i-th asynchronous sampling sensor The sampling time of the sub-sampling, , The state variable sampled by the i-th asynchronous sampling sensor at time is ; Designing a secure communications controller for: ； in, represents the safety control gain to be designed based on asynchronous sampling safety communication, represents the sampling state set of all state variables, and there is ; When facing a DoS attack, during the active attack period The sampling data transmission within will be interrupted. To cope with the adverse effects of DoS attacks, a flexible asynchronous sampling strategy is designed as follows: ； in, Represents the i-th asynchronous sampling sensor In the gth controller working range The initial sampling time, , Represents the i-th asynchronous sampling sensor In the gth controller working range No. The sampling time of the sub-sampling, Represents the i-th asynchronous sampling sensor In the gth controller working range No. The sampling time of the sub-sampling; All sampling moments of the sensor will be sampled asynchronously Integrate into a new time series, namely the fused time series middle, represents the nth sampling time after integration in the gth DoS attack cycle; in, , ; A security controller with anti-attack characteristics is designed to ensure the mean square asymptotic stability of the networked system under DoS attacks. The security controller with anti-attack characteristics adopts a state feedback control law, whose control input is zero in the active attack interval. The state feedback control law is designed as follows: ； in, represents the n+1th sampling time after integration in the gth DoS attack cycle; In the gth DoS attack cycle Internally, the closed-loop system is modeled as: 。 5. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 4, characterized in that: The step 4 is specifically as follows: for 、 、 、 、 and safety control gain based on asynchronous sampling safety communication ,in and is the preset scalar, is the minimum sampling period of the asynchronous sampling sensor; If exists -dimensional positive definite matrix 、 、 、 and any matrix 、 、 、 、 、 、 、 、 ; in, , , ; So that formula (1) to formula (5) are and Established, of which Represents the fused time series If the time interval is , the networked system controlled by the security controller with anti-attack characteristics is mean square asymptotically stable; Formula (1) to Formula (5) are expressed as: (1) (2) (3) (4) (5) in, Expressed as: ； Expressed as: ； Expressed as: ； Expressed as: ； in, represents the symmetric term, represents the sum of symmetric terms, Indicates modality Transfer to modal The transfer rate, express -dimensional positive definite matrix, , and there is: ； ； ， ； ， ； ， ； ； ； ， ， ； ， ， ； ， ， ； ， ， ； ； in, to Respectively Weizhi dimensional unit matrix, represents the N-dimensional unit matrix, , express dimensional all-zero matrix, express dimensional all-zero matrix, express dimensional all-zero matrix, express Dimensional all-zero matrix; The safety control gain based on asynchronous sampling safety communication is designed as: ； in, represents the controller gain after coupling.

6. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 5, characterized in that: The step 4 also includes performing stability analysis on the networked system controlled by the security controller with anti-attack characteristics based on the switching system stability analysis idea and using the discontinuous interval dependent Lyapunov functional; The process of stability analysis of a networked system controlled by a security controller with anti-attack characteristics is as follows: For networked systems under DoS attacks, a discontinuous interval-dependent Lyapunov functional is established on the attack dormant interval and the attack active interval respectively. Solve the infinitesimal operator for the Lyapunov functional on the attack dormant interval according to the system trajectory; Solve the infinitesimal operator for the Lyapunov functional on the attack active interval according to the system trajectory; By integrating the infinitesimal operators of the attack dormant interval and the attack active interval, the stability conclusion of the closed-loop system is obtained.

7. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 6, wherein: For a networked system under DoS attack, the process of establishing the discontinuous interval-dependent Lyapunov functional on the attack dormant interval and the attack active interval is as follows: For networked systems under DoS attacks, Lyapunov functional Designed to: ； in, represents the last sampling moment in the working interval of the g-th controller, represents the first sampling moment in the gth attack active interval; and represents the Lyapunov functional on the attack dormant interval, represents the Lyapunov functional on the attack active interval; ； ； ； in: ； And there are: ； ； ； ， ； in, express The system status value at the moment, express The system status value at the moment, express The system status value at a certain moment.

8. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 7, characterized in that: The specific process of solving the infinitesimal operator of the Lyapunov functional on the attack dormant interval according to the system trajectory is as follows: In the interval Inside, compute the infinitesimal operator along the trajectory of the system ; consider In the case of hour: ； To simplify the notation, let: ； in, express System status at the moment; Calculate along the trajectory of the system ,get The estimate is: ； in, represents the mathematical expectation, express infinitesimal operators; According to formula (1), we have 、 、 、 Established, of which express hour The value of express hour The value of express hour The value of express hour The value of According to the convex combination technique, for any , the following inequality holds: ； ； get: ； in, ; In the interval Internal, Lyapunov functional is continuous and positive definite, we get: ； in, express exist The Lyapunov functional value at time , represents the initial sampling time after integration in the g-th DoS attack cycle, express exist The Lyapunov functional value at time t; Taking into account ,when When , the Lyapunov functional is selected as: ； Using convex combination technology, for any ,have and Established; when and When, according to and ,get ; The following inequality holds: ； in, express At the moment The Lyapunov functional value of , express At the moment The Lyapunov functional value of ; when When ,have Established; According to the convex combination inequality, the following relationship holds: 。 9. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 8, wherein: The specific process of solving the infinitesimal operator of the Lyapunov functional on the attack active interval according to the system trajectory is as follows: Consider the case where a networked system is attacked by DoS. hour: ； To simplify the notation, let: ； In the interval Trajectory calculation of inner edge system ,get The estimates are as follows: ； in, express infinitesimal operators; ； According to formula (2), we can get: ， ； have and Established, with the help of Schur complement technology, we get and ; in, Indicates when hour The value of Indicates when hour The value of Indicates when hour The value of Indicates when hour The value of against 、 、 、 ,in Indicates when hour The value of Indicates when hour The value of , based on the convex combination technique, for any The following inequality holds: ； in, ; get: ； in, for exist The Lyapunov functional value at time , for exist The Lyapunov functional value at time .

10. The method for controlling elastic asynchronous sampling in a networked system against denial of service attacks according to claim 9, characterized in that: The process of synthesizing the infinitesimal operators of the attack dormant interval and the attack active interval to draw conclusions about the stability of the closed-loop system is as follows: according to and ; get ; ； in, express exist The Lyapunov functional value that always tends to the left limit, for , express exist The Lyapunov functional value that always approaches the right limit, express exist The Lyapunov functional value that always tends to the left limit, express exist The Lyapunov functional value that always approaches the right limit; Considering the discontinuity of the Lyapunov functional, exist and The relationship between the moments is established as follows: ； ； in, express exist The Lyapunov functional value that always tends to the left limit; According to formula (5), we have Established; Therefore, when When Lyapunov functional is continuous and strictly decreasing, we get: ； in, ; Since the Lyapunov functional In the interval The above is continuous, so we can deduce that: ； As a constant, using the two-side clamp rule, we get: ； according to ,when When , we get: ； when When , we get: ； in, ; Under DoS attacks, the closed-loop system achieves global asymptotic stability in the mean square sense.

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