A safety control method and system for a networked multi-channel actuator system

Abstract

This invention belongs to the field of cyber-physical system security control and discloses a security control method and system for a networked multi-channel actuator system. The proposed attack-aware adaptive historical weighted event triggering mechanism utilizes weighted historical state information to adaptively adjust the triggering threshold to reduce communication overhead and switches to a shorter sampling period within a defined effective DoS attack interval to accelerate system recovery. It constructs an effective DoS attack interval model based on communication latency, establishing a closed-loop system model under scenarios where latency and attacks coexist. A Lyapunov functional dependent on the effective DoS attack interval is constructed, and the stability conditions based on the model are derived, enabling the collaborative design of the security controller and the event triggering mechanism. This invention can ensure exponential system stability under environments with both communication latency and DoS attacks using only offline data, effectively balancing control performance and communication efficiency.

Description

Technical Field

[0001] This invention belongs to the field of cyber-physical system security control technology, specifically relating to a networked multi-channel actuator system security control method and system, which is particularly suitable for network environments where communication delays and DoS attacks coexist. Background Technology

[0002] Networked multi-channel actuator systems, as a typical type of cyber-physical system, tightly couple sensing, computing, and control processes through communication networks, enabling coordinated regulation of complex physical objects. These systems have been widely applied in fields such as intelligent manufacturing, autonomous driving, smart healthcare, and smart cities. However, the operation of networked multi-channel actuator systems is highly dependent on open communication networks and is susceptible to network uncertainties. Communication delays and denial-of-service (DoS) attacks are the main security threats. Communication delays are usually caused by network congestion or bandwidth limitations, which may lead to data out-of-order processing and packet loss, significantly reducing system stability and control performance. DoS attacks, by blocking data transmission, prevent the actuator from receiving control commands in a timely manner, potentially causing system lag, performance degradation, or even instability. To reduce communication overhead and enhance the system's resilience against DoS attacks, resilient event-triggered control mechanisms have gradually become a research hotspot. However, existing mechanisms typically trigger control updates immediately after the attack ends, failing to fully consider the performance requirements of the recovery phase, potentially leading to redundant communication burdens. Furthermore, existing security control methods often rely on accurate system dynamics models, while real-world engineering systems are typically nonlinear, complex, and subject to variable disturbances, making accurate models difficult to obtain. With the development of industrial digitalization, data-driven control methods have attracted attention because they can directly utilize system operating data to design controllers. Therefore, in network environments where communication latency and DoS attacks coexist, how to achieve data-driven safe control of unknown nonlinear networked multi-channel actuator systems remains a key problem that existing technologies urgently need to solve. Summary of the Invention

[0003] The purpose of this invention is to propose a security control method for a networked multi-channel actuator system. This method can make full use of historical system state information and detect DoS attacks in real time to adaptively adjust communication strategies, thereby effectively resisting DoS attacks with less data transmission even when the system model is unknown.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A safety control method for a networked multi-channel actuator system includes the following steps:

[0006] Step 1. Establish a dynamic model of the nonlinear networked multi-channel actuator system;

[0007] Step 2. Establish a mathematical model of DoS attacks and communication latency;

[0008] Step 3. Based on the established mathematical model of DoS attack and communication delay, an adaptive historical weighted event triggering mechanism based on periodic sampling attack awareness is proposed, and its triggering condition design is given.

[0009] Step 4. Based on the relationship between DoS attacks and triggering time and communication latency, construct an effective DoS attack range, and design a security controller by combining an adaptive historical weighted event triggering mechanism for attack awareness.

[0010] Step 5. Based on the designed security controller, establish a closed-loop system model for a scenario where communication latency and DoS attacks coexist;

[0011] Step 6. Offline acquisition of noisy data from the nonlinear networked multi-channel actuator system and construction of system data representation;

[0012] Step 7. Based on the constructed system data representation, a data-based stability criterion is proposed for scenarios where communication delay and DoS attacks coexist. Based on this criterion, the collaborative design of the security controller and the event triggering mechanism is realized, thereby achieving data-based networked multi-channel actuator system security control.

[0013] Furthermore, based on the aforementioned safety control method for networked multi-channel actuator systems, this invention also proposes a corresponding safety control system for networked multi-channel actuator systems, the scheme of which is as follows:

[0014] A safety control system for a networked multi-channel actuator system includes the following modules:

[0015] The dynamics model building module is used to establish the dynamics model of a nonlinear networked multichannel actuator system.

[0016] The DoS attack and communication delay model building module is used to establish a mathematical model of DoS attacks and communication delays.

[0017] The triggering mechanism design module is used to propose an adaptive historical weighted event triggering mechanism based on periodic sampling attack awareness, based on the established mathematical model of DoS attack and communication delay, and to give its triggering condition design.

[0018] Security controller design module. It is used to construct an effective DoS attack range based on the relationship between DoS attacks and triggering time and communication latency, and to design a security controller in combination with an attack-aware adaptive historical weighted event triggering mechanism.

[0019] The closed-loop system modeling module is used to combine the designed security controller to establish a closed-loop system model under the scenario of coexistence of communication delay and DoS attack.

[0020] The system data representation module is used to collect noisy data from a nonlinear networked multichannel actuator system offline and construct a system data representation.

[0021] It also includes a data-based stability verification and collaborative solution module, which is used to propose data-based stability criteria in scenarios where communication delay and DoS attack coexist, based on the constructed system data representation. Based on this, it realizes the collaborative design of security controller and event triggering mechanism, and thus realizes the security control of data-based networked multi-channel actuator system.

[0022] The present invention has the following advantages:

[0023] As described above, this invention addresses the security control problem of cyber-physical systems (CPS) in scenarios where system models are unknown and communication delays and DoS attacks coexist. It proposes a security control method for networked multi-channel actuator systems. This method, through a proposed attack-aware adaptive historical weighted event triggering mechanism, not only adaptively adjusts the trigger threshold using weighted historical system state information to reduce communication overhead while maintaining control performance, but also, by sensing DoS attacks, employs a shorter sampling period during the effective DoS attack interval, enabling the system to quickly recover to normal operation after the attack ends. Furthermore, this invention, combined with the constructed effective DoS attack interval and the input delay method, constructs a unified closed-loop system model that accurately describes the scenario of coexisting communication delays and DoS attacks. This model clearly characterizes the switching characteristics of the system between normal control and zero-input control modes and can be extended to other complex networked control systems. This method does not rely on a system model; it only utilizes offline collected system data to ensure exponential stability of the system in scenarios where communication delays and DoS attacks coexist, while simultaneously achieving faster convergence speeds with lower data transmission rates. Thus, it balances control performance and communication efficiency in harsh network environments. Attached Figure Description

[0024] Figure 1 This is a flowchart of a cyber-physical system security control method based on attack-aware event triggering in an embodiment of the present invention;

[0025] Figure 2 This is a schematic diagram of the networked multi-channel actuator system in an embodiment of the present invention;

[0026] Figure 3 This is a time-domain diagram of the system state under the scenario of coexistence of communication delay and DoS attack in an embodiment of the present invention;

[0027] Figure 4This is a time-domain diagram of the control input in a scenario where communication delay and DoS attack coexist in an embodiment of the present invention.

[0028] Figure 5 This is a time-domain graph of the adaptive threshold parameter under the scenario of coexistence of communication delay and DoS attack in an embodiment of the present invention;

[0029] Figure 6 This is a time-domain diagram showing the trigger interval of the event triggering mechanism in a scenario where communication delay and DoS attack coexist in an embodiment of the present invention. Detailed Implementation

[0030] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0031] Example 1

[0032] To address the challenge of balancing control performance and communication efficiency in existing nonlinear networked multi-channel actuator systems under DoS attacks and communication delays, this invention proposes a security control method for such systems. This method focuses on solving the problems of closed-loop system modeling, stability analysis, and controller co-design under conditions of unknown system model, communication delays, and DoS attacks. To reduce network communication load and effectively resist aperiodic DoS attacks, this invention first designs an attack-aware adaptive historical weighted event triggering mechanism. This mechanism, based on periodic sampling, has two key features: first, it adaptively adjusts the triggering threshold according to the system's historical state, significantly reducing communication load while maintaining control performance; second, it switches to a shorter sampling period within the effective DoS attack interval, enabling the system to quickly assess performance and decide whether to update control inputs after the attack ends, thereby accelerating system recovery. Based on this, this invention proposes the concept of an "effective DoS attack interval" considering the impact of communication delays and DoS attacks, and establishes a closed-loop system switching model incorporating DoS attacks and communication delays. This model accurately characterizes the dynamic switching behavior of the system between the normal communication interval and the effective DoS attack interval. To analyze the stability of this closed-loop system, this invention constructs a class of Lyapunov functionals that depend on the effective DoS attack interval. These functionals fully utilize the system's state information within different intervals, thereby deriving model-based exponential stability conditions. Furthermore, a system data representation is constructed using offline-collected noisy data, and the model-based stability conditions are transformed into data-based stability conditions based on the matrix S-lemma, thus achieving the collaborative design of the security controller and the trigger matrix. Finally, numerical simulations of a nonlinear networked multi-channel actuator system verify the effectiveness of the proposed data-driven security control method. The proposed method does not rely on a system model; it utilizes only offline-collected system data to ensure exponential stability of the system in scenarios with both communication latency and DoS attacks, while simultaneously achieving faster convergence speeds with lower data transmission rates. This balances control performance and communication efficiency in harsh network environments.

[0033] like Figure 1 As shown, the safety control method for a networked multi-channel actuator system in this embodiment includes the following steps:

[0034] Step 1. Establish a dynamic model of the nonlinear networked multi-channel actuator system.

[0035] For each actuator channel of a networked multichannel actuator system Its dynamic equation is expressed as:

[0036] .

[0037] in Indicates the first The equivalent dynamic state of each actuator channel can include output position, speed, or internal actuator state, etc. . The middle part indicates that it is sent to the first through the communication network. The first actuator channel Road control signals, , express to integers, Indicates from to Integers.

[0038] Description of the Nonlinear effects of individual channels, such as actuator saturation, friction, or flexible coupling, etc. Indicates the first The nonlinear function corresponding to the nonlinear effect of each channel, for any different time... ,exist , making the first The slope of the nonlinear function corresponding to the nonlinear effect of each channel is bounded, i.e. The initial value of the nonlinear function satisfies , .

[0039] For the first The linear dynamic coefficient of each actuator channel can represent the attenuation or amplification of the channel. To control the elements of the input matrix, describe the first... The control signal for the first The function of each actuator channel.

[0040] These are elements of a nonlinear coupling matrix, describing the nonlinear coupling strength between channels.

[0041] The above The dynamic equations of each actuator channel are combined to obtain the overall continuous-time dynamic model of the networked multi-channel actuator system: .

[0042] in Represents the state vector of the system. , , , for A system state, For the system dimension, Represents a column vector.

[0043] For the safety controller to be designed, To control the number of inputs; , , , For safety controllers One control input.

[0044] It is a vector of nonlinear functions.

[0045] , and These are the state matrix, control matrix, and nonlinear coupling matrix, respectively.

[0046] , and All are constant matrices and are unknown.

[0047] Step 2. Establish a mathematical model of DoS attacks and communication delays.

[0048] Step 2.1. Establish a mathematical model for DoS attacks.

[0049] Figure 2 The structure of a networked multi-channel actuator system is demonstrated. Its closed-loop process begins with a sensor that continuously measures the state of the controlled object and outputs a continuous signal. This signal is discretized by a periodic sampler, which, based on the designed event triggering mechanism, operates within a nominal sampling period. With a shorter sampling period It can switch dynamically between these modes.

[0050] The discretized data is fed into an event generator, which determines whether to generate and send data packets based on the designed triggering conditions. DoS attacks occur in the communication network between the event generator and the security controller.

[0051] To counter DoS attacks, the security controller can switch between zero input and a buffer storing historical trigger states. The zero-order hold converts the discrete signals from the security controller into a stepped, continuous signal to drive the actuator.

[0052] Definition of the first Active range of DoS attacks for:

[0053] .in For the first The start time of a DoS attack At its end time, For the duration of the attack, Represents an integer greater than or equal to 0.

[0054] For any time interval Define the union of all active DoS attack intervals within this time interval. for:

[0055] .

[0056] Record the union of all inactive DoS intervals within this time interval. for:

[0057] .

[0058] in Indicates time interval Internal belonging to But not belonging to The range.

[0059] definition For this time interval The total length of all active DoS attack zones within the defined area. For this time interval The number of attacks in an internal DoS attack.

[0060] Considering that DoS attackers are limited by energy in practice, their attack behavior is usually finite in time; to characterize this feature, the DoS attacks that this method defends against are limited as follows:

[0061] There are positive numbers , , , This makes it possible for any time interval The total duration of the DoS attack within this time interval and number of attacks It satisfies the following constraints:

[0062] , .

[0063] Step 2.2. Establish a mathematical model for communication delay. Communication delay It is a known time-varying delay that occurs in the communication network between the event generator and the security controller. ,Right now With upper bound on communication delay .

[0064] Step 3. Based on the established mathematical model of DoS attack and communication delay, an adaptive historical weighted event triggering mechanism based on periodic sampling attack awareness is proposed, and its triggering condition design is given.

[0065] To alleviate communication burden and defend against DoS attacks, this invention proposes an adaptive historical weighted event triggering mechanism based on periodic sampling for attack awareness. The triggering conditions are designed as follows:

[0066]

[0067] .

[0068] in Indicates the sampling period of the periodic sampler; Indicates the trigger time. Indicates the first A trigger moment. This indicates the system state at the current sampling time. Indicates from the first The number of steps taken starting from the trigger moment. .

[0069] This represents the trigger matrix to be designed. For the weighting factor corresponding to the historical triggering state, satisfying and ; This represents the historical triggering state stored in the event generator buffer. Indicates the historical trigger point; Indicates the adaptive threshold parameter. ; This represents time-varying dynamic parameters. , Indicates 1 to Integers; Represents a given positive integer; Represents the time-varying dynamic parameters at the current sampling moment; Indicates from the first Starting from a trigger moment, find the minimum number of steps. This makes the triggering condition true.

[0070] The sampling period It features a switchable characteristic: switching from the DoS attack invalidation period to the nominal sampling period. Within the effective range of a DoS attack, switch to a shorter sampling period. And satisfy , .

[0071] Threshold parameter It is time-varying, and its mathematical expression is:

[0072] .

[0073] in , Given a positive constant.

[0074] ;

[0075] in Indicates the first The system state at each trigger point.

[0076] Time-varying dynamic parameters Its interval The evolution equation on is:

[0077] .

[0078] definition for initial value, , Given a nonnegative constant, , Given positive constants, Indicates index Time-varying dynamic parameters at the sampling time, This is the trigger evolution matrix to be designed.

[0079] Indicates index The system state at the sampling time. Indicates the sampling time index; For index The sampling time below, For index The sampling time below.

[0080] To ensure dynamic parameters For any initial value All remain non-negative. System parameters: for a given matrix and normal numbers , , When inequalities At the time of its establishment, for all All satisfy .

[0081] Step 4. Based on the relationship between DoS attacks and triggering time and communication latency, construct an effective DoS attack range, and design a security controller by combining an adaptive historical weighted event triggering mechanism for attack awareness.

[0082] To facilitate the description of the effective and ineffective intervals of a DoS attack under conditions of communication delay, the following implementation conditions are set:

[0083] I: Set the upper limit of communication delay ,in The nominal sampling period; this condition I is used to ensure that at most one trigger moment is rejected due to delay before a DoS attack begins, in order to avoid packet out-of-order delivery.

[0084] II: Real-time detection of each DoS attack zone The beginning moment and end time Once detected Configure the event generator immediately. During this period, data packets are stopped from being transmitted to the controller to save communication resources.

[0085] The moment when a trigger signal is successfully transmitted to the security controller is defined as the successful trigger moment, and the moment when a trigger signal is rejected due to a DoS attack is defined as the failed trigger moment; The start time of each effective DoS attack zone is denoted as .

[0086] Based on the first failure trigger time and attack range Based on the relationship, the DoS attack range can be divided into the following three cases:

[0087] Case I: If in the first The start time of a DoS attack The last trigger moment The failure trigger moment is when the condition is met. Then set .in , Indicates the first The trigger time and the first Index of sampling times related to DoS attacks. Indicates time The communication delay. In this case I, the periodic sampler is immediately commanded to change the sampling period from... Switch to and instruct the safety controller to set .

[0088] Case II: If Case I is not satisfied, and a triggering time exists. Then set:

[0089] .

[0090] Similarly, immediately switch the periodic sampler to the sampling period. and set .

[0091] Case III: If neither Case I nor Case II is satisfied, then it is considered... This is the invalid DoS attack range, i.e. It does not exist; the sampling period remains unchanged during the attack. Based on the above three cases, the definition corresponding to... The effective DoS attack range is:

[0092] .

[0093] in Indicates being The last failure trigger moment of rejection is defined as:

[0094] .

[0095] Here express The termination time, because it runs during the sampling period. The periodic sampler needs to be in Then add one more Only after the interval can the original sampling period be restored. ; For sampling time index, Duration of the attack.

[0096] Considering that multiple DoS attacks may occur adjacently or overlap in time, the first one is defined as... The effective non-intersecting DoS attack ranges are:

[0097] .

[0098] definition initial value , express initial value, ; Indicates the first The start time of an effective DoS attack range Indicates the first The start time of a non-intersecting effective DoS attack zone; Indicates the first The duration of a non-intersecting effective DoS attack zone.

[0099] No. A non-intersecting effective DoS attack zone Duration Defined as:

[0100] .

[0101] in Indicates belonging to the first One effective DoS attack zone, but not belonging to the [number]th [section / region]. The range of an effective DoS attack zone Indicates corresponding to The effective DoS attack range Indicates corresponding to The effective DoS attack range.

[0102] Define any time interval Union of all non-intersecting valid DoS attack ranges within the range for:

[0103] .

[0104] For any time interval Define the union of all regions unaffected by DoS attacks. for:

[0105] .

[0106] in Indicates the first A region unaffected by DoS attacks, when When it is 0, The initial value is , They represent the first The and the first A region unaffected by DoS attacks.

[0107] Based on the aforementioned effective DoS attack range, and combined with an attack-aware adaptive historical weighted event triggering mechanism, a security controller is designed. Its mathematical expression is:

[0108] .

[0109] in It is the gain of the safety controller to be designed. , To control the number of inputs; Indicates time interval The union of all regions within the range that were not affected by the DoS attack. Indicates time interval The union of all non-intersecting valid DoS attack zones within the range.

[0110] Step 5. Based on the designed security controller, establish a closed-loop system model for a scenario where communication latency and DoS attacks coexist.

[0111] In the trigger zone inside, if , This indicates that the interval is... The memory is located within one or more valid DoS attack zones; and They are respectively and Positive integers in the range of 1 and 2.

[0112] According to the designed safety controller, In-range control input Therefore, when establishing a closed-loop system model, only the interval where the control is in the active state is considered. .

[0113] The active range Divided into the following sub-intervals:

[0114] .

[0115] in , , .

[0116] Indicates the first The start time of a non-intersecting effective DoS attack zone Indicates the first The start time of a non-intersecting effective DoS attack zone Indicates the first The start time of a non-intersecting effective DoS attack zone.

[0117] Indicates the first The duration of a non-intersecting effective DoS attack zone Indicates the first The duration of a non-intersecting effective DoS attack zone.

[0118] If the interval Include A complete sampling period Then Subdivided into Sub-intervals:

[0119] .

[0120] in .

[0121] This represents the sampling time index. .

[0122] express The Sub-intervals, .

[0123] express The Sub-intervals, .

[0124] when hour, .

[0125] Based on the above interval division, the input delay is defined. The mathematical expression is:

[0126] .

[0127] according to The expression has , The symbol represents the defined error signal. , to obtain within the time interval Union of all regions unaffected by DoS attacks The closed-loop system model is as follows:

[0128] .

[0129] in , express 3D identity matrix They represent the first The lower bound of the slope of the nonlinear function for each actuator channel Indicates time The system state at that time, This indicates an error signal.

[0130] , It means for any time For each nonlinear function The constructed scalar-aided nonlinear function, .

[0131] according to The inequalities satisfied, for each scalar nonlinear function satisfy:

[0132] .

[0133] The above closed-loop system model in and Applicable at the time, and in and Both are in a zone unaffected by DoS attacks , The same applies at the same time. ; Indicates the first The upper bound of the slope of the nonlinear function for each actuator channel. Indicates the first The lower bound of the slope of the nonlinear function for each actuator channel.

[0134] By combining the expressions of the security controller, a unified closed-loop system model is established for scenarios where communication latency and DoS attacks coexist:

[0135] .

[0136] The initial conditions of the system are: , .

[0137] Step 6. Collect noisy data of the nonlinear networked multi-channel actuator system offline and construct a system data representation.

[0138] Step 6.1. Construct an offline dataset;

[0139] During normal system operation, system data was collected offline to construct the following dataset:

[0140] .

[0141] in The sampling period is The total number of samples.

[0142] Step 6.2. Establish a noisy data model.

[0143] Dataset The samples were collected by acquiring data from the following disturbed systems:

[0144] ;

[0145] in This represents unknown but bounded measurement noise. express The dimension of.

[0146] Step 6.3. Construct the data matrix;

[0147] The collected data was organized into the following matrix form:

[0148] ;

[0149] ;

[0150] ;

[0151] ;

[0152] .

[0153] in , , , Given a data matrix, The noise matrix is ​​unknown.

[0154] The measured noise satisfies the energy bounded condition, i.e., the noise matrix... Belongs to the following set :

[0155] ;

[0156] Among them, positive real numbers Given the noise boundary constant, Represents the total number of samples. Represents an identity matrix of appropriate dimension.

[0157] Step 6.4. Establish the data equations.

[0158] Based on the disturbed system model, the data matrix satisfies the following relationship:

[0159] .

[0160] Step 6.5. Define the set of permissible system matrices;

[0161] Incorporating noise constraints, define a set of all admissible system matrices consistent with the data. for:

[0162] .

[0163] The equivalent expression can be represented by the following quadratic matrix inequality:

[0164] ;

[0165] in .

[0166] Step 7. Based on the constructed system data representation, a data-based stability criterion is proposed for scenarios where communication delay and DoS attacks coexist. Based on this criterion, the collaborative design of the security controller and the event triggering mechanism is realized, thereby achieving data-based networked multi-channel actuator system security control.

[0167] For a given sampling period and satisfy scalar parameters , , ,as well as , , , , .

[0168] If a positive definite matrix exists , , , , Positive definite diagonal matrix Arbitrary matrix ,

[0169] scalar and invertible matrices This makes the following linear matrix inequality hold:

[0170] (1)

[0171] (2)

[0172] (3)

[0173] (4)

[0174] (5)

[0175] (6)

[0176] The closed-loop system achieves exponential stability under the attack-aware adaptive historical weighted event triggering mechanism, and the security controller gain, trigger matrix, and trigger evolution matrix are explicitly obtained through the following formulas:

[0177] ;

[0178] in and Take 1 and 2, .

[0179] Matrix blocks under non-intersecting effective DoS attack range , Matrix blocks in the region unaffected by DoS attacks , Define a matrix block that contains all permissive system matrices consistent with the data. , , , The formula is as follows:

[0180]

[0181] .

[0182] in , , , , , .

[0183] Symbols , ; , .

[0184] , , , .

[0185] express .

[0186]

[0187] .

[0188] ; .

[0189] ; ; .

[0190] in express 3D identity matrix.

[0191] .

[0192] In addition, the present invention includes stability verification of the safety controller, the process of which is as follows:

[0193] Step 7.1. Establish a Lyapunov functional that depends on the effective DoS attack range.

[0194] For the closed-loop system model constructed in step 5 under the effective DoS attack range and communication latency, a Lyapunov functional dependent on the effective DoS attack range is established. as follows:

[0195] .

[0196] in , Choose 1, 2.

[0197] ;

[0198] ;

[0199] .

[0200] in , , Let Lyapunov be the matrix under different Lyapunov functionals.

[0201] right Differentiating each term individually yields:

[0202] (7)

[0203] (8)

[0204] (9)

[0205] (10)

[0206] Step 7.2. Obtain the model-based stability conditions.

[0207] I. Estimating the functional within the non-intersecting effective DoS attack range, i.e. When, choose .

[0208] Using Jensen's integral inequality and the method of mutual convexity, the following estimate can be obtained:

[0209]

[0210] (11)

[0211] in and It is an arbitrary matrix.

[0212] According to the closed-loop system model, for invertible matrices ,have:

[0213] (12)

[0214] in, , express Error signal at time, express Error signal at that time.

[0215] according to Properties for positive definite diagonal matrices ,have:

[0216] (13)

[0217] Based on threshold parameter The mathematical expression is: , The following estimates are made:

[0218] (14)

[0219] Combining equations (7) and (14), we have:

[0220] .

[0221] in,

[0222]

[0223] .

[0224] Depend on ,according to The nonnegativity properties of are:

[0225] .

[0226] remember , , , , , , , , , .

[0227] express 3D identity matrix.

[0228] In formula (3) The situation ensured Established.

[0229] If guaranteed

[0230] (15)

[0231] We can obtain:

[0232] (16).

[0233] II. Estimating the functional within the region unaffected by DoS attacks, i.e. When, choose .

[0234] Using Jensen's integral inequality and the method of mutual convexity again, we can obtain the following estimate:

[0235]

[0236] (17)

[0237] in and It is an arbitrary matrix.

[0238] According to the closed-loop system model, for invertible matrices ,have:

[0239] (18)

[0240] in .

[0241] Combining equations (7)-(10), (13), (17), and (18), we have:

[0242] .

[0243] in,

[0244] .

[0245] Depend on ,according to The nonnegativity properties of are:

[0246] .

[0247] remember , , , , , . express 3D identity matrix.

[0248] In formula (3) The situation ensured Established.

[0249] If guaranteed

[0250] (19)

[0251] We can obtain:

[0252] (20)

[0253] III. Combine steps I and II above. Combining equations (16) and (20), we have:

[0254] (twenty one)

[0255] Combining linear matrix inequalities (4) and (5), we can obtain , , ,

[0256] , , .Depend on , combined The nonnegativity properties of are:

[0257] (twenty two)

[0258] remember , .

[0259] if Combining equations (21) and (22), we have:

[0260]

[0261]

[0262]

[0263]

[0264]

[0265]

[0266] (twenty three)

[0267] if Combining equations (21) and (23), we have:

[0268]

[0269]

[0270]

[0271] (twenty four)

[0272] remember , , , The duration is , , , .

[0273] according to For any given time period, we have:

[0274] (25)

[0275] Combining the constraints satisfied by the DoS attack and equations (23)-(25), we have:

[0276]

[0277]

[0278] .

[0279] in:

[0280] ;

[0281] .

[0282] Furthermore, .

[0283] Depend on , , ,have:

[0284]

[0285] .

[0286] Condition (6) guarantees If equations (15) and (19) hold, it can be guaranteed that under the attack-aware adaptive history-weighted event triggering mechanism, the closed-loop system achieves exponential stability, and its state convergence decay rate is... .

[0287] Step 7.3. Based on the matrix S lemma, transform the model-based stability conditions into data-based stability conditions.

[0288] Equation (15) contains an unknown system matrix, which will This can be equivalently transformed into the following quadratic matrix inequality form:

[0289] (26)

[0290] This can be equivalently transformed into:

[0291] (27)

[0292] in, .

[0293] Applying the matrix lemma S to equations (26) and (27), we can obtain that for any Equation (26) is equivalent to the existence of a scalar This makes equation (1) hold, that is, the linear matrix inequality (1) guarantees that equation (15) holds.

[0294] Equation (19) contains an unknown system matrix, which will This can be equivalently transformed into the following quadratic matrix inequality form:

[0295] (28)

[0296] Applying the matrix lemma S again to equations (27) and (28), we can obtain that for any Equation (26) is equivalent to the existence of a scalar This makes equation (2) hold, that is, the linear matrix inequality (2) guarantees that equation (19) holds.

[0297] Since the linear matrix inequalities (3)-(6) do not contain the unknown system matrix, these conditions do not need to be modified.

[0298] In summary, the linear matrix inequalities (1)-(6) guarantee the exponential stability of the closed-loop system under the attack-aware adaptive history-weighted event triggering mechanism, while the decay rate of its state convergence is... .

[0299] Based on this, the gain of the safety controller can be calculated. Trigger matrix and the triggering evolution matrix .

[0300] In addition, to verify the effectiveness of the method proposed in this invention, the following specific experiments were conducted: numerical simulation of a networked multi-channel actuator system was used to verify the effectiveness of the proposed data-driven safety control method.

[0301] Consider a networked multichannel actuator system with the following parameter settings:

[0302] .

[0303] Calculations show that , .

[0304] Time-varying communication delay set to Its upper boundary .

[0305] The two sampling periods are set to and Thus, the upper bound of delay is obtained. .

[0306] The system initial conditions are set as follows: .

[0307] Offline measurement dataset The acquisition parameters are: measurement period Total number of samples The input data In the interval Generated by uniform sampling within the area.

[0308] Measurement data is affected by noise Interference, the noise in Uniformly distributed within the range and satisfying constraints ,in At the same time, set the following parameters:

[0309] , , , , , , , , , , , , , , , , , , .

[0310] Solving equations (1)-(6) using the above parameters, the gain of the safety controller is obtained as follows:

[0311] , , ;

[0312] The corresponding trigger matrix is: ;

[0313] The trigger evolution matrix is: .

[0314] Consider a DoS attack that satisfies certain constraints, where the first... The start time of each DoS attack active zone is determined by Given, its duration is defined as .

[0315] Based on this attack sequence, time-varying communication delay, and the aforementioned security controller gain, trigger matrix, and trigger evolution matrix, a closed-loop system is simulated and verified. The time-domain graphs of the system state, control input, adaptive threshold parameters, and the trigger interval of the attack-aware event triggering mechanism are obtained as follows: Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown.

[0316] Depend on Figures 3 to 6 It is evident that, under the attack-aware adaptive historical weighted event triggering mechanism proposed in this invention, the designed data-based security controller successfully achieves global exponential stability of the networked multi-channel actuator system. Furthermore, the zero-input strategy employed by the security controller precisely matches the effective attack range, effectively avoiding ineffective control behavior.

[0317] Figure 6 The study demonstrates two scenarios, Case I and Case II, of the DoS attack range, verifying the correctness of the effective DoS attack range model. Figure 6 The event generator was shown to be delayed until a subsequent sampling period instead of being triggered immediately at the end of the effective attack period. This feature can effectively reduce unnecessary transmissions compared to the conservative strategy of the existing elastic mechanism that forces the generator to be triggered immediately after an attack.

[0318] The networked multi-channel actuator system safety control method proposed in this invention releases a total of 58 data packets. Compared with traditional point-to-point control, this data-driven safety control method improves communication efficiency.

[0319] Compared to traditional methods, the attack-aware adaptive historical weighted event triggering mechanism proposed in this invention adaptively adjusts the triggering threshold using weighted historical state information to reduce communication overhead, and switches to a shorter sampling period within the defined effective DoS attack range to accelerate system recovery. It constructs an effective DoS attack range model based on communication latency, establishing a unified closed-loop system model for scenarios where latency and attacks coexist. A Lyapunov functional dependent on the effective DoS attack range is constructed, and model-based stability conditions are derived, enabling the collaborative design of the security controller and the event triggering mechanism. Furthermore, the model-based stability conditions are transformed into data-based stability conditions. This invention does not rely on a system model; it can guarantee exponential system stability in environments with both communication latency and DoS attacks using only offline data, achieving an effective balance between control performance and communication efficiency.

[0320] Example 2

[0321] This embodiment 2 describes a networked multi-channel actuator system safety control system, which is based on the same inventive concept as the networked multi-channel actuator system safety control method in embodiment 1.

[0322] A safety control system based on a networked multi-channel actuator system includes the following modules:

[0323] The dynamics model building module is used to establish the dynamics model of a nonlinear networked multichannel actuator system.

[0324] The DoS attack and communication delay model building module is used to establish a mathematical model of DoS attacks and communication delays.

[0325] The triggering mechanism design module is used to propose an adaptive historical weighted event triggering mechanism based on periodic sampling attack awareness, based on the established mathematical model of DoS attack and communication delay, and to give its triggering condition design.

[0326] Security controller design module. Used to construct an effective DoS attack range based on the relationship between DoS attacks, trigger times, and communication latency, and combined with an attack-aware adaptive historical weighted event triggering mechanism. Design the security controller;

[0327] The closed-loop system modeling module is used to combine the designed security controller to establish a closed-loop system model under the scenario of coexistence of communication delay and DoS attack.

[0328] The system data representation module is used to collect noisy data from a nonlinear networked multichannel actuator system offline and construct a system data representation.

[0329] It also includes a data-based stability verification and collaborative solution module, which is used to propose data-based stability criteria in scenarios where communication delay and DoS attacks coexist, based on the constructed system data representation, thereby realizing the collaborative design of security controller and event triggering mechanism.

[0330] It should be noted that the implementation process of the functions and roles of each functional module in the system described in this embodiment 2 is detailed in the implementation process of the corresponding steps in the method of embodiment 1 above, and will not be repeated here.

[0331] Example 3

[0332] This embodiment 3 describes a computer device used to implement the steps of the networked multi-channel actuator system security control method described in embodiment 1 above. The computer device includes a memory and one or more processors. Executable code is stored in the memory, and when the processor executes the executable code, it is used to implement the steps of the networked multi-channel actuator system security control method described above.

[0333] The computer equipment described in this embodiment includes, but is not limited to, any device or apparatus with data processing capabilities, such as a programmable logic controller, embedded controller, edge computing device, or server in an industrial control system.

[0334] Example 4

[0335] This embodiment 4 describes a computer-readable storage medium loaded with program instructions that can be called by a processor to execute the steps of the networked multi-channel actuator system security control method in embodiment 1. The computer-readable storage medium can be an internal storage unit of a device with data processing capabilities, such as a hard disk or memory, or an external storage component, such as a pluggable hard disk, smart memory card (SMC), SD card, flash memory card, or other removable storage medium.

[0336] 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 safety control method for a networked multi-channel actuator system, characterized in that, Includes the following steps: Step 1. Establish a dynamic model of the nonlinear networked multi-channel actuator system; Step 2. Establish a mathematical model of DoS attacks and communication latency; Step 3. Based on the established mathematical model of DoS attack and communication delay, an adaptive historical weighted event triggering mechanism based on periodic sampling attack awareness is proposed, and its triggering condition design is given. Step 3 specifically involves: The attack-aware adaptive historical weighted event triggering mechanism based on periodic sampling has the following triggering conditions: ； in Indicates the sampling period of the periodic sampler; Indicates the trigger time. Indicates the first One trigger moment; This indicates the system state at the current sampling time. Indicates from the first The number of steps taken starting from the trigger moment. ; For the weighting factor corresponding to the historical triggering state, satisfying and ; This represents the historical triggering state stored in the event generator buffer. Indicates the historical trigger point; Indicates the adaptive threshold parameter. ; Indicates time-varying dynamic parameters; , Indicates 1 to Integers; Represents a given positive integer; Represents the time-varying dynamic parameters at the current sampling moment; This represents the trigger matrix to be designed; Indicates from the first Starting from a trigger moment, find the minimum number of steps. This makes the triggering condition true; The sampling period It features a switchable characteristic: switching from the DoS attack invalidation period to the nominal sampling period. ; Within the effective range of a DoS attack, switch to a shorter sampling period. And satisfy , ; Threshold parameter It is time-varying, and its mathematical expression is: ； in , Given a positive constant; ； in Indicates the first The system state at each trigger point; In the interval The evolution equation on is: ； definition for initial value, , Given a nonnegative constant, , Given positive constants, Indicates index Time-varying dynamic parameters at the sampling time, The trigger evolution matrix to be designed; Indicates index The system state at the sampling time. Indicates the sampling time index. For index The sampling time below, For index The sampling time below; for For any initial value All remain non-negative, and the system parameters must satisfy the following: for a given matrix and normal numbers , , When inequalities At the time of its establishment, for all All satisfy ; Step 4. Based on the relationship between DoS attacks and triggering time and communication latency, construct an effective DoS attack range, and design a security controller by combining an adaptive historical weighted event triggering mechanism for attack awareness. Step 5. Based on the designed security controller, establish a closed-loop system model for a scenario where communication latency and DoS attacks coexist; Step 6. Offline acquisition of noisy data from the nonlinear networked multi-channel actuator system and construction of system data representation; Step 7. Based on the constructed system data representation, a data-based stability criterion is proposed for scenarios where communication delay and DoS attacks coexist. Based on this, the collaborative design of the security controller and the event triggering mechanism is realized, thereby achieving data-based networked multi-channel actuator system security control.

2. The safety control method for a networked multi-channel actuator system according to claim 1, characterized in that, In step 1, the process for constructing the dynamic model of the nonlinear networked multi-channel actuator system is as follows: Firstly, each actuator channel of the networked multi-channel actuator system Its dynamic equation is expressed as: ； in Indicates the first Equivalent dynamic state of each actuator channel; ; The middle part indicates that it is sent to the first through the communication network. The first actuator channel Road control signals, ; Indicates the first The nonlinear effect of each actuator channel, with initial values ​​satisfying , ; For the first Linear dynamic coefficients of each actuator channel; To control the elements of the input matrix, describe the first... The control signal for the first The function of each actuator channel; Indicates the system status; These are elements of a nonlinear coupling matrix, describing the strength of nonlinear coupling between actuator channels; Indicates 1 to integers, Indicates from to Integers; Then the above The dynamic equations of each actuator channel are combined to obtain the overall continuous-time dynamic model of the networked multi-channel actuator system: ; in Represents the state vector of the system; , , , for A system state, For the system dimension, Represents a column vector; For the safety controller to be designed, To control the number of inputs; , , , For safety controllers One control input; It is a vector of nonlinear functions; , and These are the state matrix, control matrix, and nonlinear coupling matrix, respectively. This represents a diagonal matrix.

3. The safety control method for a networked multi-channel actuator system according to claim 2, characterized in that, Step 2 specifically involves: Step 2.

1. Establish a mathematical model for DoS attacks; DoS attacks occur in the communication network between the event generator and the security controller, which are to be designed to trigger the attack. Definition of the first Active range of DoS attacks for: ； in For the first The start time of a DoS attack At its end time, For the duration of the attack, Represents an integer greater than or equal to 0; For any time interval Define the union of all active DoS attack intervals within this time interval. for: ； Record the union of all inactive DoS intervals within this time interval. for: ； in Indicates time interval Internal belonging to But not belonging to The interval; definition For this time interval The total length of all active DoS attack zones within the defined area. For this time interval The number of attacks allowed by an internal DoS attack; the following limitations are imposed on the DoS attacks defended against: There are positive numbers , , , This makes it possible for any time interval The total duration of the DoS attack within this time interval and number of attacks It satisfies the following constraints: ， ； Step 2.

2. Establish a mathematical model for communication delay; communication delay It is a known time-varying delay that occurs in the communication network between the event generator and the security controller. ,Right now With upper bound on communication delay .

4. The safety control method for a networked multi-channel actuator system according to claim 3, characterized in that, Step 4 specifically involves: Define the concept of an effective DoS attack zone and set the following implementation conditions: I. Set an upper bound for communication delay ,in The nominal sampling period; II. Real-time detection of each DoS attack zone The beginning moment and end time Once detected Configure the event generator immediately. During this period, data packets are not transmitted to the controller; The moment when a trigger signal is successfully transmitted to the security controller is defined as the successful trigger moment, and the moment when a trigger signal is rejected due to a DoS attack is defined as the failed trigger moment; The start time of each effective DoS attack zone is denoted as ; Based on the first failure trigger time and attack range Based on the relationship, the DoS attack range can be divided into the following three cases: Case I: If in the first The start time of a DoS attack The last trigger moment The failure trigger moment is when the condition is met. Then set ;in , Indicates the first The trigger time and the first Index of sampling times related to DoS attacks. Indicates time Communication delay; Immediately command the periodic sampler to change the sampling period from Switch to and instruct the safety controller to set ; Case II: If Case I is not satisfied, and a triggering time exists. Then set: ； Similarly, immediately switch the periodic sampler to the sampling period. and set ; Case III: If neither Case I nor Case II is satisfied, then it is considered... This is the invalid DoS attack range, i.e. It does not exist; the sampling period remains unchanged during the attack. Based on the above three situations, the definition corresponding to The effective DoS attack range is: ； in Indicates being The last failure trigger moment of rejection is defined as: ； Here express The termination time, because it runs during the sampling period. The periodic sampler needs to be in Then add one more Only after the interval can the original sampling period be restored. ; For sampling time index, Duration of the attack; Considering that multiple DoS attacks may occur adjacently or overlap in time, the first one is defined as... The effective non-intersecting DoS attack ranges are: ； in Indicates the first The start time of a non-intersecting effective DoS attack zone is defined as follows: initial value , express initial value, ; Indicates the first The start time of an effective DoS attack zone; Indicates the first The start time of a non-intersecting effective DoS attack zone; Indicates the first The duration of a non-intersecting effective DoS attack zone; No. A non-intersecting effective DoS attack zone Duration Defined as: ； in Indicates belonging to the first One effective DoS attack zone, but not belonging to the [number]th [section / region]. The range of an effective DoS attack zone Indicates corresponding to The effective DoS attack range Indicates corresponding to The effective DoS attack range; Define any time interval Union of all non-intersecting valid DoS attack ranges within the range for: ； For any time interval Define the union of all regions unaffected by DoS attacks. for: ； in Indicates the first A region unaffected by DoS attacks, when When it is 0, The initial value is , They represent the first The and the first A region unaffected by DoS attacks; Based on the aforementioned effective DoS attack range, and combined with an attack-aware adaptive historical weighted event triggering mechanism, a security controller is designed. Its mathematical expression is: ； in It is the gain of the safety controller to be designed. , To control the number of inputs; Indicates time interval The union of all regions within the range that were not affected by the DoS attack. Indicates time interval The union of all non-intersecting valid DoS attack zones within the range.

5. The safety control method for a networked multi-channel actuator system according to claim 4, characterized in that, Step 5 specifically involves: In the trigger zone inside, if , This indicates that the interval is... The memory is located within one or more valid DoS attack zones. and They are respectively and Positive integers above; According to the designed safety controller, In-range control input ; Therefore, when establishing a closed-loop system model, only the interval where the control is in the active state is considered. ; The active range Divided into the following sub-intervals: ； in , , ; Indicates the first The start time of a non-intersecting effective DoS attack zone Indicates the first The start time of a non-intersecting effective DoS attack zone Indicates the first The start time of a non-intersecting effective DoS attack zone; Indicates the first The duration of a non-intersecting effective DoS attack zone; Indicates the first The duration of a non-intersecting effective DoS attack zone; If the interval Include A complete sampling period Then Subdivided into Sub-intervals: ； in , Indicates the sampling time index. ; express The Sub-intervals, ; express The Sub-intervals, ; when hour, ; Based on the above interval division, the input delay is defined. The mathematical expression is: ； according to The expression has , The symbol represents the definition; Define error signal , to obtain within the time interval Union of all regions unaffected by DoS attacks Closed-loop system model: ； in , express 3D identity matrix They represent the first The lower bound of the slope of the nonlinear function for each actuator channel; Indicates time The system state at that time, Indicates the error signal; , It means for any time For each nonlinear function The constructed scalar-aided nonlinear function, ; according to The inequalities satisfied, for each scalar nonlinear function satisfy: ； The above closed-loop system model in and Applicable at the time, and in and Both are in a zone unaffected by DoS attacks , The same applies at the same time. ; Indicates the first The upper bound of the slope of the nonlinear function for each actuator channel. Indicates the first The lower bound of the slope of the nonlinear function for each actuator channel; By combining the expressions of the security controller, a unified closed-loop system model is established for scenarios where communication latency and DoS attacks coexist: ； The initial conditions of the system are: , .

6. The safety control method for a networked multi-channel actuator system according to claim 5, characterized in that, Step 6 specifically involves: Step 6.

1. Construct an offline dataset; During normal system operation, system data was collected offline to construct the following dataset: ； in The sampling period is The total number of samples; Step 6.

2. Establish a noisy data model; Dataset The samples were collected by acquiring data from the following disturbed systems: ； in This represents unknown but bounded measurement noise. express dimensionality; Step 6.

3. Construct the data matrix; The collected data was organized into the following matrix form: ； ； ； ； ； in , , , Given a data matrix, The noise matrix is ​​unknown. The measured noise satisfies the energy bounded condition, i.e., the noise matrix... Belongs to the following set : ； Among them, positive real numbers Given the noise boundary constant, Represents the total number of samples. Represents an identity matrix of appropriate dimension; Step 6.

4. Establish the data equations; Based on the disturbed system model, the data matrix satisfies the following relationship: ； Step 6.

5. Define the set of permissible system matrices; Incorporating noise constraints, define a set of all admissible system matrices consistent with the data. for: ； The equivalent expression can be represented by the following quadratic matrix inequality: ； in .

7. The safety control method for a networked multi-channel actuator system according to claim 6, characterized in that, Step 7 specifically involves: For a given sampling period and satisfy scalar parameters , , ,as well as , , , , ; If a positive definite matrix exists , , , , Positive definite diagonal matrix Arbitrary matrix , scalar and invertible matrices This makes the following linear matrix inequality hold: (1) (2) (3) (4) (5) (6) The matrix blocks under the non-intersecting effective DoS attack range are , The matrix blocks in the area unaffected by DoS attacks are , Define the matrix block as the set of all permissive system matrices consistent with the data. , , , ; The closed-loop system achieves exponential stability under the attack-aware adaptive historical weighted event triggering mechanism, and the security controller gain, trigger matrix, and trigger evolution matrix are explicitly obtained through the following formulas: ； in and Take 1 and 2, .

8. The safety control method for a networked multi-channel actuator system according to claim 7, characterized in that, In step 7 , , , , , , , The formula is as follows: ； in , , , , , ; Symbols , ; , ; ， ， ， ； express ; ； ； ； ； ； ； in express 3D identity matrix; 。 9. A networked multi-channel actuator system safety control system for implementing the networked multi-channel actuator system safety control method as described in claim 1, characterized in that, The networked multi-channel actuator system safety control system includes the following modules: The dynamics model building module is used to establish the dynamics model of a nonlinear networked multichannel actuator system. The DoS attack and communication delay model building module is used to establish a mathematical model of DoS attacks and communication delays. The triggering mechanism design module is used to propose an adaptive historical weighted event triggering mechanism based on periodic sampling attack awareness, based on the established mathematical model of DoS attack and communication delay, and to give its triggering condition design. Security controller design module. It is used to construct an effective DoS attack range based on the relationship between DoS attacks and triggering time and communication latency, and to design a security controller in combination with an attack-aware adaptive historical weighted event triggering mechanism. The closed-loop system modeling module is used to combine the designed security controller to establish a closed-loop system model under the scenario of coexistence of communication delay and DoS attack. The system data representation module is used to collect noisy data from a nonlinear networked multichannel actuator system offline and construct a system data representation. It also includes a data-based stability verification and collaborative solution module, which is used to propose data-based stability criteria in scenarios where communication delay and DoS attack coexist, based on the constructed system data representation. Based on this, it realizes the collaborative design of security controller and event triggering mechanism, and thus realizes the security control of data-based networked multi-channel actuator system.

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