Active control method for network control system based on memory controller under dos attack

Abstract

This invention provides an active control method for network control systems under DoS attacks based on a memory controller, belonging to the field of network control technology. It solves the technical problem of unstable system performance caused by the lack of appropriate control signals in network control systems under DoS attacks. The technical solution involves using a state feedback controller for control during the DoS attack's dormant period, and reconstructing the system state signals using a memory controller during the active period of the DoS attack, achieving continuous control signal updates and system control. The beneficial effects of this invention are: considering external interference in the actual environment, the application of a memory controller during the DoS attack period not only effectively reduces the system's computational load but also enhances the system's resistance to DoS attacks and external interference.

Description

Technical Field

[0001] This invention relates to the field of network control technology, and in particular to an active control method for a network control system under a DoS attack based on a memory controller. Background Technology

[0002] Networked control systems are spatially distributed control systems characterized by digitalization, integration, and networking. They enable interconnection between different components through network signal transmission and have been widely applied in daily life. However, the increased complexity of networked control systems makes the design of security protection measures difficult, allowing attackers to easily exploit vulnerabilities. DoS attacks, the most common and easily accessible type of network attack, consume limited communication resources by generating large amounts of redundant data, causing data transmission delays. This prevents the controller from obtaining the latest transmission signals in time to calculate control input signals, thereby reducing system control performance or even causing it to malfunction.

[0003] Since passive control methods such as zero-input control do not update control signals during DoS attacks, this leads to a certain degree of performance degradation. Therefore, active control methods that update control signals in a timely manner have received continuous attention and research. Currently, common active control methods mainly estimate the current system state by constructing an internal model. For example, Li Jing proposed a predictor-based active control method in the paper "Predictive control based on event-triggering mechanism of cyber-physical systems under denial-of-service attacks." Although such methods can effectively improve system control performance, the computational load and complexity of internal models based on differential equations are high, increasing the computational burden on the system. Furthermore, Jiayuan Yin et al., in "Observer-Based Active Control Strategy for Networked Switched Systems against Two-Channel Asynchronous DoS Attacks," argue that widespread disturbances significantly affect the control accuracy of active control methods and compromise system stability. Based on the above analysis, the technical challenges that active control methods currently need to address are:

[0004] (1) How to effectively reduce the complexity of calculating control input signals;

[0005] (2) How to improve the resistance to DoS attacks and external disturbances and ensure the stability of the system.

[0006] In addition, data-driven state signal reconstruction has significantly lower computational complexity than model-driven state signal reconstruction, and the memory controller itself has the advantage of compensating for network control systems under DoS attacks. However, current memory controllers are mainly based on passive control methods to defend against DoS attacks. Therefore, considering nonlinear disturbances and communication delays, how to establish an active control method based on memory controllers to defend against DoS attacks requires further research. Summary of the Invention

[0007] The purpose of this invention is to provide an active control method for a network control system based on a memory controller under DoS attacks, which can not only effectively reduce the complexity of calculating control input signals, but also improve the system's resistance to DoS attacks and external disturbances.

[0008] To achieve the above-mentioned objectives, the present invention employs the following technical solution: an active control method for a network control system under a DoS attack based on a memory controller, comprising the following steps:

[0009] Step 1: Considering external interference, construct the state-space expression of the network control system, determine the non-periodic DoS attack mode, and establish the data transmission mechanism in the network control system under DoS attack.

[0010] Step 1.1: Considering external disturbances, construct the state-space expression of the controlled object:

[0011] (1)

[0012] in, This indicates the state of the controlled object in the system. for The derivative of Indicates control input, Indicates control output. This indicates a bounded external disturbance. , , and Given a known constant coefficient matrix with appropriate dimensions, Indicates time;

[0013] Step 1.2: Determine the non-periodic DoS attack pattern:

[0014] (2)

[0015] Among them, the DoS attack time interval, using To indicate, in the first Within a DoS attack interval, the attack is not continuous; therefore, the attack interval is divided into an active attack interval and a dormant attack interval. The dormant interval is... Description, active interval Expression. Among them, For the first The start time of each active DoS attack interval. For the first The end time of each active DoS attack interval Indicates the first The sleep duration corresponding to this DoS attack meets the following conditions. ;

[0016] Step 1.3: Due to inherent energy limitations, the duration and frequency of aperiodic DoS attacks are restricted as follows:

[0017] (3)

[0018] in, This is the minimum sleep duration for a DoS attack. This represents the maximum active duration of a DoS attack. It is an interval The number of DoS attacks that occurred within the region. , ,and , is the set of positive integers, Represents a set;

[0019] Step 1.4: Event triggering mechanism without DoS attack:

[0020] (4)

[0021] In the formula, The triggering condition is specifically expressed as follows:

[0022] (5)

[0023] Among them, the triggering time For the first Each sampling period, subscript Indicates the trigger time sequence number. Indicates the sampling period. , For the first The system sampling time after the next trigger. It is the first After the first trigger The state vector at the next sampling time. , It is the trigger weight matrix to be designed;

[0024] Step 1.5: The adaptive threshold parameters are designed and implemented as follows:

[0025] (6)

[0026] in, , , For predefined positive integers, The maximum value of the adaptive threshold parameter. Represents the L2 norm;

[0027] Step 1.6: Due to It can only transmit when there is no DoS attack, therefore, when a DoS attack occurs, Unable to transmit, therefore the event trigger condition is:

[0028] (7)

[0029] Among them, the The first DoS attack under the Each transmission time is used express.

[0030] Step 2: Establish a closed-loop model of the active control method and network control system under aperiodic DoS:

[0031] Step 2.1: In the absence of a DoS attack, the transmission is determined by step 1.3. The data can be transmitted normally to the memory via the communication network, at which point the memory stores the transmission status signal. :

[0032] (8)

[0033] in, These are the status signals stored in the memory. The time interval between two adjacent signals received by the memory is... , This represents random transmission delay, which can also be considered as delay since the memory is configured on the controller side. It is the time interval between two adjacent signals received by the controller;

[0034] Step 2.2: When a DoS attack occurs, the communication network is blocked, and the transmission is determined by step 1.3. Unable to transmit, the memory stores the reconstructed state signal. :

[0035] (9)

[0036] In the formula, It is a storage status signal The weight parameters simultaneously satisfy the condition and , ; The number of state signals to store. For the first The first DoS attack A historical transmission moment, It is the first The memory under the second DoS attack A historical state vector; in addition, the latest stored signal Historical stored signals in memory The weighted reconstruction yields the result. It's important to note that the memory follows a first-in, first-out (FIFO) principle; when the latest stored signal... The stored signal with the longest storage time when stored in memory. It will be discarded;

[0037] Step 2.3: Therefore, the memory's storage state signal is represented as:

[0038] (10)

[0039] Step 2.4: Based on steps 2.1 to 2.3, construct a state feedback controller based on the state signals stored in the memory as follows:

[0040] (11)

[0041] Since the state signals stored in different time intervals in step 2.3 are utilized, the state feedback controller (6) is a memory controller. In addition, the memory controller (6) generates control input signals in different time intervals to form an active control method, which can effectively deal with the negative impact caused by DoS attacks and realize the whole process of control signal update and system control.

[0042] Step 2.5: Divide the interval Dividing the data into sub-intervals similar to sampling intervals, we obtain a random time delay function. The relevant conditional inequalities;

[0043] Step 2.6: Based on the above steps, the final closed-loop state-space expression of the network control system is obtained as follows:

[0044] (12)

[0045] Step 3: Determine the sufficient conditions for asymptotic stability of the networked control system, and obtain the joint design scheme of event triggering mechanism and active control method:

[0046] Step 3.1: Using the Lyapunov stability method and LMI technique, determine the sufficient conditions for asymptotic stability of the networked control system:

[0047] For a given , , and control gain If it has a positive definite matrix of appropriate dimensions , , , and a real matrix of appropriate dimension The following conditions must be met:

[0048] (13)

[0049] (14)

[0050] in,

[0051] ,

[0052] , ,

[0053] , ,

[0054] , ,

[0055] , , , ,

[0056] , , , ;

[0057] Therefore, the controlled object (1) becomes asymptotically stable under the active control strategy based on the memory controller, and satisfies the given conditions. Performance parameters ;

[0058] Step 3.2: Based on Step 3.1, determine the joint design method of the event triggering mechanism and the active control method based on the memory controller:

[0059] For a given and If it has a positive definite matrix of appropriate dimension , , , and a real matrix of appropriate dimension The following conditions must be met:

[0060] (15)

[0061] (16)

[0062] in,

[0063] ,

[0064] , ,

[0065] , , ,

[0066] , ,

[0067] , , ,

[0068] , , , ;

[0069] definition , , Then the event triggering parameters and control gain It can be given by (15):

[0070] (17)

[0071] (18).

[0072] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0073] (1) The active control method based on memory controller proposed in this invention can reconstruct historical data stored in memory using memory controller, avoiding the introduction of internal parameter models with high computational load and high complexity, and effectively reducing the computational complexity of control input signals.

[0074] (2) The active control method based on memory controller proposed in this invention can reconstruct historical state signals to replace the state signals lost due to DoS attacks. The system can have a faster convergence speed and stronger resistance to DoS attacks and external disturbances.

[0075] (3) Based on the Lyapunov stability method, this invention derives a joint design method for event triggering mechanism and memory controller gain. Attached Figure Description

[0076] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0077] Figure 1 This is a flowchart illustrating the overall process of an active control method based on a memory controller for a network control system under a DoS attack.

[0078] Figure 2 This is a schematic diagram of a network control system under a DoS attack using an active control method based on a memory controller.

[0079] Figure 3 This is a schematic diagram of the state response curve of a network control system under a DoS attack using an active control method based on a memory controller.

[0080] Figure 4 This is a schematic diagram of the state response curve of a network control system under a DoS attack using a zero-input control method.

[0081] Figure 5 This is a schematic diagram of the state response curve of a network control system under a DoS attack using a predictor-based active control method. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0083] Example 1

[0084] See Figures 1 to 5 This embodiment provides a technical solution: an active control method for a network control system under a DoS attack based on a memory controller, specifically including the following steps:

[0085] Step 1: Considering external interference, construct the state-space expression of the network control system, determine the non-periodic DoS attack mode, and establish the data transmission mechanism in the network control system under DoS attack.

[0086] Step 1.1: Considering external disturbances, construct the state-space expression of the controlled object:

[0087] (1)

[0088] in, This indicates the state of the controlled object in the system. for The derivative of Indicates control input, Indicates control output. This indicates a bounded external disturbance. , , and Given a known constant coefficient matrix with appropriate dimensions, Indicates time;

[0089] Step 1.2: Determine the non-periodic DoS attack pattern:

[0090] (2)

[0091] Among them, the DoS attack time interval, using To indicate, in the first Within a DoS attack interval, the attack is not continuous; therefore, the attack interval is divided into an active attack interval and a dormant attack interval. The dormant interval is... Description, active interval Expression. Among them, For the first The start time of each active DoS attack interval. For the first The end time of each active DoS attack interval Indicates the first The sleep duration corresponding to this DoS attack meets the following conditions. ;

[0092] Step 1.3: Due to inherent energy limitations, the duration and frequency of aperiodic DoS attacks are restricted as follows:

[0093] (3)

[0094] in, This is the minimum sleep duration for a DoS attack. This represents the maximum active duration of a DoS attack. It is an interval The number of DoS attacks that occurred within the region. , ,and , is the set of positive integers, Represents a set;

[0095] Step 1.4: Event triggering mechanism without DoS attack:

[0096] (4)

[0097] In the formula, The triggering condition is specifically expressed as follows:

[0098] (5)

[0099] Among them, the triggering time For the first Each sampling period, subscript Indicates the trigger time sequence number. Indicates the sampling period. , For the first The system sampling time after the next trigger. It is the first After the first trigger The state vector at the next sampling time. , It is the trigger weight matrix to be designed;

[0100] Step 1.5: The adaptive threshold parameters are designed and implemented as follows:

[0101] (6)

[0102] in, , , For predefined positive integers, The maximum value of the adaptive threshold parameter. Represents the L2 norm;

[0103] Step 1.6: Due to It can only transmit when there is no DoS attack, therefore, when a DoS attack occurs, Unable to transmit, therefore the event trigger condition is:

[0104] (7)

[0105] Among them, the The first DoS attack under the Each transmission time is used express.

[0106] Step 2: Establish a closed-loop model of the active control method and network control system under aperiodic DoS:

[0107] Step 2.1: In the absence of a DoS attack, the transmission is determined by step 1.3. The data can be transmitted normally to the memory via the communication network, at which point the memory stores the transmission status signal. :

[0108] (8)

[0109] in, These are the status signals stored in the memory. The time interval between two adjacent signals received by the memory is... , This represents random transmission delay, which can also be considered as delay since the memory is configured on the controller side. It is the time interval between two adjacent signals received by the controller;

[0110] Step 2.2: When a DoS attack occurs, the communication network is blocked, and the transmission is determined by step 1.3. Unable to transmit, the memory stores the reconstructed state signal. :

[0111] (9)

[0112] In the formula, It is a storage status signal The weight parameters simultaneously satisfy the condition and , ; The number of state signals to store. For the first The first DoS attack A historical transmission moment, It is the first The memory under the second DoS attack A historical state vector; in addition, the latest stored signal Historical stored signals in memory The weighted reconstruction yields the result. It's important to note that the memory follows a first-in, first-out (FIFO) principle; when the latest stored signal... The stored signal with the longest storage time when stored in memory. It will be discarded;

[0113] Step 2.3: Therefore, the memory's storage state signal is represented as:

[0114] (10)

[0115] Step 2.4: Based on steps 2.1 to 2.3, construct a state feedback controller based on the state signals stored in the memory as follows:

[0116] (11)

[0117] Since the state signals stored in different time intervals in step 2.3 are utilized, the state feedback controller (6) is a memory controller. In addition, the memory controller (6) generates control input signals in different time intervals to form an active control method, which can effectively deal with the negative impact caused by DoS attacks and realize the whole process of control signal update and system control.

[0118] Step 2.5: Due to the different update time intervals of the controller and the system, it is difficult to directly deduce the closed-loop system. For further analysis, the interval is... Divide into sub-intervals similar to sampling intervals, that is:

[0119] (12)

[0120] in, , Delay Conditions met:

[0121] (13)

[0122] in, Indicates the upper bound of the delay. Representation and delay and sampling period The relevant upper bound parameter;

[0123] Step 2.6: Based on the above steps, the final closed-loop model of the network control system is as follows:

[0124] (14)

[0125] in, It is the first The first DoS attack under the The sampling time is after the transmission time.

[0126] Step 3: Determine the sufficient conditions for asymptotic stability of the networked control system, and obtain the joint design scheme of event triggering mechanism and active control method:

[0127] Step 3.1: Using the Lyapunov stability method and LMI technique, determine the sufficient conditions for asymptotic stability of the networked control system:

[0128] For a given , , and control gain If it has a positive definite matrix of appropriate dimensions , , , and a real matrix of appropriate dimension The following conditions must be met:

[0129] (15)

[0130] (16)

[0131] in,

[0132] ,

[0133] , ,

[0134] , ,

[0135] , ,

[0136] , , , ,

[0137] , , , ;

[0138] Proof: Construct the following Lyapunov function:

[0139] (17)

[0140] in,

[0141] ,

[0142] ,

[0143] ,

[0144] Differentiating equation (17), we get:

[0145] ,

[0146] ,

[0147] ,

[0148] Applying Jensen's inequality The integral term in the equation can be obtained as follows:

[0149] (18)

[0150] in,

[0151] , ,

[0152] Considering the event triggering mechanism (4) and The following inequalities hold:

[0153] (19)

[0154] in, , The Schuler complement lemma can be used to... Transform it into equation (15);

[0155] And because ,and hour Since it is continuous, integrating both sides of equation (19) simultaneously yields...

[0156] (20)

[0157] It is obvious that system (1) is asymptotically stable and has Performance. Q.E.D.

[0158] Step 3.2: Based on Step 3.1, determine the joint design method of the event triggering mechanism and the active control method based on the memory controller:

[0159] For a given and If it has a positive definite matrix of appropriate dimension , , , and a real matrix of appropriate dimension The following conditions must be met:

[0160] (twenty one)

[0161] (twenty two)

[0162] in,

[0163] ,

[0164] , ,

[0165] , , ,

[0166] , ,

[0167] , , ,

[0168] , , , ;

[0169] From this, we can obtain the event triggering parameters. Control gain .

[0170] Proof: Definition , , , , , Then, multiply equation (15) by a diagonal matrix on both sides. ,in accordance with Will Rewritten as Finally, we obtain equation (21). Q.E.D.

[0171] In the specific implementation, the symbols are explained in Table 1:

[0172] Table 1. Symbol Explanation

[0173]

[0174] The following describes this embodiment in detail with reference to the examples:

[0175] To verify the effectiveness and feasibility of the method, consider the following network control system:

[0176] , , , ,

[0177] Set system parameters , , , , , , , , , , , and set initial values. Set external interference as ,in It is in the interval Random values ​​within;

[0178] By solving the linear matrix inequality in step 4, we can obtain... Performance parameters The control gain is 8.6237. intermediate matrix and event triggering parameters for:

[0179] , , ;

[0180] Figure 3 The diagram shows the state response curve of the active control method based on the memory controller proposed in this embodiment. It can be seen that the system can stabilize in about 12 seconds, and the number of peaks and troughs is small, with the highest peak value close to 2.1.

[0181] Figure 4 The diagram shows the state response curve of the predictor-based active control method. It can be seen that the system is easily affected by external disturbances under this strategy and takes about 18 seconds to stabilize. There are also a few peaks and troughs, with the highest peak value approaching 2.5.

[0182] Figure 5 The diagram shows the state response curve of the zero-input non-active control method. It can be seen that the system under zero-input control is more susceptible to DoS attacks, takes about 22 seconds to stabilize, and has a large number of peaks and troughs, with the highest peak value approaching 4.1.

[0183] As can be seen, the effectiveness of the present invention under the active control method based on a memory controller is as follows:

[0184] ①Compared Figure 4 , Figure 5 This method achieves an improvement of nearly 33% and 50% in convergence speed, respectively;

[0185] ②Compared Figure 4 and Figure 5 The system under this method did not exhibit jitter or multiple peaks and troughs, indicating that the system has a stronger resistance to DoS attacks and external disturbances.

[0186] ③ This method uses a weighted summation type memory controller to reconstruct the state signal and calculate the control signal under a DoS attack, instead of using an internal model based on differential equations to calculate the state signal, which has lower complexity.

[0187] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for active control based on memory controller of network control system under DoS attack, characterized in that, Includes the following steps: Step 1: Considering external interference, construct the state-space expression of the network control system, determine the non-periodic DoS attack mode, and establish the data transmission mechanism in the network control system under DoS attack. Step 2: Establish a closed-loop model of the active control method and network control system under aperiodic DoS. Step 2 includes the following steps: Step 2.1 : At the time of no DoS attack, at which time the memory stores the transmission status signal : （3）； in, These are the status signals stored in the memory. The time interval between two adjacent signals received by the memory is... , This represents random transmission delay, which can also be considered as delay since the memory is configured on the controller side. It is the time interval between two adjacent signals received by the controller; Step 2.2: When a DoS attack occurs, the communication network is blocked, therefore the memory stores the reconstructed state signal. : （4）； In the formula, It is a storage status signal The weight parameters simultaneously satisfy the condition and , ; The number of state signals to store. For the first The first DoS attack A historical transmission moment, It is the first The memory under the second DoS attack A historical state vector; in addition, the latest stored signal Historical stored signals in memory The weighted reconstruction yields the result. It's important to note that the memory follows a first-in, first-out (FIFO) principle; when the latest stored signal... The stored signal with the longest storage time when stored in memory. It will be discarded; Step 2.3: Therefore, the memory's storage state signal is represented as: （5）； Step 2.4: Based on steps 2.1 to 2.3, construct a state feedback controller based on the state signals stored in the memory as follows: （6）； Since it utilizes the state signals stored in different time intervals in step 2.3, this state feedback controller is a memory controller. In addition, this memory controller generates control input signals in different time intervals, thereby forming an active control method, which can effectively cope with the negative impact caused by DoS attacks and realize the continuous update of control signals and system control. Step 2.5: Divide the interval Dividing the data into sub-intervals similar to sampling intervals, we obtain a random time delay function. The relevant conditional inequalities; Step 2.6: Based on the above steps, the final closed-loop state-space expression of the network control system is obtained as follows: （7）； in, It is the first The first DoS attack under the The sampling time after a transmission time; Step 3: Determine the sufficient conditions for asymptotic stability of the network control system and obtain the joint design scheme of event triggering mechanism and active control method.

2. The active control method for a network control system under a DoS attack based on a memory controller according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: Considering external disturbances, construct the state-space expression of the controlled object: （1）； in, This indicates the state of the controlled object in the system. for The derivative of Indicates control input, Indicates control output. This indicates a bounded external disturbance. , , and For a constant matrix with appropriate dimensions, Indicates time; Step 1.2: Determine the non-periodic DoS attack pattern and identify the period during the DoS attack hibernation interval. Set the attack signal to the dormant signal "0" during the DoS attack active interval. Set the attack signal to the active signal "1". Indicates the first The sleep duration corresponding to each DoS attack; Step 1.3: In a network control system vulnerable to DoS attacks, the data transmission mechanism is as follows: （2）； In the formula, Indicates the first The first DoS attack Each transmission moment, It is the triggering condition. It is the first The moment the DoS attack ended.

3. The active control method for a network control system under a DoS attack based on a memory controller according to claim 1, characterized in that, Step 3 includes the following steps: Step 3.1: Using the Lyapunov stability method and LMI technique, determine the sufficient conditions for asymptotic stability of the networked control system: For a given , , and control gain If it has a positive definite matrix of appropriate dimensions , , , and a real matrix of appropriate dimension The following conditions must be met: （8）； Therefore, the controlled object (1) becomes asymptotically stable under the active control method based on the memory controller, and satisfies the given conditions. Performance parameters ; Step 3.2: Based on Step 3.1, determine the joint design method of the event triggering mechanism and the active control method based on the memory controller: For a given and If it has a positive definite matrix of appropriate dimension , , , and a real matrix of appropriate dimension The following conditions must be met: （9）； in , , Event triggering parameters and control gain It can be given by (8): （10）； （11）。

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