CPS model-free adaptive prediction control method and system under hybrid network attack

Abstract

The invention relates to the technical field of network security, in particular to a CPS model-free adaptive prediction control method and system under hybrid network attacks, and the method comprises the 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 cyber-physical system under the non-periodic DoS attack and the random FDI attack, and designing a predictive control algorithm of the model-free adaptive controller; an evaluation index with a tracking error bounded is introduced, and security control is performed on the information physical system based on a designed predictive control algorithm, so that the output of the information physical system can still stably track a reference signal when receiving a hybrid network attack. According to the method, stable tracking of the reference signal by the system can still be ensured under the hybrid network attack, and the adaptability to the uncertainty and complexity of the system is improved.

Description

Technical Field

[0001] The present invention relates to the field of network security technology, and more particularly to a model-free adaptive predictive control method and system for CPS under hybrid network attacks. Background Art

[0002] Currently, the controllable, trustworthy, and scalable Cyber-physical system (CPS), which deeply integrates computing, communication, and control functions, has attracted much attention. As an integrated technical system for deeply practicing the "integration of industrialization and informatization", CPS is leading a new round of technological revolution and industrial revolution, enabling intelligent innovation applications in fields such as industrial production, smart grid, intelligent transportation, and assisted medical care. Due to the introduction of communication networks, the originally closed physical system has become more open, thus increasing the risk of the cyber-physical system being attacked from the outside. Compared with traditional control systems, CPS has a wider attack surface, and attackers can cause huge damage through malicious attacks on different network levels. Since CPS has complex non-linear characteristics and it is difficult to model the system, it is almost impossible to obtain an accurate CPS model in control practice. Therefore, the model-free adaptive control (MFAC) method based on pure data-driven emerged. This method constructs a controller only using input / output data without using system model information and has better applicability in the field of CPS security control.

[0003] Currently, research on system security control mainly focuses on Denial of Service (DoS) attacks or False Data Injection (FDI) attacks. However, it should be noted that attackers often launch more than two types of network attacks simultaneously to maximize the destruction of system performance. Therefore, researching the security control problem of CPS under hybrid network attacks has theoretical significance and practical value.

[0004] It should be noted that although some security control methods under network attacks have been proposed in existing research, there are still some deficiencies: 1) Currently, rich research results have been achieved in the CPS security control problem under specific types of network attacks (such as DoS attacks or FDI attacks), but the research on CPS security control involving hybrid network attacks is still in its infancy and further in-depth research is needed. 2) In the field of CPS security control, a large number of research results have been obtained on the model-free adaptive control problem based on data-driven, but most of them are for system security control research against a single type of network attack. Considering the less research on the model-free adaptive control problem of CPS under hybrid network attacks that cause greater damage to the system, therefore, the model-free adaptive security control problem under hybrid network attacks still needs further in-depth research; 3) Due to the complex non-linear characteristics of CPS and the great difficulty in system modeling, it is almost impossible to obtain an accurate CPS model in control practice.

[0005] Therefore, how to solve the above problems and deeply study the model-free adaptive predictive control problem of non-linear cyber-physical systems under hybrid network attacks is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a CPS model-free adaptive predictive control method and system under hybrid network attacks, aiming to consider the impact of hybrid network attacks on system output and effectively solve the problem of difficult CPS modeling for security control.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] In the first aspect, the present invention provides a CPS model-free adaptive predictive control method under hybrid network attacks, including the following steps:

[0009] S1. Construct a data model of the non-linear cyber-physical system;

[0010] S2. Perform dynamic linearization on the established data model to obtain the linearized data model;

[0011] S3. Based on the linearized data model, construct a model-free adaptive controller for the cyber-physical system under non-periodic DoS attacks and random FDI attacks, and design a predictive control algorithm for the model-free adaptive controller.

[0012] S4. Introduce an evaluation index with bounded tracking error, and perform safety control on the cyber-physical system based on the designed predictive control algorithm. If the output of the cyber-physical system satisfies the evaluation index, it indicates 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, repeat S3 - S4 until the output of the cyber-physical system can track the reference signal.

[0013] Further, in S1, the expression of the data model of the nonlinear cyber-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 respectively represent the unknown orders of the output y(t) and the input u(t), and f(·) represents an unknown nonlinear function; t represents the discrete time instant.

[0016] Further, S2 includes:

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

[0018] Δy(t + 1) = φ(t)Δu(t)

[0019] where |φ(t)| ≤ k, k represents a positive constant; 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 non-periodic DoS attack and random FDI attack in the measurement channel are designed as:

[0022]

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

[0024] Suppose Among them, Prob{·} represents the probability of a random variable; the random multiplicative attack coefficient g(t) satisfies The random additive attack coefficient ω(t) satisfies Among them, E{·} represents the expectation, represents the multiplicative attack signal energy of the FDI attack, represents the additive signal attack energy of the FDI.

[0025] Furthermore, in S3, the model-free adaptive controller is expressed as:

[0026]

[0027] Among them, y * (t + 1) represents the reference signal; λ > 0, representing the weight factor; ν ∈ (0, 1], representing the step size factor; u(t - 1) represents the output value of the controller at the previous moment; is the estimated value of the pseudo partial derivative φ(t);

[0028]

[0029] Among them, χ represents the weight factor; κ represents the step size factor; l represents a small positive constant; is the initial value of.

[0030] Furthermore, in S3, considering the network-induced delay and the hybrid network attack factors, the predictive control algorithm of the model-free adaptive controller is designed and expressed as:

[0031]

[0032] If or |Δu(t - 1)| ≤ l or

[0033] Among them, represents the estimated value of the pseudo partial derivative φ(t) at ; Δz a (t) represents the output increment of the system after being

[0034] attacked;

[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] where r = 1, 2,..., τ, denotes the continued product from r = 1 to ; α(r) represents the attenuation factor, α(r) varies from m 1 to m 2 and the rate of change is determined by the parameter m ∈ [0.05, 0.15], and the positive constants m 1 and m 2 satisfy the condition 0 ≤ m 2 ≤ m 1 < 1, and τ represents the network-induced delay; denotes the increment of the input signal at time; denotes the increment of the input signal at time; Δu(t + r|t) represents the increment of the input signal predicted at time t for time t + r - 1; Δu(t + r - 1|t) represents the cumulative value of the increment of the input signal predicted at time t for time t + r; Δu c (t + r|t) represents the cumulative value of the increment of the input signal predicted at time t for time t + r; Δu c (t + r - 1|t) represents the cumulative value of the increment of the input signal predicted at time t for time t + r - 1; Δu c (t + τ|t) represents the cumulative value of the increment of the input signal predicted at time t for time t + τ.

[0040] Furthermore, in S4, if the output of the cyber-physical system meets the evaluation index, it indicates that the output of the cyber-physical system can track the reference signal, and there exists:

[0041]

[0042] where K represents a constant, K = d 0 k + 2k, and k represents a positive constant; y * represents the reference output; d 0 , d 1 , d2 ∈(0,1), and σ ∈(0,1) is the time proportion of the DoS attack at time t; represents the system estimation error; represents the error between the estimated value and the true value of the system parameters at the initial time t = 1; represents d 1 to the power of t - 1; represents d 2 to the power of (1 - σ)t; e(t + 1) represents the tracking error at time t + 1; e(0) represents the tracking error value at the initial time t = 0.

[0043] In a second aspect, the present invention provides a CPS model-free adaptive predictive control system under hybrid network attacks, which is applicable to the CPS model-free adaptive predictive control method under hybrid network attacks as described above, including:

[0044] A data construction module for constructing a data model of a nonlinear cyber-physical system;

[0045] A linearization module for dynamically linearizing the established data model to obtain a linearized data model;

[0046] An adaptive predictive algorithm design module for constructing a model-free adaptive controller for a cyber-physical system under non-periodic DoS attacks and random FDI attacks based on the linearized data model, and designing a predictive control algorithm for the model-free adaptive controller;

[0047] A tracking error evaluation module for introducing an evaluation index with bounded tracking error, and performing secure control on the cyber-physical system based on the designed predictive control algorithm, so that the output of the cyber-physical system can track the reference signal.

[0048] In a third aspect, the present invention provides an electronic device, including: 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 CPS model-free adaptive predictive control method under hybrid network attacks as described above are implemented.

[0049] In a fourth aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored, and characterized in that 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] Through the above technical solutions, compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention first establishes a data model for a non - linear cyber - physical system, and performs dynamic linearization on the established data model to obtain a linearized model. Secondly, considering the false data injection attack and the aperiodic denial - of - service attack on the measurement channel, a model - free adaptive controller and a pseudo - partial - derivative estimate for the cyber - physical system are derived, and a model - free adaptive predictive control algorithm is proposed, enabling the system output to stably track the reference signal under hybrid network attacks.

[0052] The model - free adaptive predictive controller designed according to the prior art for CPS with complex non - linear characteristics and difficult system modeling can construct an equivalent dynamic linearized time - varying model at the dynamic operating point of the controlled object, enabling the controller to adaptively respond to changes in parameters and structures, and having excellent self - adaptability and robustness.

[0053] In addition, based on model - free adaptive control, the present invention gives a design method for model - free adaptive predictive control, and uses the contraction mapping principle analysis method to prove that the proposed model - free adaptive predictive control algorithm can guarantee the boundedness of the tracking error in the mean - square sense, and then obtains system evaluation indexes. The present invention can directly use input - output data for control, reducing the modeling difficulty, improving the adaptability to the uncertainty and complexity of the cyber - physical system, and enhancing the robustness and security of the cyber - physical system. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to the provided drawings.

[0055] Figure 1 It is a flowchart of the model - free adaptive predictive control method for CPS under hybrid network attacks provided by the present invention;

[0056] Figure 2 It is a detailed flowchart of the model - free adaptive predictive control method for CPS under hybrid network attacks provided by the present invention;

[0057] Figure 3 It is an FDI attack signal diagram provided by the present invention;

[0058] Figure 4 It is an FDI attack occurrence time diagram provided by the present invention;

[0059] Figure 5 It is an aperiodic DoS attack occurrence time diagram provided by the present invention;

[0060] Figure 6 Output tracking trajectory diagram of the cyber-physical system under hybrid cyber attacks provided by the present invention;

[0061] Figure 7 Output tracking trajectory diagram of the cyber-physical system under different FDI attack parameters provided by the present invention. Specific implementation manners

[0062] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0063] As Figure 1 shown, an embodiment of the present invention discloses a model-free adaptive predictive control method for a CPS under hybrid cyber attacks, including the following steps:

[0064] S1. Construct a data model of the nonlinear cyber-physical system;

[0065] S2. Perform dynamic linearization on the established data model to obtain a linearized data model;

[0066] S3. Based on the linearized data model, construct a model-free adaptive controller for the cyber-physical system under non-periodic DoS attacks and random FDI attacks, and design a predictive control algorithm for the model-free adaptive controller;

[0067] S4. Introduce an evaluation index with a bounded tracking error, and perform security control on the cyber-physical system based on the designed predictive control algorithm. 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, repeat S3 - S4 until the output of the cyber-physical system can track the reference signal.

[0068] Next, the specific implementation processes of the above steps will be described in detail, and the specific process is as Figure 2 shown. S1. Construct a data model of the nonlinear cyber-physical system, and its expression is:

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

[0070] where n y , n uThey respectively represent the unknown orders of the output \(y(t)\) and the input \(u(t)\), and \(f(\cdot)\) represents an unknown non - linear function; \(t\) represents the discrete - time instant.

[0071] S2. For the above cyber - physical system, the partial derivative of \(f(\cdot)\) with respect to the control - input signal \(u(t)\) is continuous, and the cyber - physical system satisfies the generalized Lipschitz condition. For any system input \(u(t)\neq0\) at time \(t\), there exists a pseudo - partial derivative \(\varphi(t)\) such that the non - linear cyber - physical system model constructed in S1 is transformed into the following dynamic - linearized data model

[0072] \(\Delta y(t + 1)=\varphi(t)\Delta u(t)\)

[0073] where \(|\varphi(t)|\leq k\), \(k\) represents a positive constant; \(\Delta y(t + 1)\) represents the increment of the system output at time \(t + 1\); \(\Delta u(t)\) represents the input increment.

[0074] S3. Based on the linearized data model, construct a model - free adaptive controller for the cyber - physical system under non - periodic DoS attacks and random FDI attacks, and design a predictive - control algorithm for the model - free adaptive controller.

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

[0076] Design the performance - index function of \(u(t)\) as:

[0077] J 1 [u(t)]=[y * (t + 1)-y(t + 1)] 2 +\(\lambda[u(t)-u(t - 1)] 2

[0078] where \(y * (t + 1)\) represents the reference signal, and \(\lambda\gt0\) represents the weight factor.

[0079] Substitute the data model in S2 into the index function, and we can get:

[0080] J[u(t)] = |y * (t + 1)-y(t)-\varphi(t)\Delta u(t)| 2 +\(\lambda|u(t)-u(t - 1)|\) 2

[0081] =[y * (t + 1)-y(t)] 2 +[\(\varphi(t)\Delta u(t)\)] 2 -2[y * (t + 1)-y(t)]\(\varphi(t)\Delta u(t)+\lambda[u(t)-u(t - 1)]\)2

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

[0083]

[0084] Let We can get:

[0085] \(\vert\varphi(t)\vert\) 2 \(\Delta u(t)-[y * (t + 1)-y(t)]\varphi(t)+\lambda[u(t)-u(t - 1)] = 0

[0086] After rearrangement, we can get:

[0087]

[0088] To make the control algorithm more general, a step-size factor \(v\in(0,1]\) is introduced, and the model-free adaptive controller is derived in the following form:

[0089]

[0090] where \(v\in(0,1]\) represents the step-size factor, is the estimated value of \(\varphi(t)\).

[0091] Design the performance index function of the pseudo partial derivative estimate value as follows:

[0092]

[0093] where \(\chi\) represents the weight factor.

[0094] Referring to the process of solving the controller, design the parameter estimation algorithm as follows:

[0095]

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

[0097] Design the non-periodic DoS attack and random FDI attack in the measurement channel as:

[0098]

[0099] where when the system is in the DoS attack dormant period, the communication channel is normal, but it is suffering from a random FDI attack; when At this time, the DoS attack is in the active period, causing the communication channel to be blocked and unable to transmit signals. Therefore, 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 that follows a Bernoulli distribution and represents the occurrence of the random FDI attack; ψ(t) = g(t)(y(t) + ω(t)), representing the FDI attack signal, where g(t) represents the random multiplicative attack coefficient and ω(t) represents the random additive attack coefficient; z a (t) represents the system output received by the model-free adaptive controller for calculating the control signal;

[0100] Suppose Among them, Prob{·} represents the probability of a random variable; the random multiplicative attack coefficient g(t) satisfies The random additive attack coefficient ω(t) satisfies Among them, E{·} represents the expectation, represents the energy of the multiplicative attack signal of the FDI attack, represents the energy of the additive signal attack of the FDI.

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

[0102]

[0103] Among them, y * (t + 1) represents the reference signal; λ > 0, representing the weight factor; ν ∈ (0, 1], representing the step size factor; u(t - 1) represents the control input at time t - 1; is the estimated value of the pseudo partial derivative φ(t);

[0104]

[0105] Among them, χ represents the weight factor; κ represents the step size factor; l ∈ (0, 0.00005), representing a small positive constant; is the initial value of.

[0106] S32. Considering the network-induced delay and the factors of hybrid network attacks, a predictive control algorithm for the model-free adaptive controller is designed, which specifically includes:

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

[0108]

[0109] To enable the pseudo - partial - derivative estimation algorithm to have a stronger tracking ability for time - varying parameters, the following parameter reset algorithm is introduced:

[0110] If

[0111] where, represents the estimated value of the pseudo - partial - derivative φ(t) at ; Δz a (t) represents the output increment of the system after being attacked;

[0112] Secondly, according to the model - free controller designed in S2 and considering the existence of hybrid network attacks, when , the DoS attack is in the dormant period and the random FDI attack exists; when the DoS attack is in the active period. Although the random FDI attack exists, due to the communication channel blockage, the random FDI attack does not need to be considered. According to different attack situations, the controller is designed as follows:

[0113]

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

[0115] Next, considering the influence of network - induced delay, model - predictive control is introduced to mitigate the influence of delay 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] Among them, 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) serves as an attenuation factor, causing the predicted input signal to gradually decrease over time, which helps reduce the impact of network latency and hybrid attacks on the system.

[0118] The predicted input signal increment at future times is calculated by accumulation. The calculated predicted input signal Δu(t+r|t) is accumulated onto the predicted input signal increment Δu(t+r-1|t) at the previous time to obtain the predicted input signal increment Δu c (t+r|t). This increment reflects the change in the input signal from the current time t to the future time t+r. The designed algorithm is as follows:

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

[0120] Among them, Δu c (t+r|t) represents the cumulative value of the increment of the input signal at time t+r predicted at time t; Δu c (t+r-1|t) represents the cumulative value of the increment of the input signal at time t+r-1 predicted at time t.

[0121] Finally, in order to compensate for network latency, the calculated predicted 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, taking into account the effects of network latency τ and hybrid attacks. By prediction and compensation, the control performance of the system is improved, and the following control signal is designed:

[0122] u(t) = u(t-1) + Δu c (t+τ|t)

[0123] Among them, Δu c (t+τ|t) represents the cumulative value of the increment of the input signal at time t+τ predicted at time t.

[0124] S4. Introduce an evaluation index with a bounded tracking error. Based on the designed predictive control algorithm, perform security control on the cyber-physical system. If the output of the cyber-physical system satisfies the evaluation index, that is, when the tracking error is bounded, it indicates that the output of the cyber-physical system can track the reference signal, and there exists:

[0125]

[0126] Among them, K represents a constant, K = d 0 k + 2k, where k represents a positive constant; y * represents the reference output; d 0 , d 1 , d 2 ∈(0, 1), σ ∈(0, 1) is the time proportion of the DoS attack at time t;

[0127] represents the system estimation error; represents the error between the estimated value and the true value of the system parameters at the initial time t = 1; represents d 1 to the power of t - 1; represents d 2 to the power of (1 - σ)t; e(t + 1) represents the tracking error at time t + 1; e(0) represents the tracking error value at the initial time t = 0.

[0128] If the output of the cyber - physical system does not meet the evaluation index, repeat S3 - S4 until the output of the cyber - physical system can track the reference signal.

[0129] In one embodiment, the present invention further provides a model - free adaptive predictive control system for CPS under hybrid network attacks, which is applicable to the model - free adaptive predictive control method for CPS under hybrid network attacks as described above, including:

[0130] A data construction module for constructing a data model of the non - linear cyber - physical system;

[0131] A linearization module for dynamically linearizing the established data model to obtain a linearized data model;

[0132] An adaptive predictive algorithm design module for constructing a model - free adaptive controller for the cyber - physical system under non - periodic DoS attacks and random FDI attacks based on the linearized data model, and designing a predictive control algorithm for the model - free adaptive controller;

[0133] A tracking error evaluation module for introducing an evaluation index with a bounded tracking error, and performing security control on the cyber - physical system based on the designed predictive control algorithm, so that the output of the cyber - physical system can track the reference signal.

[0134] In other embodiments, the present invention further provides an electronic device, including: 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 for CPS under hybrid network attacks as described above are implemented.

[0135] In another embodiment, the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the CPS model-free adaptive predictive control method under the hybrid network attack as described above are implemented.

[0136] Next, the correctness and effectiveness of the CPS model-free adaptive predictive control method under the hybrid network attack of the present invention are verified through simulation examples. The specific implementation method is as follows:

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

[0138]

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

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

[0141]

[0142] At the same time, the controller parameters are selected as ν = 1, χ = 1, l = 10 -5 , λ = 30, κ = 1, m = 0.1, m 1 = 0.8, m 2 = 0.5 and τ = 3.

[0143] Assume that the aperiodic DoS attack intervals are (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, resulting in data loss; when in other intervals, z a (t) = β(t)ψ(t) + (1 - β(t))y(t), and the system is under a random FDI attack. Assume that the FDI attack probability is The random FDI attack signal is ψ(t) = g(t)(y(t) + ω(t)), where the multiplicative attack factor is set to The additive attack factor is set to g(t) = 0.2*(rand(1) - 0.5) + 0.4, ω(t) = 0.2*(rand(1) - 0.5) + 0.2.

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

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

[0146] Figure 3 is the FDI attack signal diagram of the present invention; Figure 4 is the FDI attack occurrence time diagram of the present invention, where the ordinate "1" indicates that the system is under FDI attack, and "0" indicates that the system is not under FDI attack; Figure 5 is the aperiodic DoS attack occurrence time diagram of the present invention, where the ordinate "1" indicates that the system is under DoS attack, and "0" indicates that the system is not under DoS attack; Figure 6 is the system output tracking trajectory diagram under the hybrid network attack of the present invention; Figure 7 is the system output tracking trajectory diagram under different FDI attack parameters of the present invention. From Figure 6 it can be seen that when under DoS attack and FDI attack, the output signal of the system shows certain fluctuations, which has a certain impact on the tracking effect of the reference signal. However, under the action of the model-free adaptive predictive control (MFAPC) scheme proposed in the present invention, the system output signal realizes effective tracking of the reference signal, thus verifying the effectiveness of the control scheme of the present invention.

[0147] To study the influence of the multiplicative FDI attack coefficient g(t) and the additive FDI attack coefficient ω(t) on the system performance, we define the mean square error index as Assume that the occurrence situation of the DoS attack remains unchanged, and 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 Figure 7 shown, 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 parameter increases continuously, the tracking effect on the reference output becomes worse. However, generally speaking, under the action of the control scheme proposed in the present invention, 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 situation where the system modeling is difficult, there are multiple influencing factors such as hybrid network attacks and time delays, a model-free adaptive predictive control strategy is proposed in the method of designing the controller to suppress the influence of hybrid network attacks on the system stability. From the simulation results, the system output and network attack time diagrams are clearly obtained, which further confirms the feasibility and applicability of the model-free adaptive predictive control method constructed in this embodiment.

[0151] In the present specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[0152] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A model-free adaptive predictive control method for CPS under hybrid network attacks, characterized in that: The following steps are involved: S1. Construct a data model for nonlinear cyber-physical systems; S2. Dynamically linearize the established data model to obtain a linearized data model; S3. Based on the linearized data model, a model-free adaptive controller for cyber-physical systems under non-periodic DoS attacks and random FDI attacks is constructed, and a predictive control algorithm for the model-free adaptive controller is designed; S4. Introduce an evaluation index with bounded tracking error, and perform safety control on the cyber-physical system based on the designed predictive control algorithm. If the output of the cyber-physical system meets 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 meet the evaluation index, repeat S3-S4 until the output of the cyber-physical system can track the reference signal.

2. The CPS model-free adaptive predictive control method under hybrid network attack according to claim 1 is characterized in that: In S1, the data model of the nonlinear cyber-physical system is expressed as: y(t+1)=f(y(t),...,y(t-n y ),u(t),...,u(t-n u )) Among them, n y ,n u They represent the unknown orders of output y(t) and input u(t), respectively, and f(·) represents an unknown nonlinear function; t represents the discrete time moment.

3. The CPS model-free adaptive predictive control method under hybrid network attack according to claim 2 is characterized in that S2 include: The partial derivative of f(·) with respect to the control input signal u(t) is continuous, and the cyber-physical system satisfies the generalized Lipschitz condition. For any time t, the system input u(t)≠0, and there exists a pseudo partial derivative φ(t), so that the nonlinear cyber-physical system model constructed in S1 is constructed into the following dynamic linearized data model Δy(t+1)=φ(t)Δu(t) Among them, |φ(t)|≤k, k is a positive constant; Δy(t+1) is the increment of the system output at time t+1; Δu(t) is the input increment.

4. The CPS model-free adaptive predictive control method under hybrid network attack according to claim 3 is characterized in that: In S3, define It is the DoS network attack time period. is the time period without DoS attack, and the attack start and end time are defined as and The non-periodic DoS attack and random FDI attack in the designed measurement channel are expressed as: Where β(t) represents a random variable that satisfies the Bernoulli distribution; ψ(t) = g(t)(y(t) + ω(t)), represents the FDI attack signal, g(t) represents the random multiplicative attack coefficient, and ω(t) represents the random additive attack coefficient; z a (t) represents the system output received by the model-free adaptive controller for calculating the control signal; Assumptions in, Prob{·} represents the probability of a random variable; the random multiplicative attack coefficient g(t) satisfies The random additive attack coefficient ω(t) satisfies Among them, E{·} represents expectation, represents the multiplicative attack signal energy of FDI attack, Represents the FDI additive signal attack energy.

5. The CPS model-free adaptive predictive control method under hybrid network attack according to claim 4 is characterized in that: In S3, the model-free adaptive controller is expressed as: Among them, y * (t+1) represents the reference signal; λ>0, represents the weight factor; ν∈(0,1], represents the step factor; u(t-1) represents the output value of the controller at the previous moment; is the estimated value of the pseudo partial derivative φ(t); Among them, χ represents the weight factor; κ represents the step size factor; l represents a small positive constant; yes The initial value of .

6. The CPS model-free adaptive predictive control method under hybrid network attack according to claim 5 is characterized in that: In S3, considering the network-induced delay and hybrid network attack factors, a predictive control algorithm of the model-free adaptive controller is designed, which is expressed as: if or |Δu(t-1)|≤l or in, Indicated in The estimated value of the pseudo partial derivative φ(t) when Δz a (t) represents the output increment after the system is attacked; Δu c (t+r|t)=Δu c (t+r-1|t)+Δu(t+r|t) In order to compensate for network delay, the following control signals are designed: u(t)=u(t-1)+Δu c (t+τ|t) Where r = 1, 2, ..., τ, Indicates that r ranges from 1 to The continuous multiplication of; α(r) represents the attenuation factor, The rate of change of α(r) from m1 to m2 is determined by the parameter m∈[0.05,0.15]. The positive constants m1 and m2 satisfy the condition 0≤m2≤m1<1, and τ represents the network-induced delay; Indicated in The increment of the input signal at time t; 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; Δu c (t+r|t) represents the cumulative value of the input signal increment at time t+r predicted by time t; Δu c (t+r-1|t) represents the cumulative value of the input signal increment at time t+r-1 predicted by time t; Δu c (t+τ|t) represents the cumulative value of the input signal increment at time t+τ predicted by time t.

7. The CPS model-free adaptive predictive control method under hybrid network attack according to claim 1 is characterized in that: In S4, if the output of the cyber-physical system meets the evaluation index, it means that the output of the cyber-physical system can track the reference signal, and there exists: Wherein, K represents a constant, K=d0k+2k, and k represents a positive constant; y * represents the reference output; d0,d1,d2∈(0,1), σ∈(0,1) is the time proportion of DoS attack at time t; represents the system estimation error; Represents the error between the estimated value and the true value of the system parameter at the initial time t = 1; represents d1 to the power of t-1; represents d2 to the power of (1-σ)t; e(t+1) represents the tracking error at time t+1; e(0) represents the tracking error value at the initial time t=0.

8. A CPS model-free adaptive predictive control system under hybrid network attacks, characterized in that: It is applicable to the CPS model-free adaptive predictive control method under hybrid network attack as claimed in any one of claims 1 to 7, comprising: Data construction module, used to construct data models of nonlinear cyber-physical systems; A linearization module is used to dynamically linearize the established data model to obtain a linearized data model; The adaptive prediction algorithm design module is used to construct a model-free adaptive controller for cyber-physical systems under non-periodic DoS attacks and random FDI attacks based on the linearized data model, and to design a predictive control algorithm for the model-free adaptive controller; The tracking error evaluation module is used to introduce the evaluation index of bounded tracking error, and to perform safe control of the cyber-physical system based on the designed predictive control algorithm so that the output of the cyber-physical system can track the reference signal.

9. An electronic 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 computer program, the steps of the CPS model-free adaptive predictive control method under a hybrid network attack as described in 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 computer program is executed by a processor, the steps of the CPS model-free adaptive predictive control method under hybrid network attacks as described in any one of claims 1 to 7 are implemented.

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