Cps model-free adaptive predictive control method and system under mixed network attack

Abstract

The present application relates to the technical field of network security, and particularly relates to a CPS model-free adaptive predictive control method and system under hybrid network attack, which comprises the following steps: constructing a data model of a nonlinear information physical system; performing dynamic linearization on the established data model to obtain a linearized data model; based on the linearized data model, constructing a model-free adaptive controller of the information physical system under non-periodic DoS attack and random FDI attack, and designing a predictive control algorithm of the model-free adaptive controller; introducing an evaluation index with bounded tracking error, and based on the designed predictive control algorithm, performing safety control on the information physical system, so that the output of the information physical system can still stably track the reference signal when receiving hybrid network attack. The present application can still guarantee stable tracking of the system to the reference signal under hybrid network attack, and improve the adaptability to system uncertainty and complexity.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of network security, and more particularly to a CPS model-free adaptive predictive control method and system under hybrid network attacks. BACKGROUND

[0002] At present, the controllable, trusted and scalable information physical system (Cyber-physical system, CPS) with deep integration of computing, communication and control functions is attracting much attention. As a comprehensive technology system for deep practice of industrialization and informatization "two integration", CPS is leading a new round of technological revolution and industrial revolution, and empowering intelligent innovation applications in the fields of industrial production, smart grid, intelligent transportation and assisted medical treatment. Due to the introduction of communication network, the originally closed physical system becomes more open, thereby increasing the risk of information physical system being attacked from outside. Compared with traditional control systems, CPS has a wider attack surface, and attackers can cause great damage through malicious attacks on different network levels. Due to the complex nonlinear characteristics of CPS and the difficulty of system modeling, it is almost impossible to obtain an accurate CPS model in control practice. Therefore, a model-free adaptive control (Model-Free Adaptive Control, MFAC) method based on pure data driving is emerging, which uses input / output data without using system model information to construct a controller, and has better applicability in the field of CPS security control.

[0003] At present, the system security control research is mainly aimed at denial of service (Denial of Service, DoS) attacks or false data injection (False Data Injection, FDI) attacks, but it should be noted that attackers often launch two or more network attacks at the same time to maximize the damage to system performance. Therefore, it has theoretical significance and practical value to study the security control problem of CPS under hybrid network attacks.

[0004] It is worth noting that although existing research has proposed some security control methods under network attack conditions, there are still some deficiencies: 1) current CPS security control problems under specific types of network attacks (such as DoS attacks or FDI attacks) have made rich research results, but the CPS security control research involving mixed network attacks is still in its infancy and needs further in-depth research. 2) A large number of research results have been achieved in the field of CPS security control based on data-driven model-free adaptive control, but most of them are for system security control research under single type of network attack, while considering the CPS model-free adaptive control problem under mixed network attack conditions that cause greater damage to the system, therefore, the model-free adaptive security control problem under mixed network attack needs further in-depth research; 3) Due to the complex nonlinear characteristics of CPS and the difficulty of system modeling, it is almost impossible to obtain an accurate CPS model in control practice.

[0005] Therefore, how to solve the above problems and further study the problem of nonlinear information physical system model-free adaptive predictive control under mixed network attack is a problem that needs to be solved by those skilled in the art. SUMMARY

[0006] Therefore, the present application provides a CPS model-free adaptive predictive control method and system under mixed network attack, which aims to consider the influence of mixed network attack on system output and effectively solve the problem of difficult CPS modeling for security control.

[0007] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0008] In a first aspect, the present application provides a CPS model-free adaptive predictive control method under mixed network attack, comprising the following steps:

[0009] S1, constructing a data model of a nonlinear information physical system;

[0010] S2, dynamically linearizing the established data model to obtain a linearized data model;

[0011] S3, based on the linearized data model, constructing a model-free adaptive controller of the information physical system under aperiodic DoS attack and random FDI attack, and designing a predictive control algorithm of the model-free adaptive controller;

[0012] S4, introducing a tracking error bounded evaluation index, based on the designed predictive control algorithm to perform safety control on the information physical system, if the output of the information physical system satisfies the evaluation index, it means that the output of the information physical system can track the reference signal, if the output of the information physical system does not satisfy the evaluation index, repeat S3-S4, until the output of the information physical system can track the reference signal.

[0013] Further, in S1, the expression of the data model of the nonlinear information physical system is:

[0014] y(t+1) = f(y(t),..., y(t-n y ), u(t),..., u(t-n u ))

[0015] Where n y , n u represent the unknown order of the output y(t) and the input u(t) respectively, and f(·) represents an unknown nonlinear function; t represents the time of discrete time.

[0016] Further, S2 includes:

[0017] The partial derivative of f(·) with respect to the control input signal u(t) is continuous, and the information physical system satisfies the generalized Lipschitz condition, for any time t, the system input u(t)≠0, there exists a pseudo partial derivative φ(t), so that the nonlinear information physical system model constructed in S1 is constructed into the following dynamic linearization data model

[0018] Δy(t+1) = φ(t)Δu(t)

[0019] Where |φ(t)|≤k, k represents a normal number; Δy(t+1) represents the increment of the system output at time t+1; Δu(t) represents the input increment.

[0020] Further, in S3, define As the DoS network attack time period, As the time period without DoS attack, the attack start and end times are defined as And

[0021] The design of non-periodic DoS attack and random FDI attack in the measurement channel is represented as:

[0022]

[0023] wherein β(t) represents a random variable satisfying Bernoulli distribution; ψ(t) = g(t)(y(t) + ω(t)) represents FDI attack signal, g(t) represents random multiplicative attack coefficient, and ω(t) represents random additive attack coefficient; z a (t) represents system output received by the model-free adaptive controller for calculating control signal;

[0024] It is assumed that wherein Prob{·} represents probability of a random variable; random multiplicative attack coefficient g(t) satisfies random additive attack coefficient ω(t) satisfies wherein E{·} represents expectation, represents multiplicative attack signal energy of FDI attack, represents additive signal attack energy of FDI.

[0025] Further, in S3, the model-free adaptive controller is represented as:

[0026]

[0027] wherein y * (t+1) represents reference signal; λ>0 represents weight factor; v∈(0, 1] represents step factor; and u(t-1) represents output value of the controller at last time; is an estimated value of pseudo partial derivative φ(t);

[0028]

[0029] wherein χ represents weight factor; κ represents step factor; and l represents a small normal number; is an initial value of .

[0030] Further, in S3, considering network-induced time delay and mixed network attack factors, a predictive control algorithm of the model-free adaptive controller is designed, and is represented as:

[0031]

[0032] if or |Δu(t-1)|≤l or

[0033] wherein represents an estimated value of pseudo partial derivative φ(t) at t ; Δz a (t) represents output increment of the system after

[0034] attack;

[0035]

[0036] Δu c (t+r|t)=Δu c (t+r-1|t)+Δu(t+r|t)

[0037] In order to compensate for network delay, the following control signal is designed:

[0038] u(t)=u(t-1)+Δu c (t+τ|t)

[0039] Wherein, r=1,2,...,τ, Indicates the continuous multiplication of r from 1 to ; α(r) indicates an attenuation factor, The rate of change of α(r) from m1 to m2 is determined by the parameter m∈[0.05,0.15], and the normal numbers m1 and m2 satisfy the condition 0≤m2≤m1<1, and τ indicates network-induced delay; Indicates the input signal increment at time; Indicates the input signal increment at time; Δu(t+r|t) indicates the input signal increment at t+r-1 predicted at t; Δu c (t+r|t) indicates the cumulative value of the input signal increment at t+r predicted at t; Δu c (t+r-1|t) indicates the cumulative value of the input signal increment at t+r-1 predicted at t; Δu c (t+τ|t) indicates the cumulative value of the input signal increment at t+τ predicted at t.

[0040] Further, in S4, if the output of the information physical system satisfies the evaluation index, it indicates that the output of the information physical system can track the reference signal, and there exists:

[0041]

[0042] Wherein, K indicates a constant, K=d0k+2k, and k indicates a normal number; y * Indicates a reference output; d0, d1, d2∈(0,1), and σ∈(0,1) is the time proportion of DoS attack at time t; Indicates a system estimation error; Indicates the error between the estimated value and the true value of the system parameter at the initial time t=1; t-1 power of d1 is represented; (1-σ)t power of d2 is represented; e(t+1) represents the tracking error at t+1 time; e(0) represents the tracking error value at initial time t=0.

[0043] In a second aspect, the present application provides a CPS model-free adaptive predictive control system under hybrid network attacks, which is suitable for the CPS model-free adaptive predictive control method under hybrid network attacks as described above, and comprises:

[0044] a data construction module, configured to construct a data model of the nonlinear information physical system;

[0045] a linearization module, configured to dynamically linearize the constructed data model to obtain a linearized data model;

[0046] an adaptive prediction algorithm design module, configured to construct a model-free adaptive controller of the information physical system under non-periodic DoS attacks and random FDI attacks based on the linearized data model, and design a prediction control algorithm of the model-free adaptive controller;

[0047] a tracking error evaluation module, configured to introduce an evaluation index of bounded tracking error, and perform safety control on the information physical system based on the designed prediction control algorithm, so that the output of the information physical system can track the reference signal.

[0048] In a third aspect, the present application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor; when the processor executes the computer program, the steps of the CPS model-free adaptive predictive control method under hybrid network attacks as described above are implemented.

[0049] In a fourth aspect, the present application provides a computer readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the CPS model-free adaptive predictive control method under hybrid network attacks as described above are implemented.

[0050] According to the above technical solution, compared with the prior art, the present application has the following beneficial effects:

[0051] Firstly, the present application establishes a data model of a nonlinear information physical system, and dynamically linearizes the constructed data model to obtain a linearized model; secondly, considering the false data injection attacks and non-periodic denial of service attacks on the measurement channel, the present application derives a model-free adaptive controller of the information physical system and a pseudo partial derivative estimation value, and proposes a model-free adaptive predictive control algorithm, so that the system output can still stably track the reference signal under hybrid network attacks.

[0052] The model-free adaptive predictive controller designed according to the prior art can cope with the problems of complex nonlinear characteristics of CPS and great difficulty in system modeling, can construct an equivalent dynamic linearization time-varying model at a dynamic operating point of a control object, and can adaptively cope with parameter and structure changes, and has excellent adaptability and robustness.

[0053] In addition, the model-free adaptive predictive control design method is given based on the model-free adaptive control, and the contraction mapping principle analysis method is applied to prove that the model-free adaptive predictive control algorithm can guarantee the boundedness of tracking error in the mean square sense, and then the system evaluation index is obtained, the model-free adaptive predictive control method can directly utilize input and output data for control, reduces the modeling difficulty, improves the adaptability to the uncertainty and complexity of the information physical system, and enhances the robustness and safety of the information physical system. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0055] Figure 1 The flowchart of the model-free adaptive predictive control method of CPS under hybrid network attack provided by the present application is shown in the figure.

[0056] Figure 2 The detailed flowchart of the model-free adaptive predictive control method of CPS under hybrid network attack provided by the present application is shown in the figure.

[0057] Figure 3 The FDI attack signal diagram provided by the present application is shown in the figure.

[0058] Figure 4 The FDI attack occurrence time diagram provided by the present application is shown in the figure.

[0059] Figure 5 The non-periodic DoS attack occurrence time diagram provided by the present application is shown in the figure.

[0060] Figure 6 The information physical system output tracking trajectory diagram under hybrid network attack provided by the present application is shown in the figure.

[0061] Figure 7 The information physical system output tracking trajectory diagram under different FDI attack parameters provided by the present application is shown in the figure. DETAILED DESCRIPTION

[0062] With reference to the accompanying drawings, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0063] As shown in Figure 1 , the embodiment of the present application discloses a CPS model-free adaptive predictive control method under hybrid network attacks, comprising the following steps:

[0064] S1, constructing a data model of a nonlinear cyber-physical system;

[0065] S2, dynamically linearizing the established data model to obtain a linearized data model;

[0066] S3, based on the linearized data model, constructing a model-free adaptive controller of the cyber-physical system under non-periodic DoS attacks and random FDI attacks, and designing a predictive control algorithm of the model-free adaptive controller;

[0067] S4, introducing a tracking error bounded evaluation index, based on the designed predictive control algorithm, performing security control on the cyber-physical system, if the output of the cyber-physical system satisfies the evaluation index, it means that the output of the cyber-physical system can track the reference signal, if the output of the cyber-physical system does not satisfy the evaluation index, repeating S3-S4 until the output of the cyber-physical system can track the reference signal.

[0068] The specific implementation process of each step is described in detail below, and the specific flow is shown in Figure 2 . S1, constructing a data model of a nonlinear cyber-physical system, the expression is:

[0069] y(t+1)=f(y(t),...,y(t-n y ),u(t),...,u(t-n u ))

[0070] Where n y , n u represent the unknown orders of the output y(t) and the input u(t) respectively, and f(·) represents an unknown nonlinear function; t represents the time of discrete time.

[0071] S2, for the above information physical system, the partial derivative of f(·) with respect to the control input signal u(t) is continuous, and the information physical system satisfies the generalized Lipschitz condition, for any time t, when the system input u(t)≠0, there is a pseudo partial derivative φ(t), so that the nonlinear information physical system model constructed in S1 is constructed into the following dynamic linearization data model

[0072] Δy(t+1)=φ(t)Δu(t)

[0073] Wherein, |φ(t)|≤k, k represents a normal number; Δy(t+1) represents the increment of system output at time t+1; Δu(t) represents the input increment.

[0074] S3, based on the linearized data model, a non-periodic DoS attack and a random FDI attack are constructed. The model-free adaptive controller of the information physical system is constructed, and the predictive control algorithm of the model-free adaptive controller is designed.

[0075] S31, the construction process of the model-free adaptive controller includes:

[0076] The performance index function of u(t) is designed as:

[0077] J1[u(t)]=[y * (t+1)-y(t+1)] 2 +λ[u(t)-u(t-1)] 2

[0078] Wherein, y * (t+1) represents the reference signal, and λ>0 represents the weight factor.

[0079] The data model in S2 is brought into the index function to obtain:

[0080] J[u(t)]=|y * (t+1)-y(t)-φ(t)Δu(t)| 2 +λ|u(t)-u(t-1)| 2

[0081] =[y * (t+1)-y(t)] 2 +[φ(t)Δu(t)] 2 -2[y * (t+1)-y(t)]φ(t)Δu(t)+λ[u(t)-u(t-1)] 2

[0082] The derivative of J[u(t)] with respect to u(t) is obtained:

[0083]

[0084] Let We have

[0085] |φ(t)| 2 Δu(t)-[y * (t+1)-y(t)]φ(t)+λ[u(t)-u(t-1)]=0

[0086] We have

[0087]

[0088] To make the control algorithm more general, we introduce a step factor v∈(0,1], and derive the model-free adaptive controller as follows:

[0089]

[0090] where ν∈(0,1] represents the step factor, is the estimate of φ(t).

[0091] The performance index function of the pseudo partial derivative estimator is designed as follows:

[0092] where χ represents the weight factor.

[0093] Based on the process of solving the controller, the parameter estimation algorithm is designed as follows:

[0094]

[0095]

[0096] Define as the DoS network attack period, as the DoS attack dormant period, and the attack start and end times are defined as and

[0097] The non-periodic DoS attack and random FDI attack in the measurement channel are designed as follows:

[0098]

[0099] where when , the system is in the DoS attack dormant period, the communication channel is normal, but it is subjected to random FDI attack; when ​At this time, the DoS attack is active, causing the communication channel to be blocked and unable to transmit signals, so although the random FDI attack always exists, due to the existence of the DoS attack, the system output is 0. β(t) represents a random variable satisfying a Bernoulli distribution and representing the occurrence of a random FDI attack; ψ(t) = g(t)(y(t) + ω(t)) represents an FDI attack signal, g(t) represents a random multiplicative attack coefficient, and ω(t) represents a random additive attack coefficient; z a (t) represents the system output received by the model-free adaptive controller for calculating the control signal;

[0100] It is assumed that wherein, Prob{·} represents the probability of a random variable; the random multiplicative attack coefficient g(t) satisfies the random additive attack coefficient ω(t) satisfies wherein, E{·} represents an expectation, represents the multiplicative attack signal energy of the FDI attack, represents the additive signal attack energy of the FDI.

[0101] Finally, the model-free adaptive controller is represented as:

[0102]

[0103] wherein, y * (t+1) represents a reference signal; λ > 0 represents a weight factor; v ∈ (0, 1] represents a step factor; and u(t-1) represents a control input at time t-1. is an estimated value of the pseudo partial derivative φ(t);

[0104]

[0105] wherein, χ represents a weight factor; κ represents a step factor; and l ∈ (0, 0.00005) represents a small normal number; is an initial value of .

[0106] S32, considering the network-induced time delay and the mixed network attack factor, a predictive control algorithm of the model-free adaptive controller is designed, specifically including:

[0107] First, considering the designed pseudo partial derivative estimation algorithm, when the communication channel is in a normal communication state at this time, and the pseudo partial derivative estimation algorithm is normally transmitted at this time; when the communication channel is blocked due to the influence of the DoS attack, and then the estimated value at the last time when the DoS attack occurs is considered, and then the pseudo partial derivative estimation algorithm is as follows:

[0108]

[0109] To enhance the pseudo-partial derivative estimation algorithm's ability to track time-varying parameters, the following parameter resetting algorithm is introduced:

[0110] if

[0111] in, Indicates in Estimates of the time pseudo-partial derivative φ(t); Δz a (t) represents the output increment after the system is attacked;

[0112] Secondly, based on the model-free controller designed in S2, and considering the existence of hybrid network attacks, when At that time, DoS attacks are dormant, while random FDI attacks exist; when DoS attacks are active. Although random FDI attacks exist, they do not need to be considered due to communication channel congestion. Based on different attack scenarios, the controller is designed as follows:

[0113]

[0114] Where r = 1, 2, ..., τ; Indicates r from 1 to The product of the products; α(r) represents the decay factor. The rate of change of α(r) from m1 to m2 is determined by the parameter m∈[0.05,0.15], and the positive constants m1 and m2 satisfy the condition 0≤m2≤m1<1; τ represents the network-induced delay; Indicates in The increment of the input signal at time t.

[0115] Next, considering the impact of network-induced latency, model predictive control is introduced to mitigate the effect of latency on the system. The predicted input signal Δu(t+r|t) is calculated based on the information at the current time t and is used to predict the input signal at time t+r. The prediction algorithm is designed as follows:

[0116]

[0117] Where Δu(t+r|t) represents the increment of the input signal at time t+r predicted at time t; Δu(t+r-1|t) represents the increment of the input signal at time t+r-1 predicted at time t; α(r) is an attenuation factor that makes the predicted input signal gradually decrease over time, which helps to reduce the impact of network latency and hybrid attacks on the system.

[0118] The prediction input signal increment at the future time is calculated in an accumulated manner, and the calculated prediction input signal increment Δu(t+r|t) is accumulated to the prediction input signal increment Δu(t+r-1|t) at the previous time, to obtain the prediction input signal increment Δu(t+r|t) at the time t+r. This increment reflects the input signal change from the current time t to the future time t+r. The algorithm is designed as follows: c

[0119] Δu c (t+r|t)=Δu c (t+r-1|t)+Δu(t+r|t)

[0120] wherein Δu c (t+r|t) represents the accumulated value of the input signal increment at the time t+r predicted at the time t; and Δu c (t+r-1|t) represents the accumulated value of the input signal increment at the time t+r-1 predicted at the time t.

[0121] Finally, in order to compensate for the network delay, the calculated prediction input signal increment Δu c (t+r|t) is used to update the control input u(t) at the current time t, and the predicted input signal increment is added to the control input u(t-1) at the previous time, to obtain the control input u(t) at the current time. The influence of the network delay τ and the hybrid attack is considered, the control performance of the system is improved through prediction and compensation, and the following control signal is designed:

[0122] u(t)=u(t-1)+Δu c (t+τ|t)

[0123] wherein Δu c (t+τ|t) represents the accumulated value of the input signal increment at the time t+τ predicted at the time t.

[0124] S4, an evaluation index with a bounded tracking error is introduced, and the information physical system is controlled based on the designed prediction control algorithm. If the output of the information physical system satisfies the evaluation index, i.e. the tracking error is bounded, it is indicated that the output of the information physical system can track the reference signal, and there exists:

[0125]

[0126] wherein K represents a constant, K=d0k+2k, and k represents a normal number; y * represents the reference output; d0, d1, d2 ∈ (0, 1), and σ ∈ (0, 1) are the time proportion of the DoS attack at the time t;

[0127] ​denotes the system estimation error; denotes the error between the estimated value and the true value of the system parameter at initial time t=1; denotes t-1 power of d1; denotes (1-σ)t power of d2; e(t+1) denotes the tracking error at t+1 time; e(0) denotes the tracking error value at initial time t=0.

[0128] If the output of the information physical system does not satisfy the evaluation index, S3-S4 are repeated until the output of the information physical system can track the reference signal.

[0129] In one embodiment, the present application also provides a CPS model-free adaptive predictive control system under hybrid network attacks, which is suitable for the CPS model-free adaptive predictive control method under hybrid network attacks as described above, and comprises:

[0130] A data construction module is configured to construct a data model of the nonlinear information physical system.

[0131] A linearization module is configured to perform dynamic linearization on the established data model to obtain a linearized data model.

[0132] An adaptive prediction algorithm design module is configured to construct a model-free adaptive controller of the information physical system under non-periodic DoS attacks and random FDI attacks based on the linearized data model, and design a prediction control algorithm of the model-free adaptive controller.

[0133] A tracking error evaluation module is configured to introduce an evaluation index of bounded tracking error, and perform safety control on the information physical system based on the designed prediction control algorithm, so that the output of the information physical system can track the reference signal.

[0134] In other embodiments, the present application also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor; when the processor executes the computer program, the steps of the CPS model-free adaptive predictive control method under hybrid network attacks as described above are implemented.

[0135] In another embodiment, the present application also provides a computer readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the CPS model-free adaptive predictive control method under hybrid network attacks as described above are implemented.

[0136] Next, the correctness and effectiveness of the CPS model-free adaptive predictive control method under hybrid network attacks of the present application are verified by a simulation example. The specific implementation method is as follows:

[0137] Consider the following nonlinear discrete system of a steam-water heat exchanger:

[0138]

[0139] where y(t) represents the inlet water temperature, and u(k) represents the process water flow rate.

[0140] Suppose that the reference output of the system is:

[0141]

[0142] At the same time, the controller parameter selection is ν = 1, χ = 1, l = 10, λ = 30, κ = 1, m = 0.1, m1 = 0.8, m2 = 0.5 and τ = 3. -5

[0143] Suppose that the non-periodic DoS attack interval is (10, 40), (80, 100), (130, 140), (250, 265), (320, 350), (410, 430), (500, 510) and (580, 585), at this time, the communication channel is blocked, causing data loss; when in other intervals, z a (t) = β(t) ψ(t) + (1 - β(t)) y(t), the system is subjected to a random FDI attack. Suppose that the FDI attack probability is The random FDI attack signal is ψ(t) = g(t) (y(t) + ω(t)), wherein the multiplicative attack factor is set as The additive attack factor is set as g(t) = 0.2 * (rand(1) - 0.5) + 0.4, ω(t) = 0.2 * (rand(1) - 0.5) + 0.2.

[0144] The initial condition is selected as y(1) = 0.5, u(1) = 0.2.

[0145] The specific simulation graph is as shown in Figures 3-7

[0146] Figure 3 is the FDI attack signal graph of the application; Figure 4 is the FDI attack occurrence time graph of the application, wherein the vertical coordinate "1" indicates that the system is subjected to the FDI attack, and "0" indicates that the system is not subjected to the FDI attack; Figure 5 is the non-periodic DoS attack occurrence time graph of the application, wherein the vertical coordinate "1" indicates that the system is subjected to the DoS attack, and "0" indicates that the system is not subjected to the DoS attack; Figure 6 is the system output tracking trajectory graph under the mixed network attack of the application; Figure 7 is the system output tracking trajectory graph under different FDI attack parameters of the application. From Figure 6 ​​It can be seen that, when subjected to DoS attack and FDI attack, the output signal of the system has certain fluctuations, and the tracking effect on the reference signal is affected to a certain extent, but under the action of the model-free adaptive predictive control (MFAPC) scheme proposed in the application, the system output signal realizes effective tracking of the reference signal, thereby verifying the effectiveness of the control scheme of the application.

[0147] In order to study the influence of multiplicative FDI attack coefficient g(t) and additive FDI attack coefficient ω(t) on system performance, we define the mean square error index as Assuming that the occurrence of DoS attack is unchanged, different FDI attack parameters are selected as follows: 1) attack parameter 1: 2) attack parameter 2: 3) attack parameter 3: At this time, the tracking trajectory of the system reference output is as shown in Figure 7 , and the mean square error evaluation index is shown in Table 1. From Figure 7 and Table 1, it can be seen that, as the FDI attack parameters increase, the tracking effect on the reference output becomes worse, but overall, under the action of the control scheme proposed in the application, the system output can still maintain a certain tracking effect on the reference signal.

[0148] Table 1 Comparison of evaluation indexes

[0149] FDI attack Attack parameter 1 Attack parameter 2 Attack parameter 3 MSE 0.0118 0.0154 0.0215

[0150] Considering the existence of multiple influence factors such as system modeling difficulty, mixed network attack and time delay, a model-free adaptive predictive control strategy is designed in the method of the controller to suppress the influence of mixed network attack on system stability. From the simulation results, the system output and network attack time diagram are clearly obtained, which further confirms the feasibility and applicability of the model-free adaptive predictive control method constructed in the embodiment.

[0151] Each embodiment in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same and similar parts between each embodiment can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the related parts can be referred to the method part.

[0152] The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Modifications of these embodiments will occur to persons of skill in the art, and that the appended claims are intended to cover all such modifications that do not depart from the true spirit and scope of the application. Therefore, the application is not limited to the embodiments shown but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A CPS model-free adaptive predictive control method under mixed network attacks, characterized in that, The method comprises the following steps: S1, constructing a data model of a nonlinear cyber-physical system; the expression of the data model of the nonlinear cyber-physical system is: y(t + 1) = f(y(t),..., y(t - n y ), u(t),..., u(t - n u )) where n y , n u represent unknown orders of output signal y(t) and input signal u(t) respectively, and f(·) represents unknown nonlinear function; t represents time of discrete time. S2, dynamically linearizing the established data model to obtain a linearized data model; S2 comprises: The partial derivative of f(·) with respect to the input signal u(t) is continuous, and the nonlinear cyber-physical system satisfies the generalized Lipschitz condition, that is, for any time t, when the input signal u(t)≠0, there exists a pseudo partial derivative φ(t) such that the data model of the nonlinear cyber-physical system constructed in S1 is constructed into the following dynamic linearization data model Δy(t+1)=φ(t)Δu(t) Wherein, |φ(t)|≤k, k represents a normal number; Δy(t+1) represents the increment of the system output at time t+1; Δu(t) represents the input increment; S3, based on the linearized data model, construct the model-free adaptive controller of the nonlinear information physical system under the non-periodic DoS attack and random FDI attack, and design the predictive control algorithm of the model-free adaptive controller; define the time period for DoS attack, the time period without DoS attack, the attack start and end times are defined as and The non-periodic DoS attack and the random FDI attack in the measurement channel are designed as: wherein β(t) represents a random variable satisfying a Bernoulli distribution; ψ(t) = g(t)(y(t) + ω(t)) represents a random FDI attack signal, g(t) represents a random multiplicative attack coefficient, and ω(t) represents a random additive attack coefficient; z a (t) represents a system output received by the model-free adaptive controller for calculating the control signal; Assume where, Prob { ·} denotes the probability of a random variable; the random multiplicative attack coefficient g(t) satisfies the random additive attack coefficient ω(t) satisfies where E{·} denotes the expectation, denotes the multiplicative attack signal energy of the random FDI attack, denotes the FDI additive signal attack energy; S4, introducing a tracking error bounded evaluation index, and performing safe control on the nonlinear cyber-physical system based on the designed predictive control algorithm; if the output of the nonlinear cyber-physical system satisfies the evaluation index, it indicates that the output of the nonlinear cyber-physical system can track the reference signal; if the output of the nonlinear cyber-physical system does not satisfy the evaluation index, repeat S3-S4 until the output of the nonlinear cyber-physical system can track the reference signal.

2. The method of claim 1, wherein, In S3, the model-free adaptive controller is represented as: where y * (t+1) denotes a reference signal; λ > 0 denotes a weight factor; v e (0, 1] denotes a step factor; u(t-1) denotes an output value of the controller at the previous time; is an estimate of the pseudo-derivative φ(t). where χ denotes a weight factor; κ denotes a step factor; and l denotes a small normal number; is the initial value of 3. The method of claim 2, wherein, In S3, considering the network-induced time delay and the hybrid network attack factor, a predictive control algorithm of the model-free adaptive controller is designed, which is represented as: If or |Δu(t-1)|≤l or wherein represents an estimate of the pseudo-derivative φ(t) at Δz a (t) represents the output increment of the system after the attack Δu c (t+r|t) = Δu c (t+r-1|t) + Δu(t+r|t) In order to compensate for the network-induced time delay, the following control signal is designed: u(t) = u(t - 1) + Δu c (t + τ | t) wherein r = 1, 2, …, τ, denotes the product of r from 1 to ; α(r) denotes an attenuation factor, The rate of change of α(r) from m1 to m2 is determined by the parameter m ∈ [0.05, 0.15], and the normal numbers m1 and m2 satisfy the condition 0 ≤ m2 ≤ m1 < 1, and τ denotes the network-induced delay; denotes the input signal increment at time t + r; Δu(t + r | t) denotes the input signal increment at time t + r predicted at time t; Δu(t + r - 1 | t) denotes the input signal increment at time t + r - 1 predicted at time t; Δu c (t + r | t) denotes the cumulative value of the input signal increment at time t + r predicted at time t; Δu c (t + r - 1 | t) denotes the cumulative value of the input signal increment at time t + r - 1 predicted at time t; Δu c (t + τ | t) denotes the cumulative value of the input signal increment at time t + τ predicted at time t.

4. The method of claim 1, wherein, In S4, if the output of the nonlinear cyber-physical system satisfies the evaluation index, it indicates that the output of the nonlinear cyber-physical system can track the reference signal, and there exists: wherein K represents a constant, K=d0k+2k, k represents a normal number; y * represents a reference output; d0, d1, d2∈(0, 1), σ∈(0, 1) is a time proportion of a DoS attack at time t; represents a system estimation error; represents an error between an estimated value and a true value of a system parameter at an initial time t=1; represents t-1 power of d1; represents (1-σ)t power of d2; e(t+1) represents a tracking error at t+1 time; e(0) represents a tracking error value at an initial time t=0.

5. A model-free adaptive predictive control system for CPS under mixed network attacks, characterized in that, It is applicable to the model-free adaptive predictive control method of CPS under the hybrid network attack according to any one of claims 1-4, comprising: a data construction module configured to construct a data model of a nonlinear cyber-physical system; a linearization module configured to dynamically linearize the established data model to obtain a linearized data model; an adaptive prediction algorithm design module configured to construct a model-free adaptive controller of the nonlinear cyber-physical system under the non-periodic DoS attack and the random FDI attack based on the linearized data model, and design a predictive control algorithm of the model-free adaptive controller; a tracking error evaluation module configured to introduce a tracking error bounded evaluation index, and perform safe control on the nonlinear cyber-physical system based on the designed predictive control algorithm, so that the output of the nonlinear cyber-physical system can track the reference signal.

6. An electronic device comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor; when the processor executes the computer program, the steps of the model-free adaptive predictive control method of CPS under the hybrid network attack according to any one of claims 1-4 are implemented.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by a processor to implement the steps of the CPS model-free adaptive predictive control method under hybrid network attacks according to any one of claims 1-4.

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