Elastic control method and system for denial of service attack of network physical system

Abstract

The invention provides an elastic control method and system for denial of service attack of a network physical system, relates to the field of security control of the network physical system, and aims to solve the problem that an aperiodic and boundless dual-channel DOS attack problem cannot be solved. Sending of the triggering data is triggered, the data are transmitted under the condition that a transmission rule is met, the observer is switched to update state estimation of the observer, and an estimation value is sent to the controller; the controller sends a confirmation signal to the switching observation device, calculates a control signal according to the estimated value, and sends the control signal to the actuator; and the actuator feeds back the confirmation signal and executes the calculated control signal. According to the invention, based on an event triggering mechanism, through designing a safe transmission strategy, switching an observer and an elastic control method, state estimation and control of a network physical system under a dual-channel independent DoS attack are realized, the stability of the system is ensured, and communication resources are optimized.

Description

Technical Field

[0001] The present invention belongs to the field of security control of cyber-physical systems (CPS), and in particular to a method and system for elastic control of denial of service attacks on cyber-physical systems. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Cyber-physical systems (CPS) integrate computing, communication, and control technologies and are widely used in electric vehicles, smart grids, manufacturing systems, smart healthcare, and other fields. However, since CPS relies on real-time network communications, they are vulnerable to denial of service (DoS) attacks, which may cause communication interruptions and thus affect the performance and stability of the system. Therefore, it is particularly important to achieve safe operation of CPS under potential malicious attacks.

[0004] Spoofing and Denial of Service (DoS) attacks are two common attacks in CPSs and have been widely studied. Unlike spoofing attacks that require prior information about the system to tamper with the transmission signal, the main purpose of DoS attacks is to prevent the transmission of signals. In recent years, security issues under DoS attacks have been widely studied. Existing methods can be roughly summarized as stochastic system methods, game theory methods, and resilient control methods. For the stochastic system method, after modeling the DoS attack as a Bernoulli process or a Markov process, the system under consideration can be regarded as a stochastic system. The sufficient conditions for guaranteeing security requirements are analyzed using stochastic system theory. In the game theory method, the security control of network control systems (NCSs) with DoS attacks is achieved through the unified game method. In previous existing studies, the optimal solution of the relevant optimality equation is solved in the established Markov game framework using the improved Nash Q-learning algorithm. The hierarchical game problem of wireless NCSs is solved using value iteration and Q-learning methods, and the interaction between the transmitter and the DoS attacker is modeled using the zero-sum Markov game method.

[0005] Researchers in this field have developed a variety of resilient control methods to enhance the stability and performance of cyber-physical systems (CPS) in the face of periodic and dual-channel DoS attacks. These methods include event-triggered H ∞A control strategy to ensure the stability of the vehicle suspension system under periodic DoS attacks; an observer-based controller design to ensure the exponential stability of the CPS under dual-channel periodic DoS attacks by analyzing the enhanced discrete-time cyclic switching system; and a resilient sliding mode controller designed based on a general DoS attack model to achieve the actual stability and dispersion performance of the input-to-state of the CPS under DoS attacks. In addition, the researchers proposed a robust integral sliding mode control algorithm to resist DoS attacks with time ratio and frequency restrictions; achieved the input-to-state stability of the CPS under dual-channel asynchronous DoS attacks, and derived the upper limit of the attack tolerance duration and frequency; and a H based on a novel resilient event-triggered transmission strategy. ∞ Filtering provides network systems with protection against DoS attacks of limited duration and interval.

[0006] In addition, the researchers also designed a switching-like event-triggered communication scheme to resist single-channel DoS attacks, and developed an active security control method based on the event-triggered mechanism to achieve asymptotic stability of CPS under asynchronous dual-channel DoS attacks. These research results significantly improved the resilience and security of CPS in the face of complex network attacks.

[0007] The inventors found that since CPS relies on real-time network communication, it is vulnerable to denial of service (DoS) attacks, which may cause communication interruption and thus affect the performance and stability of the system. Existing methods usually consider periodic DoS attacks with bounded duration and frequency, but for non-periodic and unbounded DoS attacks, especially attacks that occur independently on the sensor-to-observer (SO) and controller-to-actuator (CA) channels, the existing technology has not yet provided an effective solution. Summary of the invention

[0008] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a resilient control method and system for denial of service attacks on network-physical systems. By designing a secure transmission strategy, a switching observer and a resilient control method, the state estimation and control of the network-physical system when it is attacked by a dual-channel independent DoS attack are achieved, thereby ensuring system stability and optimizing the use of communication resources.

[0009] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0010] In a first aspect, the present invention provides a method for elastic control of denial of service attacks on a cyber-physical system, comprising:

[0011] Detect the state of the cyber-physical system, and determine whether a DoS attack occurs based on the detected state of the cyber-physical system. If a DoS attack occurs, an event is generated when the trigger condition is met, and the transmission of the cyber-physical system measurement data is triggered based on the event;

[0012] DoS attacks are: DoS attacks that occur independently and irregularly in the sensor-to-observer and controller-to-actuator channels;

[0013] sending the measurement data of the cyber-physical system to the switching observer based on a transmission rule;

[0014] The switching observer feeds back an ACK signal confirming data reception, and then the switching observer updates the state estimate and sends it to the controller;

[0015] The controller calculates the control signal based on the latest state estimation and sends the calculated control signal to the actuator. The actuator feeds back an ACK signal to confirm the receipt of the control signal and executes the calculated control signal to adjust the state of the cyber-physical system.

[0016] Check the stability of the performance indicators of the cyber-physical system, monitor and execute in a loop until the cyber-physical system is stable.

[0017] As a further technical solution, the physical process formula of the cyber-physical system under interference and DoS attack is:

[0018]

[0019] Where x(k)∈R n represents the state of the system, u(k)∈R m represents the control signal of the system, y(k)∈R p Represents the measurement data of the system; w(k)∈R q and represents process disturbance; v(k)∈R d represents the input disturbance; A, B, E, C, D are known system matrices with corresponding dimensions.

[0020] As a further technical solution, an event is generated when the trigger condition is met, specifically:

[0021] Calculate the measurement error based on the measurement data;

[0022] According to the measurement error, the event triggering condition is obtained;

[0023] Determine whether the event triggering condition is met, and if so, generate an event.

[0024] As a further technical solution, during transmission, specifically:

[0025] When the measurement data meets the trigger condition, the measurement data is packaged and sent to the observer until a confirmation signal from the observer is received;

[0026] When the observer receives the packaged measurement data, the observer sends the state estimate to the controller;

[0027] When the controller receives the state estimate, it calculates the control signal and packages the calculated control signal to send to the actuator;

[0028] When the actuator receives the calculated control signal packet, it sends a confirmation signal to the controller, clears the previous control signal, and resends the control signal in the new data packet to the actuator in sequence.

[0029] As a further technical solution, the switching observer updates the state estimation, specifically:

[0030] According to the transmission rules, a switching observer is constructed and the set of successful transmission moments is obtained;

[0031] According to the time set, the observer is switched to different observer states;

[0032] Based on the observer state, update the state estimate.

[0033] As a further technical solution, the calculation formula of the control signal is:

[0034]

[0035] Where K is the control gain matrix, represents the state estimate, A represents the parameter matrix of the same dimension as the original state matrix, and B represents the parameter matrix of the same dimension as the control signal.

[0036] As a further technical solution, under the transmission rule, the measurement data and the control signal are packaged into data packets and sent.

[0037] In a second aspect, the present invention provides a resilient control system for denial of service attacks on a cyber-physical system, comprising:

[0038] An attack detection and event generation module is configured to detect the state of the cyber-physical system and determine whether a DoS attack occurs based on the detected state of the cyber-physical system. If a DoS attack occurs, an event is generated when a trigger condition is met, and the transmission of measurement data of the cyber-physical system is triggered based on the event.

[0039] DoS attacks are: DoS attacks that occur independently and irregularly in the sensor-to-observer and controller-to-actuator channels;

[0040] a transmission mechanism module configured to send the measurement data of the cyber-physical system to the switching observer based on a transmission rule;

[0041] The switching observer module is configured to switch the observer to feed back an ACK signal confirming data reception, and then the switching observer updates the state estimation and sends it to the controller.

[0042] The control adjustment module is configured as a controller to calculate the control signal according to the latest state estimation and send the calculated control signal to the actuator. The actuator feeds back an ACK signal to confirm the reception of the control signal and executes the control signal to adjust the state of the network physical system.

[0043] The system detection module is configured to check the stability of the performance indicators of the cyber-physical system, monitor in a loop and execute in a loop until the cyber-physical system is stable.

[0044] The third aspect of the present invention aims to provide a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the method described in the first aspect of the present invention.

[0045] A fourth aspect of the present invention provides a computer device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the method described in the first aspect of the present invention are implemented.

[0046] One or more of the above technical solutions have the following beneficial effects:

[0047] In this embodiment, the remote safe state estimation and elastic control method based on event triggering is used in CPS to ensure that the cyber-physical system can achieve stability and accuracy of state estimation under predetermined performance under dual-channel independent DoS attacks. By utilizing the event-triggered secure transmission mechanism (ETSTM) to ensure the successful and timely transmission of data, the designed switching observer can achieve remote safe state estimation (SSE) of CPS within a limited predefined time. The developed elastic control method is based on ETSTM and switching observer, which ensures that CPS can still meet the specified H in the presence of process interference, output interference and DoS attacks. ∞ Performance standards. It provides an effective solution for the safe operation of CPS in complex network attack environments, enhances the system's ability to resist network attacks, and ensures the safe and reliable operation of critical infrastructure.

[0048] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0050] Figure 1 A schematic diagram of a resilient control system for denial of service attacks on a network physical system according to a first embodiment of the present invention;

[0051] Figure 2 The present invention is a flowchart of a method for elastic control of a denial of service attack on a network physical system according to a first embodiment of the present invention. DETAILED DESCRIPTION

[0052] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0053] It should be noted that the terms used herein are for describing specific embodiments only and are not intended to be limiting of exemplary embodiments according to the present invention.

[0054] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0055] The overall idea proposed by the present invention is as follows: for dual-channel independent denial of service attacks on cyber-physical systems, firstly, the state of the cyber-physical system is detected, and the system is attacked by DoS and the trigger conditions are met at the same time, triggering data sending; secondly, a secure transmission mechanism is constructed to ensure successful communication and timely data transmission, and a switching observer is constructed to ensure that the security state estimation of the cyber-physical system is achieved within a predefined limited time; finally, based on the secure transmission mechanism and the switching observer, the controller adopts a flexible control strategy to stabilize the CPS system attacked and interfered by DoS, and the system performs detection.

[0056] Embodiment 1

[0057] This embodiment discloses a method for elastic control of denial of service attacks on a cyber-physical system.

[0058] To more clearly illustrate this embodiment, the implementation process of elastic control against denial of service attacks on a cyber-physical system can be specifically described as follows:

[0059] like Figure 1 , Figure 2 As shown, the present invention provides a method for elastic control of denial of service attacks on a network physical system, comprising:

[0060] S1. Detect the state of the cyber-physical system, and determine whether a DoS attack occurs based on the detected cyber-physical system state. If a DoS attack occurs, an event is generated when a trigger condition is met, and the transmission of cyber-physical system measurement data is triggered based on the event.

[0061] S2, sending the measurement data of the cyber-physical system to the switching observer based on the transmission rule;

[0062] S3, the switching observer feeds back an ACK signal confirming data reception, and then the switching observer updates the state estimate and sends it to the controller;

[0063] S4, the controller calculates the control signal according to the latest state estimation and sends the calculated control signal to the actuator, the actuator feeds back an ACK signal to confirm the reception of the control signal, and executes the calculated control signal to adjust the state of the cyber-physical system;

[0064] S5. Check the stability of the performance indicators of the cyber-physical system, monitor and execute in a loop until the cyber-physical system is stable.

[0065] like Figure 1 , Figure 2 As shown, in this embodiment, in step S1, the state of the cyber-physical system is detected, and based on the detected state of the cyber-physical system, it is determined whether a DoS attack occurs. If a DoS attack occurs, an event is generated when the triggering conditions are met, and the sending of the cyber-physical system measurement data is triggered based on the event.

[0066] Cyber-physical systems are vulnerable to denial of service attacks, and in these attacks, DoS attacks occur independently and aperiodically in the sensor-to-observer (SO) and controller-to-actuator (CA) channels. To address this security issue, an event-triggered remote secure state estimation and resilient control method is proposed to ensure that the cyber-physical system can achieve stability and state estimation accuracy under predetermined performance under dual-channel independent DoS attacks.

[0067] S101, the cyber-physical system is detected and subjected to interference and DoS attack, the formula is:

[0068]

[0069] Where x(k)∈R n represents the state of the system, u(k)∈R m represents the control signal of the system, y(k)∈R p Represents the measurement data of the system; w(k)∈R q and represents process disturbance; v(k)∈R dDenote the input interference; A, B, E, C, D are known system matrices with corresponding dimensions. A and C represent parameter matrices of the same dimension as the original state matrix, B represents the parameter matrix of the same dimension as the control signal, and D and E represent parameter matrices of the corresponding dimensions of the process disturbance and the output disturbance respectively.

[0070] When the network system is under a DoS attack and the system state changes, an x(k + 1) will be output through formula (1), preliminarily detecting that the network system is under a DoS attack.

[0071] In addition, to ensure the existence of the switched observer, according to the existence conditions of the unknown input observer, the satisfaction conditions of the system matrix parameters E, C, D are derived, and the formula is as follows:

[0072]

[0073] where, denotes that under the consideration of output feedback and interference, the interference w(k) can still be observed in the system output y(k). It projects the output y(k) into the space that is not affected by the direct transmission interference Dv(k). This condition ensures that even when the output is interfered, the influence of the interference w(k) on the system state can still be observed; is a projection matrix, I is the identity matrix, D is the output matrix, is the pseudo-inverse matrix of D, C is the output matrix, E is the matrix representing the process interference, q is a positive integer representing the rank of the interference matrix E, which represents the dimension of the action of the interference in the system state space, d is the rank of the output interference matrix D, which represents the dimension of the action of the output interference in the output space, q < n indicates that the dimension of the action of the process interference is less than the dimension of the system state, that is, the interference cannot affect all states of the system, and q + d ≤ p indicates that the total dimension of the action of the process interference and the output interference is less than or equal to the dimension of the system output, that is, the system has enough outputs to observe these interferences.

[0074] To achieve the predefined goal, formula (2) is given, which provides the necessary information for the state estimation and control of the system and provides a theoretical basis for the design of the observer. It can ensure that even in the presence of interference, the state of the system can still be accurately estimated and controlled.

[0075] Since the energy of the attacker is always limited and the attacker tries to hide himself, the duration of each attack is usually bounded. At the same time, it is reasonable to allow a period of normal communication after each attack, otherwise it cannot be called energy-limited or duration-limited. Therefore, set the duration step size of each attack on the S - O and C - A channels to be no greater than b1 and b2 respectively, and the interval between adjacent attacks is greater than 1 step.

[0076] After the above steps, it is detected that the cyber-physical system is interfered with and attacked by DOS, that is, it is preliminarily judged that it is attacked by DOS, which provides data support for subsequent event triggering and transmission, and also provides necessary information for system state estimation and control.

[0077] S102: When the measurement data meets a specific trigger condition, events are generated, and these events trigger the sending of the measurement data.

[0078] Specific process: S1021, calculate the measurement error according to the measurement data.

[0079] e y (k) = y(k) - y(k t )(3)

[0080] Among them, e y (k) represents the measurement error, k represents the current time before the latest event triggering time occurs, k t represents the latest event triggering time, y(k) represents the measurement data at the current k moment, y(k t ) represents the measurement data at the time of the latest event triggering.

[0081] According to formula (3), at each time k, the current measurement output y(k) and the measurement output y(k) at the last trigger are calculated. t ) y (k).

[0082] S1022. Obtain an event triggering condition according to the measurement error.

[0083] The calculated measurement error e y (k) is compared with the preset threshold, which is determined by the parameters α1, α2 and To determine the event triggering conditions, the formula is as follows:

[0084]

[0085] Among them, 0<α1<1,α2>0, the positive integer h is the given parameter, Represents the bound on the measurement noise.

[0086] S1023: Determine whether the event triggering condition is met, and if so, generate an event.

[0087] When the system's measurement data satisfies formula (4), the system state has changed significantly, and the event trigger will trigger an event. Once the event is triggered, the current measurement data y(k) is packaged and sent to the observer, and the trigger time k is updated. tFor the current time k, continue to monitor the state change of the next time step; if it is not satisfied, continue to monitor until the condition is met.

[0088] When the system measurement data satisfies formula (4), an event is generated and the sending of the system measurement data is triggered.

[0089] like Figure 1 , Figure 2 As shown, in step S2, the measurement data of the cyber-physical system is sent to the switching observer based on the transmission rule.

[0090] S201. Based on the event triggering condition in formula (4), an event-triggered secure transmission mechanism ETSTM is constructed, that is, the transmission rule is:

[0091] 1) When the event trigger condition in formula (4) is met, the measurement data in formula (1) are packaged into Y(k), Y(k+1), ..., Y(k+b1), and k∈{k t ,k t +1,...,k t +b1} is sent to the observer at the same time until an ACK signal is received from the observer.

[0092]

[0093] Among them, k in formula (4) t is the time when the event trigger is satisfied, and τ is the designed observer parameter.

[0094] 2) When k∈S s When , the observer estimates the state Sent to the controller, where S s ={k s ,k s,1 ,...,k s,i ,i∈N +} represents the time set when the measurement data is successfully transmitted, k s,i Indicates the moment of successful transmission.

[0095] 3) When the controller receives the state estimate When the control signal [u(k s ),u(k s +1),…,u(k s +h2)], and pack it into U(k s,i ),U(k s,i +1),...,U(k s,i +b2), in k∈{k s,i ,k s,i +1,…,ks,i +b2} period until receiving the ACK signal from the actuator, where U(k s,i + l) = {u(k s+i +l),u(k s+i +l+1),…,u(k s+i +h2)} and h2=h+b1+b2-1, and the controller stops sending and discards the unsent control signals, and sends the latest control signal to the switching observer.

[0096] 4) When a new data packet is received, the actuator clears the previous control signal and resends the control signal in the new data packet to the actuator in sequence.

[0097] S202. Verify the performance of the event-triggered secure transmission mechanism ETSTM.

[0098] Since data is usually transmitted in the network in the form of packets, and the communication resources consumed in the payload of the packet are the same, the proposed ETSTM is feasible as long as the data transmitted each time can be packaged into one packet and the consumption of network resources will not increase.

[0099] The specific performance analysis is as follows:

[0100] 1) Interference may lead to an increase in the trigger frequency. The impact of interference can be reduced.

[0101] 2) When k∈[k t ,+∞), Interference may cause the event not to be triggered. The upper limit h of the trigger interval can prevent this from happening and ensure the timely triggering of the event.

[0102] 3) Since the maximum duration of each attack in the SO channel is b1, ETSTM can guarantee that the attack will be completed within k seconds at the latest. s,i =k t +b1 successfully transmits the measurement data packet due to Δk t =k t+1 -k t ≤h,Δk s =k s,i+1 -k s,i ≤h1 holds true, where h1=h+b1, ensuring timely update of measurement data.

[0103] 4) Since the maximum duration of each attack in the CA channel is b2, ETSTM can ensure that the control data is successfully transmitted within k d,i =k s,i +b2, where k d,i ∈Sd Indicates the time when the control packet is successfully transmitted and S d ={k d,1 ,k d,2 ,...,k d,i},i∈N + represents the set of successful transmission times. Since, Δk s ≤h1, so Δk d =k d,i+1 -k d,i ≤h2+1 can be established, ensuring the timely update of control signal data. At the same time, although the DoS attack occurs independently in two channels, the remote observer can know the control signal executed by the actuator at any time through the ACK signal.

[0104] The above analysis shows that building an event-triggered secure transmission mechanism (ETSTM) can save communication resources, resist independent dual-channel DoS attacks, and ensure timely updating of measurement and control signals; in addition, the designed ETSTM can ensure that the control inputs used by the observer and the actuator are the same.

[0105] S203: Pack the measurement data into data packets based on the transmission rule and transmit them.

[0106] According to the transmission rules, the measurement data is first packaged and sent to the switching observer. Then, in accordance with the SO and CA transmission rules, the state estimate updated by the switching observer is sent to the controller. The controller sends the calculated control signal to the actuator.

[0107] In this embodiment, the event-triggered secure transmission mechanism can also be applied to the interior of a remote data processing center having functional modules such as an observer and a controller; it can also be used as a signal transmission strategy within a factory.

[0108] like Figure 1 , Figure 2 As shown, in this embodiment, in step S3, the switching observer feeds back an ACK signal confirming data reception, and then the switching observer updates the state estimation and sends it to the controller.

[0109] S301. Switching observer based on transmission rules.

[0110] In this embodiment, the switching observer includes a temporary observer, a FT observer, and a RT (Real Time, RT) observer.

[0111] In order to ensure that the event-triggered remote security state estimation SSE is within a known bounded range within a predefined finite time, a switching observer is constructed based on the event-triggered security transmission mechanism ETSTM. The formula is as follows:

[0112]

[0113] in, and denote the set of successful transmission times when k∈[0,τ-1] and k∈[τ,+∞) respectively; is the state estimate at time k, is the initial state estimate; F1 k and F τ is the dynamic matrix of the observer; and is the control signal matrix based on the observer dynamics; U s1 (k) and U s2 (k) is a control signal; and is the output disturbance matrix based on the observer dynamics; Y s1 (k) and Y s2 (k) measurement data; M is a matrix used to s2 Switch the observer dynamically when ; N is a parameter matrix used to define the switching logic of the observer; τ is the time interval for observer switching; the specific expression is as follows:

[0114] When k∈S s1 , Y s1 (k) = [y T (k) y T (k-1) … y T (0)] T ,

[0115]

[0116] T=I-GQC,

[0117] U s1 (k)=[u T (k-1) u T (k-2) … u T (0)] T ,

[0118]

[0119] When k∈S s1 , Y s1 (k) = [y T (k) y T (k-1) … y T (0)] T and

[0120]

[0121] M=[I n 0 n ][NF τ N] -1 ,

[0122]

[0123] L1 and L2 are when k∈S s2 The gain matrix at .

[0124] Below are the existence conditions and validity proofs for the SSE method.

[0125] If the eigenvalues ​​of F satisfy

[0126] 0<|λ 1,min |<|λ 1,max |<|λ 2,min |<|λ 2,max |<1 (6)

[0127] in, l λ =1,2There is a positive integer τ that can make

[0128] det([NF τ N])≠0 (7)

[0129] Established;

[0130] At the same time, formula (2) is satisfied, and is observable, then, based on the designed ETSTM, the designed switching observer exists, and when k ≥ k s2,1 When the designed switching observer can ensure that the state estimation error of CPS under DoS attack Within a certain bounded range.

[0131] Substitute the parameter matrices A, B, C, E and D in formula (1) into formula (3) and obtain all the parameter matrices F1, F2, Q and G through MATLAB calculation.

[0132] According to ETSTM, when k∈S s1 And k∈S s2 When Y s1 (k) and Y s2 (k) is available, and the control signal used by the system at each moment can also be determined by the ACK signal. When the characteristic value of F satisfies formula (6), M exists. When observable, the eigenvalues ​​of F can be chosen arbitrarily, so we can design F1 and F2 to satisfy (6) to ensure the existence of M. At the same time, when formula (2) is satisfied, Q and G also exist.

[0133] According to the structure of the switching observer and the above proof process, when the given conditions are met, it can be known that the designed switching observer exists.

[0134] S302: Switch the observer to update the state estimate.

[0135] The observer update state estimation is completed by formula (5). According to the time set of successful communication between the sensor and the observer, we divide the switching observer into three observation states: temporary observer state, FT (finite time) observer state, and RT (Real Time, RT) observer.

[0136] The following process is a specific analysis process of the state estimation of CPS security at different time sets.

[0137] First, it introduces the matrix and the interference matrix T = (I-GQC), To re-express the state of the system, the introduction of these matrices is to transform the system model into a form that is easier to analyze. The formula is:

[0138]

[0139] From formula (2) and known Q and G, we get the following:

[0140]

[0141] Then the state x(k) can be expressed as the formula:

[0142]

[0143] According to the switching observer and formula (10), the state estimation error is obtained, which is divided into the following stages according to the different communication time sets. The state estimation error in each stage tends to be stable, so the state estimation update is effective.

[0144] When k <k s1,1 When, that is, when the time set is at other time, the observer is in the RT observer state, and at this time, the sensor and the observer will not successfully communicate with each other. At this time, according to the switching observer formula (5), the observer expression is: Then the state estimation error The state estimation error of the time period selected by the switching observer to update the state estimation is as follows:

[0145]

[0146] E e1 =[E AE…A k-1 E] and w e1 (k)=[w T (k-1)w T (k-2)…w T (0)] T ,That

[0147] middle is the initial state estimation error.

[0148] When k <k s2,1 and k∈S s1 When , the observer is in the temporary observer state, which is the set of moments when the sensor and the observer can successfully communicate.

[0149] From the observer formula (5), we can know the temporary observer expression:

[0150] Then the state estimation error The state estimation error of the time period selected by the switching observer to update the state estimation is as follows:

[0151]

[0152] When k <k s2,1 and When , the observer is in the RT observer state, and there is no successful communication between the sensor and the observer. At this time, the observer expression can be obtained from the switching observer (5): Then the state estimation error The state estimation error of the time period selected by the switching observer to update the state estimation is as follows:

[0153]

[0154] in

[0155]

[0156] When k∈S s2 Define z(k)∈R 2n×1 , the observer is in the FT observer state, which belongs to the time set when the sensor and the observer can successfully communicate. At this time, the observer expression can be obtained from the switching observer (5): Then the state estimation error The state estimation update by the switching observer is expressed as: z(k) = Fz(k-1) + B su(k-1)+NGQy(k)+L s Qy(k-1), where z(k) is the state estimate at this moment. z(k) is combined with (10) to derive the expression as follows:

[0157]

[0158] The process of iterating τ times is derived as follows:

[0159]

[0160] The derivation of formulas (14) and (15) is to ensure that when the cyber-physical system is subjected to DoS attacks, the proposed switching observer can accurately estimate the system state, thereby providing support for the stable control and safe operation of the system.

[0161] By design The state estimation update result in this time period can be obtained, and the formula is:

[0162]

[0163] When k>k s2,1 and When , the observer is in the RT observer state, at which time the sensor and the observer will not successfully communicate with each other. Based on the state estimation update (16), e(k) satisfies

[0164]

[0165] in

[0166]

[0167] and

[0168] According to the analysis of ETSTM performance, kk s,i ≤h1-1,k s1,1 ≤b1 and k s2,1 ≤h3 where h3=τ+b1+h-1. At the same time, according to formula (11), when k <k s1,1 When and e(k) satisfies the following formula:

[0169]

[0170] When k <k s2,1 When e(k) satisfies

[0171]

[0172] Among them

[0173] According to formula (18), when k ∈ S s2

[0174] e(k) = 0 (20)

[0175] According to formula (19), when k > k s2 , when

[0176]

[0177] In the worst case, when k < h3

[0178]

[0179] and when k ≥ h3

[0180]

[0181] In summary, the SSE method developed based on the designed ETSCM exists and can achieve the SSE of CPS within a pre-determined finite time. In addition, when w(k) = 0, it can be achieved when k ≥ h3

[0182] After the above steps, the switching observer designed based on ETSTM can achieve the security state estimation of the cyber-physical system within a predetermined finite time. After receiving the data, the switching observer updates the state estimation by combining the new measurement data according to the system model and the previous estimated state, that is, the process of iteration according to the formula. When suffering from a denial-of-service attack, the switching observer can ensure the completion of the state estimation within a predetermined finite time according to the event-triggering mechanism, ensuring that the system state can be accurately estimated even when the communication is interfered. In addition, the switching observer uses the sending confirmation (ACK) signal to ensure the consistency of the control signal, so as to ensure that the actuator and the observer use the same control input; finally, based on the latest state estimation and the designed control gain matrix, the control signal is calculated and sent to the actuator to achieve the robust control of the cyber-physical system.

[0183] As Figure 1 、 Figure 2 shown, in this embodiment, in step S4, the controller calculates the control signal according to the latest state estimation and sends the calculated control signal to the actuator. The actuator feeds back the ACK signal for confirming the reception of the control signal and executes the calculated control signal to adjust the state of the cyber-physical system.

[0184] S401: A controller receives a data packet and calculates a control signal in the data packet according to a state estimation value of a switching observer in the data packet.

[0185] After the data is successfully received, the controller sends a confirmation signal to the switching observer to confirm that the data packet has successfully reached the destination.

[0186] S4011. Calculate a control signal based on the received state estimation value.

[0187] Next, the controller receives the state estimate from the switching observer According to the state estimate Calculate the control signal at current and future time, the formula is:

[0188]

[0189] Where K is obtained by design based on formula (25), as follows:

[0190]

[0191] Among them, A represents the parameter matrix of the same dimension as the original state matrix, and B represents the parameter matrix of the same dimension as the control signal. is the estimated state at time k, is the estimated state at the previous moment, u(k-1) is the control signal at the previous moment, u(k) is the control signal calculated at moment k, K is the control gain matrix, the first formula represents the state prediction; the second formula is the control rate.

[0192] Based on ETSTM, when k∈(k d,i ,k d,i+1 ), the system will be controlled by the calculated control signal in the data packet.

[0193] After the above steps, the mathematical relationship between the state update and control signal of the cyber-physical system (CPS) can be established. Formula (25) is a basic component in the control system design, which can combine how the system can achieve closed-loop control based on the current state estimate and control input. The first formula represents the state prediction, which is used to predict the state estimate of the next time step; the second formula is the control rate, which provides the basis for designing the control strategy so that the control gain matrix K can be selected according to the required system performance.

[0194] S4012, according to the control signal obtained after calculation, set the H of the control system ∞ The performance indicators are γ and the stability of the closed-loop system.

[0195] According to the designed controller, the control rate formula in formula (25) is substituted into formula (1), and the closed-loop system formula is obtained as follows:

[0196]

[0197] Among them, A, B, E, C, D are known system matrices with corresponding dimensions; A and C represent parameter matrices of the same dimensions of the original state matrix, B represents the parameter matrix of the same dimension of the control signal, k is the control gain matrix, D and E represent the parameter matrices of the corresponding dimensions of the process disturbance and output disturbance respectively; x(k) represents the state of the original system, y(k) represents the measured data of the system; w(k) represents the process disturbance of the system; v(k) represents the input disturbance of the system; is the estimated state at time k, and x(k+1) is the updated state of the system at the next moment. u(k) is based on Designed by.

[0198] according to The system formula (26) is written as:

[0199]

[0200] Where e(k) is the state estimation error, is the state estimation based on the observer; A s =A+BK,A s is the system matrix, which represents the state transition of the system when there is no external input and attack; A is the original system matrix, B is the input matrix, K is the control gain matrix, D and E represent the parameter matrices of the corresponding dimensions of the process disturbance and output disturbance respectively; x(k) represents the state of the original system at time k, and y(k) represents the measurement data of the system.

[0201] In formula (27), the controller can control the H of the system when the following conditions are met: ∞ The performance indicators are γ and closed-loop system stability.

[0202] (1) When w(k) = 0, the closed-loop system (27) is asymptotically stable;

[0203] (2) Under zero initial conditions, for any and the requirement that γ>0 gives Among them, ||x(k)|| is the Euclidean norm of x(k), is the maximum norm of process noise, γ is H ∞ Performance indicators. represents the sum of the norms of the system states from time k = 0 to infinity, which can be viewed as the cumulative energy of the system states; is the performance index γ and the upper bound of the process noise The infinite sum of the products of .

[0204] The following analysis process is given when there is interference and denial of service attack, the closed-loop system H ∞ The necessary condition for the stability of the performance indicator γ is that the linear matrix inequality holds.

[0205] For a CPS with process disturbances, output disturbances, and dual-channel independent denial-of-service attacks, if for a given γ1>0, there exists α3>0, matrix P1>0, Φ>0, X, such that the following linear matrix inequality (LMI) holds:

[0206] The designed elastic control method can be designed by K = XP1 -1 To ensure that the H of the closed-loop system (27) ∞ The performance index γ is stable. The control gain matrix K is obtained by solving the linear matrix inequalities (LMIs) in formulas (28) and (29) and finding the matrices P1, Φ and X that satisfy the inequalities.

[0207] Based on the basic state space model and control strategy of the system, by introducing the state estimation and control gain matrix, it solves the K value through the LMI matrix (28), that is, K = XP1 -1 .

[0208] S402: Send the calculated control signal to the actuator, and the actuator feeds back an ACK signal to confirm the reception of the control signal, and executes the calculated control signal to adjust the state of the network-physical system.

[0209] The data containing the calculated control signals are packaged into b2+1 packets and sent to the actuators according to ETSTM.

[0210] When the actuator receives the calculated control signal, it feeds back an ACK signal to confirm the receipt of the data, and adjusts the network physical state according to the calculated control signal in step S401, and controls the system performance index and system stability by controlling the gain matrix K.

[0211] like Figure 1 , Figure 2 As shown, in this embodiment, in step S5, the stability of the performance indicator of the cyber-physical system is checked, and the monitoring and execution are performed in a loop until the cyber-physical system is stable.

[0212] The following formulas together form a theoretical framework to analyze and prove the stability and H of cyber-physical systems under DoS attacks and interference. ∞Performance. By solving and analyzing these inequalities, we can derive control strategies that meet the performance requirements and ensure the robustness and stability of the system under various attacks and uncertainties.

[0213] First, the Lyapunov function is introduced as

[0214] V(k)=x T (k)P2x(k)(30)

[0215] Among them, V(k) represents the Lyapunov function, P2 is a positive definite matrix, x(k) is the state matrix of the original system, and x T (k) is the transposed matrix of the original system state.

[0216] First, according to Schur complement lemma, we ensure that the closed-loop system is ∞ It is stable in the sense of norm, and LMI(28) is equivalent to the formula:

[0217]

[0218] Among them, A s1 =AP1+B s1 , B s1 =BX.A s1 represents the state transfer matrix of the closed-loop system, B s1 is the control signal matrix, A is the state transfer matrix of the original system, B is the input matrix of the original system, and X is a design parameter matrix used to calculate the control gain K. s1 is the system matrix, is the transpose of the system matrix; is the transpose of the control signal matrix, E T is the transposed matrix of the interference matrix; P1 is a positive definite matrix, is the inverse matrix of the positive definite matrix, used for Lyapunov stability analysis; Φ2 is a positive definite matrix, used to represent the weight of system performance; γ1I q represents the performance limit of the system when it is disturbed, γ1I q It is a preset performance indicator used to ensure the stability and performance of a closed-loop system when subjected to bounded disturbances.

[0219] The left and right sides of inequality (31) are multiplied by the matrix The following inequality can be obtained:

[0220]

[0221] Among them A d =A+B d And B d =BXP1 -1 ,Φ2=P1-1 ΦP1 -1 . Let P2 = P1 -1 , according to K = XP1 -1 , inequality (32) is equivalent to the formula:

[0222]

[0223] According to the closed-loop system formula (27), we can get:

[0224]

[0225]

[0226] Based on (33) and (34), we can get:

[0227] ΔV(k)+x T (k)Φ2x(k)-γ1e T (k)Φ2e(k)-γ1w T (k)w(k)<0(35)

[0228] Under the initial condition of zero, we can obtain:

[0229]

[0230] in,

[0231] Φ3=diag(Φ2,I q ),

[0232] w s (k) = [e T (k) w T (k)] T ,

[0233] λ min (Φ2)=min{λ(Φ2)}, u(k)=0;

[0234] When k <k s1 When u(k)=0, it is equivalent to Since the system is based on The designed control signal is controlled when k∈[k d,i ,k d,i+1 ) and k d,i+1 -k d,i ≤h2+1, then in therefore,

[0235] Therefore, the designed resilient control method can ensure H ∞ Stability of the performance indicator γ.

[0236] After the above steps, the stability and H of the cyber-physical system under DoS attack and interference are analyzed and proved. ∞ Performance. By solving these inequalities, a control strategy that meets the performance requirements can be derived, ensuring the robustness and stability of the system under various attacks and uncertainties.

[0237] In this embodiment, the maximum duration step of the two-channel denial of service attack that the method can tolerate is related to the estimation effect of the capacity of the data packet and the performance of the CPS is related to the event trigger interval and the maximum duration step of each attack. This is because when there is no measurement signal transmission, interference may reduce the estimation and control performance. The designed method can ensure that the accurate state estimation of the CPS is obtained within a given finite time, and the closed-loop system is stable when w(k)=0.

[0238] In this embodiment, the problem is solved by MATLAB, and the parameters and matrices related to system stability and control performance are mainly solved. The control gain matrix K, observer gain matrices L1 and L2, observer parameters τ, F1 and F2, and event trigger parameters α1, α2, h, are solved by LMI. These solved elements are crucial for designing event-triggered remote safety state estimation (SSE) and resilient control strategies.

[0239] In the embodiment, designing the control gain matrix K, the observer gain matrix L1 and L2 observer parameters and the event triggering parameters plays a vital role in updating the state estimation and realizing the elastic control.

[0240] At present, no similar scheme has been proposed for the safety control system of linear discrete systems based on non-periodic DoS attacks with limited total duration and frequency. This paper explores the design strategies of remote safe state estimation (SSE) and resilient control systems for cyber-physical systems (CPSs) with process disturbances, output disturbances and denial of service (DoS) attacks. The considered DoS attacks occur independently and aperiodically in the sensor-to-observer (SO) and controller-to-actuator (CA) channels. In order to achieve successful signal transmission and save communication resources, an event-triggered secure transmission mechanism (ETSTM) system is designed. This study collaboratively develops transmission strategies, state estimation and control methods that can resist non-periodic independent DoS attacks, and explains the attack intensity that the method can tolerate.

[0241] Embodiment 2

[0242] This embodiment provides a resilient control system against denial of service attacks on a cyber-physical system, including:

[0243] An attack detection and event generation module is configured to detect the state of the cyber-physical system and determine whether a DoS attack occurs based on the detected state of the cyber-physical system. If a DoS attack occurs, an event is generated when a trigger condition is met, and the transmission of measurement data of the cyber-physical system is triggered based on the event.

[0244] DoS attacks are: DoS attacks that occur independently and irregularly in the sensor-to-observer and controller-to-actuator channels;

[0245] a transmission mechanism module configured to send the measurement data of the cyber-physical system to the switching observer based on a transmission rule;

[0246] The switching observer module is configured to switch the observer to feed back an ACK signal confirming data reception, and then the switching observer updates the state estimation and sends it to the controller.

[0247] The control adjustment module is configured as a controller to calculate the control signal according to the latest state estimation and send the calculated control signal to the actuator. The actuator feeds back an ACK signal to confirm the receipt of the control signal and executes the calculated control signal to adjust the state of the network physical system.

[0248] The system detection module is configured to check the stability of the performance indicators of the cyber-physical system, monitor in a loop and execute in a loop until the cyber-physical system is stable.

[0249] Embodiment 3

[0250] The purpose of this embodiment is to provide a computer-readable storage medium on which a program is stored. When the program is executed by a processor, the method steps described in the first embodiment are implemented.

[0251] Embodiment 4

[0252] The purpose of this embodiment is to provide an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor implements the method steps described in the first embodiment when executing the program.

[0253] The steps involved in the apparatus of the above embodiment correspond to the method embodiment 1, and the specific implementation method can refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0254] Those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0255] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for elastic control of denial of service attacks on a cyber-physical system, characterized in that: include: Detect the state of the cyber-physical system, and determine whether a DoS attack occurs based on the detected state of the cyber-physical system. If a DoS attack occurs, an event is generated when the trigger condition is met, and the transmission of the cyber-physical system measurement data is triggered based on the event; DoS attacks are: DoS attacks that occur independently and irregularly in the sensor-to-observer and controller-to-actuator channels; sending the measurement data of the cyber-physical system to the switching observer based on a transmission rule; The switching observer feeds back an ACK signal confirming data reception, and then the switching observer updates the state estimate and sends it to the controller; The controller calculates the control signal based on the latest state estimate and sends the calculated control signal to the actuator. The actuator feeds back an ACK signal to confirm the receipt of the control signal and executes the calculated control signal to adjust the state of the cyber-physical system. Check the stability of the performance indicators of the cyber-physical system, monitor and execute in a loop until the cyber-physical system is stable.

2. A method for elastic control of denial of service attacks on a cyber-physical system as claimed in claim 1, characterized in that: The cyber-physical system, under interference and denial of service attacks, has the following formula: Where x(k)∈R n represents the state of the system, u(k)∈R m represents the control signal of the system, y(k)∈R p Represents the measurement data of the system; w(k)∈R q and represents process disturbance; v(k)∈R d represents the input disturbance; A, B, E, C, D are known system matrices with corresponding dimensions.

3. A method for elastic control of denial of service attacks on a cyber-physical system as claimed in claim 1, characterized in that: Generates an event when the trigger conditions are met, specifically: Calculate the measurement error based on the measurement data; According to the measurement error, the event triggering condition is obtained; Determine whether the event triggering condition is met, and if so, generate an event.

4. A method for elastic control of denial of service attacks on a cyber-physical system as claimed in claim 1, characterized in that: When transmitting based on the transmission rule, when the measurement data meets the trigger condition, the measurement data is packaged and sent to the observer until a confirmation signal from the observer is received; When the observer receives the packaged measurement data, the observer sends the state estimate and the packaged control signal to the controller; When the controller receives the state estimate, it calculates the control signal and packages the calculated control signal to send to the actuator; When the actuator receives the calculated control signal packet, it sends a confirmation signal to the controller, clears the previous control signal, and resends the control signal in the new data packet to the actuator in sequence.

5. A method for elastic control of denial of service attacks on a cyber-physical system as claimed in claim 1, characterized in that: The switching observer updates the state estimate, specifically: According to the transmission rules, a switching observer is constructed and the set of successful transmission moments is obtained; According to the time set, the observer is switched to different observer states; Based on the observer state, update the state estimate.

6. A method for elastic control of denial of service attacks on a cyber-physical system as claimed in claim 1, characterized in that: The calculation formula of the control signal is: Where K is the control gain matrix, represents the state estimate, A represents the parameter matrix of the same dimension as the original state matrix, and B represents the parameter matrix of the same dimension as the control signal.

7. A method for elastic control of denial of service attacks on a cyber-physical system as claimed in claim 1, characterized in that: Under the transmission rules, both measurement data and control signals are packaged into data packets and sent.

8. A resilient control system against denial of service attacks on a cyber-physical system, characterized in that: include: An attack detection and event generation module is configured to detect the state of the cyber-physical system and determine whether a DoS attack occurs based on the detected state of the cyber-physical system. If a DoS attack occurs, an event is generated when a trigger condition is met, and the transmission of measurement data of the cyber-physical system is triggered based on the event. DoS attacks are: DoS attacks that occur independently and irregularly in the sensor-to-observer and controller-to-actuator channels; a transmission mechanism module configured to send the measurement data of the cyber-physical system to the switching observer based on a transmission rule; A switching observer module is configured to switch the observer to feedback an ACK signal confirming data reception, and then the switching observer updates the state estimate and sends it to the controller; A control adjustment module is configured such that the controller calculates a control signal according to the latest state estimation and sends the calculated control signal to the actuator, the actuator feeds back an ACK signal confirming receipt of the control signal, and executes the calculated control signal to adjust the state of the cyber-physical system; The system detection module is configured to check the stability of the performance indicators of the cyber-physical system, monitor in a loop and execute in a loop until the cyber-physical system is stable.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are performed.

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