Event-triggered adaptive sliding mode control method and device for cyber-physical system under hybrid network attack

Abstract

This invention discloses an event-triggered adaptive sliding mode control method and apparatus for cyber-physical systems (CPS) under hybrid network attacks. The method includes the following steps: constructing a CPS model for the hybrid network attack modes affecting the CPS, and introducing an adaptive event-triggered communication mechanism into the CPS model; constructing a state observer based on the CPS model; establishing a sliding mode function based on the state observer and obtaining the sliding mode conditions; obtaining the system sliding mode dynamics, system error dynamics, and system equivalent control law based on the sliding mode conditions; constructing an augmented closed-loop system based on the system sliding mode dynamics and system error dynamics; constructing an adaptive sliding mode controller based on the system equivalent control law, and using the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system. This invention can optimize control performance by adjusting adaptive parameters, thereby effectively coping with complex network environments such as system uncertainty and hybrid network attacks.

Description

Technical Field

[0001] The present invention relates to the technical field of information-physical system security control, and more specifically to an event-triggered adaptive sliding mode control method and device for information-physical system under hybrid network attacks. Background Art

[0002] Cyber-Physical Systems (CPS) are a type of complex system that is highly integrated with the application layer, network layer, and physical layer. As a core element that supports and leads the Fourth Industrial Revolution, CPS is widely used in various fields of modern industrial production, such as multi-agents, intelligent transportation, and smart grids. However, while breaking the closed nature of traditional systems, CPS itself also has certain vulnerabilities, making it extremely vulnerable to security threats from malicious network attacks. In other words, due to the openness of the CPS communication network, both the control channel and the measurement channel may be threatened by network attacks, which in turn affects the stability of the system.

[0003] At present, there are three main types of network attacks against CPS: Denial of Service (DoS) attacks, replay attacks, and false data injection (FDI) attacks. In addition, due to the limited network communication bandwidth in CPS, the problem of insufficient network bandwidth often occurs during the CPS data communication process, resulting in unsatisfactory system control performance. Considering the limited network communication bandwidth of CPS, scholars have proposed an event-triggered communication scheme. Compared with the time-triggered scheme of periodic sampling, the event-triggered scheme executes tasks "on demand" while ensuring the stability of the closed-loop system, thereby effectively improving the communication utilization rate of the network and significantly improving the control performance of the system.

[0004] It is worth noting that although existing studies have proposed some sliding mode control collaborative design methods combined with event-triggered schemes under network attack conditions, there are still some shortcomings: in order to increase the destructiveness of network attacks, attackers often adopt multi-source network collaborative attacks; in addition, in response to the common chattering problem in sliding mode control methods, most current studies are at the expense of system robustness, which undoubtedly increases the conservatism of system control.

[0005] Therefore, how to conduct in-depth research on the problem of event-triggered adaptive sliding mode control of cyber-physical systems under hybrid network attacks is the main research direction for those skilled in the art. Summary of the invention

[0006] In view of the above problems, the present invention provides an event-triggered adaptive sliding mode control method and device for an information-physical system under a hybrid network attack; it aims to reduce the network communication burden while compensating for the negative impact of system nonlinearity, external disturbances and hybrid network attacks on system performance, thereby effectively improving the control performance and stability of the system.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] On the one hand, the present invention provides an event-triggered adaptive sliding mode control method for a cyber-physical system under a hybrid network attack, comprising the following steps:

[0009] S1. Constructing a cyber-physical system model for the hybrid network attack mode suffered by the cyber-physical system, and introducing an adaptive event-triggered communication mechanism into the cyber-physical system model;

[0010] S2. constructing a state observer according to the cyber-physical system model; establishing a sliding mode function according to the state observer, and obtaining a sliding mode condition;

[0011] S3. Based on the sliding mode condition, obtain the system sliding mode dynamics, system error dynamics and system equivalent control law;

[0012] S4, constructing an augmented closed-loop system according to the system sliding mode dynamics and the system error dynamics;

[0013] S5. Constructing an adaptive sliding mode controller based on the system equivalent control law, and using the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system.

[0014] Furthermore, the hybrid network attack mode is expressed as:

[0015]

[0016] in, represents the input of the actuator when attacked; u(k) represents the input of the actuator when not attacked; γ(k) represents the false data signal injected by the attacker; α(k) and β(k) both represent random variables that obey the Bernoulli distribution and satisfy And there is Indicates the probability of a DoS attack; represents the probability of suffering an FDI attack; pr{.} represents the probability of an event occurring.

[0017] Furthermore, the cyber-physical system model is expressed as:

[0018]

[0019] Among them, x(k) represents the state vector at the current moment; y(k) represents the measured output at the current moment; z(k) represents the controlled output at the current moment; represents the input of the actuator when attacked; d(k) represents the external interference of the system; g(x(k)) represents the true value of the nonlinear system; A, B, C, D, E and H all represent constant matrices.

[0020] Furthermore, the adaptive event-triggered communication mechanism is expressed as:

[0021]

[0022] Where ψ(k) represents the adaptive event-triggered communication mechanism; e y (k) represents the difference between y(k) and y(k s ), that is, e y (k) = y(k) - y(k s ); y(k) represents the measured output at the current moment; y(k s ) represents the measured output at the most recent triggering moment; T represents the transpose of the matrix; Ω1 and Ω2 both represent weight matrices, and Ω1>0, Ω2>0; σ(k) represents the trigger threshold parameter, and σ Indicates the upper bound of the trigger threshold parameter, Indicates the lower bound of the trigger threshold parameter.

[0023] Furthermore, the step S2 specifically includes:

[0024] S21. Construct a state observer according to the cyber-physical system model; the state observer is expressed as:

[0025]

[0026] in, represents the state observation value at time k+1; Represents the state observation value at the current moment; represents the measured output observation value at the current moment; y(k s ) represents the measurement output at the most recent triggering moment; represents the actuator input when attacked; L represents the state observation gain matrix; represents the nonlinear observation value of the system;

[0027] S22, based on state observation and Combined with the state feedback gain matrix K, the sliding mode function is established:

[0028]

[0029] The preset sliding surface can be obtained, which is expressed as:

[0030]

[0031] Wherein, s(k) represents the sliding mode function at the current moment; s(k+1) represents the sliding mode function at the k+1 moment; G represents the constant matrix, and GB≠0; K represents the state feedback gain matrix;

[0032] S23. According to the sliding surface, obtain the sliding condition s(k)=s(k+1)=0.

[0033] Furthermore, in step S3:

[0034] (1) The equivalent control law of the system is expressed as:

[0035]

[0036] in, represents the equivalent control law of the system;

[0037] (2) The sliding mode dynamics of the system is expressed as:

[0038]

[0039] Among them, the matrix Y2=IB(GB) -1 G, I represent the unit matrix; e(k) represents the state vector x(k) at the current moment and the state observation value at the current moment The difference, that is

[0040] (3) The system error dynamics is expressed as:

[0041]

[0042] in, Represents the nonlinear true value of the system g(x(k)) and the nonlinear observed value of the system The difference, that is

[0043] Furthermore, the augmented closed-loop system is expressed as:

[0044]

[0045] in, T represents the transpose of the matrix, Represents the state observation value at the current moment.

[0046] Furthermore, the adaptive sliding mode controller based on the equivalent control law is expressed as:

[0047]

[0048] Where u(k) represents the input of the actuator when it is not attacked; Indicates the probability of a DoS attack; It indicates the probability of being attacked by FDI; Represents the observed value of the state vector at the current moment; represents the measured output observation value at the current moment; s(k) represents the sliding mode function at the current moment; K represents the state feedback gain matrix; L represents the state observation gain matrix; G represents the constant matrix, and GB≠0; κ and ι both represent positive scalars; represents the adaptive parameters; represents the adaptive parameter variable value; Π(k) and All represent intermediate parameter variables.

[0049] Furthermore, in the process of using the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system, the sufficient condition for the augmented closed-loop system to satisfy asymptotic stability is expressed as:

[0050]

[0051] Where: * represents the symmetric terms at the corresponding positions in the matrix; T represents the transposed matrix; I represents the identity matrix; P and J both represent positive definite matrices; Ω1 and Ω2 both represent weight matrices; U represents the augmented matrix; σ(k) represents the trigger threshold parameter; H1=[CC -I]; H2=[HH 0]; H3=[I 2n 0 n-2p ]; n represents the dimension of the state vector; λ=max{|λ1(W1)|,|λ2(W1)|,...,|λ n (W1)|}+1;λ i (W1) represents the i-th eigenvalue of matrix W1; ; W2 = diag{G1+G2,G1+G2}; represents a diagonal matrix; represents the inverse matrix of the positive definite matrix P; Θ3=D T D-γ 2 I; γ represents the disturbance attenuation level; represents the inverse matrix of the weight matrix Ω1; Z = diag{Z1, Z2, Z2}; ρ = diag{ρ1, ρ2, ρ2}; Z1, Z2, ρ1 and ρ2 are all unknown matrices to be solved; τ1, and τ2 are both positive scalars.

[0052] On the other hand, the present invention provides an event-triggered adaptive sliding mode control device for a cyber-physical system under a hybrid network attack, applying the above method, the device comprising:

[0053] A cyber-physical system model building module, used to build a cyber-physical system model for the hybrid network attack mode suffered by the cyber-physical system, and introduce an adaptive event-triggered communication mechanism into the cyber-physical system model;

[0054] A sliding surface design module is used to construct a state observer according to the cyber-physical system model; establish a sliding function according to the state observer, and obtain a sliding condition;

[0055] An augmented system model building module is used to obtain the system sliding mode dynamics, system error dynamics and system equivalent control law based on the sliding mode conditions; and to build an augmented closed-loop system according to the system sliding mode dynamics and the system error dynamics;

[0056] The adaptive sliding mode control module is used to construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system.

[0057] On the other hand, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned event-triggered adaptive sliding mode control method for information-physical systems under hybrid network attacks.

[0058] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a method and device for event-triggered adaptive sliding mode control of a cyber-physical system under a hybrid network attack, which has the following features:

[0059] Beneficial effects:

[0060] The adaptive sliding mode controller designed in the present invention can adjust adaptive parameters in real time to optimize the system control performance in response to the negative impact of hybrid network attacks on the control channel of the information-physical system on the system control performance; and can effectively deal with complex characteristics such as system nonlinearity, hybrid network attacks, and external disturbances.

[0061] The present invention provides an adaptive sliding mode control strategy design method based on Lyapunov stability theory, linear matrix inequality technology and a sliding mode control law based on projection, thereby effectively improving the reliability and safety of the information-physical system.

[0062] The system studied in the present invention is more in line with reality because it is subject to mixed attacks consisting of denial of service and false data injection and the influence of uncertainties such as external disturbances on the system.

[0063] Other features and advantages of the present invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the present invention.

[0064] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0066] Figure 1 A flow chart of an adaptive sliding mode control method for information-physical system event triggering under hybrid network attacks provided in an embodiment of the present invention.

[0067] Figure 2 A schematic diagram of the occurrence time of a hybrid network attack provided by an embodiment of the present invention.

[0068] Figure 3 A schematic diagram of the state trajectory of the sliding mode function provided in an embodiment of the present invention.

[0069] Figure 4 A schematic diagram of an equivalent control input trajectory diagram of a closed-loop system provided in an embodiment of the present invention.

[0070] Figure 5 A schematic diagram of an adaptive parameter trajectory provided by an embodiment of the present invention.

[0071] Figure 6 A schematic diagram of the distribution of adaptive event-triggered communication time provided in an embodiment of the present invention.

[0072] Figure 7 A schematic diagram of the state trajectory of a closed-loop system provided in an embodiment of the present invention.

[0073] Figure 8 A schematic diagram of a system state estimation error trajectory provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0074] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] Embodiment 1:

[0076] See also Figure 1 As shown, an embodiment of the present invention discloses an event-triggered adaptive sliding mode control method for a cyber-physical system under a hybrid network attack, comprising the following steps:

[0077] S1. Build a cyber-physical system model for the hybrid cyber attack mode of the cyber-physical system, and introduce an adaptive event-triggered communication mechanism into the cyber-physical system model;

[0078] S2. Construct a state observer according to the cyber-physical system model; establish a sliding mode function according to the state observer and obtain the sliding mode condition;

[0079] S3. Based on the sliding mode conditions, the system sliding mode dynamics, system error dynamics and system equivalent control law are obtained;

[0080] S4. Construct an augmented closed-loop system based on the system sliding mode dynamics and system error dynamics;

[0081] S5. An adaptive sliding mode controller is constructed based on the system equivalent control law, and the adaptive sliding mode controller is used to perform event-triggered adaptive sliding mode control on the augmented closed-loop system.

[0082] Next, each of the above steps will be described in detail.

[0083] In the above step S1, the following contents are specifically included:

[0084] (1) The hybrid cyber attack mode of cyber-physical systems is expressed as:

[0085]

[0086] in, represents the input of the actuator when attacked; u(k) represents the input of the actuator when not attacked; γ(k) is the false data signal injected by the attacker, assuming that its energy is finite, that is, it satisfies the condition ||γ(k)||≤E a , E a is a given positive scalar; α(k) and β(k) are random variables that obey Bernoulli distribution and satisfy And there is Indicates the probability of a DoS attack; represents the probability of suffering an FDI attack; pr{.} represents the probability of an event occurring.

[0087] (2) Cyber-physical system model, expressed as:

[0088]

[0089] Among them, x(k) represents the state vector at the current moment, x(k)∈R n , n represents the dimension of the state vector; y(k) represents the measured output at the current moment, y(k)∈R p , p represents the dimension of the measured output; z(k) represents the controlled output at the current moment, z(k)∈R z , z represents the dimension of the controlled output; represents the input of the actuator when attacked, m represents the dimension of the actuator input; d(k) represents the external disturbance of the system, d(k)∈l2[0,+∞); g(x(k)) represents the true value of the system nonlinearity; A, B, C, D, E and H all represent constant matrices with appropriate dimensions.

[0090] (3) Adaptive event-triggered communication mechanism, expressed as:

[0091]

[0092] Where ψ(k) represents the adaptive event-triggered communication mechanism; e y (k) represents the difference between y(k) and y(k s ), that is, e y (k) = y(k) - y(k s ); y(k) represents the measurement output at the current moment; k represents the current moment; y(k s ) represents the measured output at the most recent triggering moment; k S represents the most recent triggering moment; T represents the transpose of the matrix; Ω1 and Ω2 both represent weight matrices, and Ω1>0, Ω2>0; σ(k) represents the triggering threshold parameter, and σ represents the upper bound of the trigger threshold parameter, represents the lower bound of the trigger threshold parameter, σ and All are scalars; the trigger threshold parameter meets the following conditions:

[0093]

[0094] Among them, the scalars Δ1, Δ2 and δ satisfy the conditions Δ1>1, 0<Δ2<1 and δ>0 respectively.

[0095] In the above step S2, the following contents are specifically included:

[0096] S21. Construct a state observer according to the cyber-physical system model; the state observer is expressed as:

[0097]

[0098] in, represents the state observation value at time k+1; Represents the state observation value at the current moment; represents the measured output observation value at the current moment; y(k s ) represents the measurement output at the most recent triggering moment; represents the input of the actuator when attacked; L represents the state observation gain matrix; Represents the nonlinear observation value of the system, that is, the nonlinear estimation value of the system;

[0099] S22, based on state observation and Combined with the state feedback gain matrix K, the sliding mode function is established:

[0100]

[0101] The preset sliding surface can be obtained, which is expressed as:

[0102]

[0103] Where s(k) represents the sliding mode function at the current time; s(k+1) represents the sliding mode function at time k+1; B and G both represent constant matrices of appropriate dimensions; and matrix G = B T X, X>0, X represents any matrix greater than 0, GB≠0; K represents the state feedback gain matrix.

[0104] S23. According to the sliding surface, obtain the sliding condition s(k)=s(k+1)=0.

[0105] In the above step S3, the following contents are specifically included:

[0106] (1) Combining the sliding surface with the sliding condition, we can obtain:

[0107]

[0108] Then the system equivalent control law It is expressed as:

[0109]

[0110] (2) The system equivalent control law Substituting into the state observer formula constructed above, the sliding mode dynamics of the system can be obtained, which is expressed as:

[0111]

[0112] Among them, the matrix Y2=IB(GB) -1 G, I represent the unit matrix; e(k) represents the state vector x(k) at the current moment and the state observation value at the current moment The difference, that is

[0113] (3) Combining the established cyber-physical system model with the state observer constructed above, the system error dynamics can be obtained; it can be expressed as:

[0114]

[0115] in, Represents the nonlinear true value of the system g(x(k)) and the nonlinear observed value of the system The difference, that is

[0116] In the above step S4, the closed-loop system is augmented and expressed as:

[0117]

[0118] in,

[0119] T represents the transpose of the matrix, Represents the state observation value at the current moment; the above ε, Y, V, and U all represent augmented matrices, which are the matrix parameters of the augmented closed-loop system.

[0120] In the above step S5, the following contents are specifically included:

[0121] (1) The adaptive sliding mode controller based on the equivalent control law is expressed as:

[0122]

[0123] Where u(k) represents the input of the actuator when it is not attacked; Indicates the probability of a DoS attack; It indicates the probability of being attacked by FDI; Represents the state observation value at the current moment; represents the measured output observation value at the current moment; s(k) represents the sliding mode function at the current moment; K represents the state feedback gain matrix, L represents the state observation gain matrix, B and G both represent matrices with appropriate bit dimensions, GB≠0; κ and ι both represent positive scalars; represents the adaptive parameters; represents the adaptive parameter variable value; Π(k) and All represent intermediate parameter variables.

[0124] (2) In order to make the above-mentioned augmented closed-loop system asymptotically stable, the present invention designs the state feedback gain matrix K and the state observation gain matrix L that the mode depends on, that is, using the Lyapunov stability theory and the linear matrix inequality analysis method, fully considering the event-triggered communication mechanism and the nonlinear sector conditions of the CPS to analyze the stability problem of the augmented system, and provides a solution algorithm for the control gain matrix; the specific process is as follows:

[0125] 1) Select the following Lyapunov function for the above system:

[0126] V ξ(k) =ξ T (k)Pξ(k)

[0127] Where P represents a positive definite matrix; V ξ(k) represents the selected Lyapunov function; ξ(k) represents the state variable of the augmented closed-loop system.

[0128] Find V along any trajectory of the augmented closed-loop system ξ(k) The forward difference of , we can get:

[0129] ΔV ξ(k) =V ξ(k+1) -V ξ(k)

[0130] =ξ T (k+1)Pξ(k+1)-ξ T (k)Pξ(k)

[0131] =d T (k)ε T Pεd(k)+G T (e(k))PG(e(k))+η T (k)(T+UYV) T P(T+UYV)η(k)

[0132] +2η T (k)(T+UYV) T Pεd(k)+2G T (e(k))Pεd(k)+2η T (k)(T+UYV) T PG(e(k))

[0133] -ξ T (k)Pξ(k)

[0134] Among them, η(k) represents the expansion of e on the basis of ξ(k). y(k), i.e., a state vector with a larger dimension;

[0135] 2) Combined with the adaptive event trigger mechanism, V ξ(k) The forward difference of is:

[0136]

[0137] Among them, I3=[0 0 I], H1=[CC -I], H2=[HH 0], H3=[I 2n 0 n-2p ].

[0138] 3) Using Lyapunov stability theory and linear matrix inequality analysis method, the asymptotic stability of the above system is judged by introducing the following system performance evaluation indicators:

[0139] That is, for the above augmented closed-loop system model:

[0140] ①When d(k)=0, if It means that the augmented closed-loop system is in an asymptotically stable state;

[0141] ② Assuming that the scalar γ>0 is known, for all non-zero d(k)∈l2[0,∞), if the augmented closed-loop system is asymptotically stable and satisfies the following conditions under the zero initial condition ξ(0)=0:

[0142]

[0143] Then the augmented closed-loop system is ∞ It is asymptotically stable at the disturbance attenuation level γ.

[0144] Then, the sufficient condition for the asymptotic stability of the augmented system is obtained as follows:

[0145]

[0146] Where: * represents the symmetric terms at the corresponding positions in the matrix; T represents the transposed matrix; I represents the identity matrix; P and J both represent positive definite matrices; Ω1 and Ω2 both represent weight matrices; U represents the augmented matrix; σ(k) represents the trigger threshold parameter; H1=[CC -I]; H2=[HH 0]; H3=[I 2n 0 n-2p ]; n represents the dimension of the state vector λ = max{|λ1(W1)|,|λ2(W1)|,...,|λ n (W1)|}+1;λ i (W1) represents the i-th eigenvalue of matrix W1; ; W2 = diag{G1+G2,G1+G2}; represents a diagonal matrix; represents the inverse matrix of the positive definite matrix P; Θ3=D T D-γ 2 I; γ represents the disturbance attenuation level; represents the inverse matrix of the weight matrix Ω1; Z=diag{Z1,Z2,Z2}; ρ=diag{ρ1,ρ2,ρ2}; Z1, Z2, ρ1 and ρ2 all represent unknown matrices to be solved.

[0147] Then the augmented closed-loop system is said to be asymptotically stable and has H ∞ Disturbance rejection level γ.

[0148] Furthermore, the unknown matrix and the unknown positive definite matrix are solved, including:

[0149] Given the weight matrices Ω1, Ω2 and the positive definite matrix P, as well as X, J, and a positive scalar τ1, and τ2, and use the LMI toolbox in MATLAB to solve the above inequality. When there is a solution, the augmented system satisfies asymptotic stability, and the corresponding state feedback gain matrix K and state observation matrix L are:

[0150] When there is no solution, the augmented closed-loop system and the adaptive sliding mode controller are reconstructed until the constructed augmented closed-loop system satisfies asymptotic stability.

[0151] Next, the embodiment of the present invention also verifies the correctness and effectiveness of the above-mentioned security control strategy through simulation examples. The specific implementation method is as follows:

[0152] Considering that the controlled object is a discrete-time nonlinear information-physical system, the corresponding system parameters are

[0153]

[0154] C=[0.105 0.095 0.115], D=0.22, H=[0.52 0 -0.31]

[0155] The nonlinear function g(x(k)) satisfies the condition g(x(k))=1 / 2(G1+G2)x(k)+1 / 2(G2-G1)sin(x(k)), where G1=0.05I and G2=0.1I.

[0156] The probability of DoS attack is selected as Assume that the maximum energy bound of FDI attack is Ea =0.5, the probability of attack is The attack signal of FDI is γ(k) = 0.3cos(2k). The external disturbance signal is d(k) = 0.1sin(0.2k). Select ι = 0.01, κ = 0.001, X = 0.5I, and the disturbance suppression rate γ = 6. Using Matlab's LMI toolbox to solve the state feedback gain matrix K and the state observation matrix L, the weight matrices Ω1, Ω2, and K and L of the adaptive event triggering are obtained as follows:

[0157] Ω1=46.8133; Ω2=20.8186; K=[-0.1924 -0.4216 -0.1764];

[0158] Select the initial state of the system as x(0) = [2 1.5 -2.5] T , The corresponding adaptive trigger parameter gains are Δ1=1.15, Δ2=0.15, and δ=0.08.

[0159] Figure 2 A schematic diagram of the occurrence time of hybrid network attacks is given, where "0" means that the system has not been attacked by the network, and "1" means that the system has been attacked by the network.

[0160] Figure 3 A schematic diagram of the state trajectory of the sliding mode function is given.

[0161] Figure 4 The schematic diagram of the equivalent control input trajectory of the closed-loop system is given. Figure 4 It can be seen that although the system control output fluctuates to a certain extent, it still tends to a balanced state in the end.

[0162] Figure 5 and Figure 6 The schematic diagram of the change trajectory of the adaptive parameters and the adaptive event triggering communication time are given respectively. Figure 6 It can be seen that, compared with the periodic communication mechanism, the adaptive trigger communication scheme adopted by the present invention saves 38% of communication resources.

[0163] Figure 7 and Figure 8 The state trajectory diagram of the closed-loop system and the system state estimation error trajectory are given respectively. Figure 7 and Figure 8 It can be seen that both the state trajectory and the error trajectory of the closed-loop system are convergent.

[0164] The above simulation results show that the event-triggered adaptive sliding mode control method for information-physical systems under hybrid network attacks proposed in the present invention is effective.

[0165] Through the above scheme, it can be known that the present invention provides an event-triggered adaptive sliding mode control method for information-physical systems under hybrid network attacks. Taking into account the characteristics of the hybrid network attack mode to which the system is subjected, an augmented closed-loop system model is established based on sliding mode dynamics and error dynamics, and a sliding mode surface based on state estimation is given; and a new adaptive sliding mode control law is adopted to design a collaborative design strategy of event triggering and adaptive sliding mode control, and the system state is driven into the quasi-sliding mode domain. The present invention can optimize the control performance by adjusting the adaptive parameters, and effectively cope with complex network environments such as system uncertainty and hybrid network attacks; it realizes the adaptive sliding mode control of the system, and effectively reduces the negative impact of DoS attacks, FDI attacks, external disturbances and system nonlinearity on the system control performance in CPS.

[0166] Embodiment 2:

[0167] The embodiment of the present invention further provides an event-triggered adaptive sliding mode control device for a cyber-physical system under a hybrid network attack, and applies the event-triggered adaptive sliding mode control method for a cyber-physical system under a hybrid network attack. The device comprises:

[0168] The cyber-physical system model building module is used to build a cyber-physical system model for the hybrid network attack mode suffered by the cyber-physical system, and introduce an adaptive event-triggered communication mechanism into the cyber-physical system model;

[0169] The sliding surface design module is used to construct a state observer according to the cyber-physical system model; establish a sliding function according to the state observer and obtain the sliding condition;

[0170] The augmented system model building module is used to obtain the system sliding mode dynamics, system error dynamics and system equivalent control law based on the sliding mode conditions; and to build an augmented closed-loop system according to the system sliding mode dynamics and system error dynamics;

[0171] The adaptive sliding mode control module is used to construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system.

[0172] Embodiment three:

[0173] An embodiment of the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned event-triggered adaptive sliding mode control method for information-physical systems under hybrid network attacks.

[0174] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments 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 relevant parts can be referred to the method part.

[0175] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may 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. An event-triggered adaptive sliding mode control method for cyber-physical systems under hybrid network attacks, characterized in that: The steps include: S1. Constructing a cyber-physical system model for the hybrid network attack mode suffered by the cyber-physical system, and introducing an adaptive event-triggered communication mechanism into the cyber-physical system model; S2. constructing a state observer according to the cyber-physical system model; establishing a sliding mode function according to the state observer, and obtaining a sliding mode condition; S3. Based on the sliding mode condition, obtain the system sliding mode dynamics, system error dynamics and system equivalent control law; S4, constructing an augmented closed-loop system according to the system sliding mode dynamics and the system error dynamics; S5. constructing an adaptive sliding mode controller based on the system equivalent control law, and using the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system; The cyber-physical system model is expressed as: Among them, x(k) represents the state vector at the current moment; y(k) represents the measured output at the current moment; z(k) represents the controlled output at the current moment; represents the input of the actuator when attacked; d(k) represents the external interference of the system; g(x(k)) represents the nonlinear true value of the system; A, B, C, D, E and H all represent constant matrices; The step S2 specifically includes: S21. Construct a state observer according to the cyber-physical system model; the state observer is expressed as: in, represents the state observation value at time k+1; Represents the state observation value at the current moment; represents the measured output observation value at the current moment; y(k s ) represents the measurement output at the most recent triggering moment; represents the actuator input when attacked; L represents the state observation gain matrix; represents the nonlinear observation value of the system; S22, based on state observation and Combined with the state feedback gain matrix K, the sliding mode function is established: The preset sliding surface can be obtained, which is expressed as: Wherein, s(k) represents the sliding mode function at the current moment; s(k+1) represents the sliding mode function at the k+1 moment; G represents the constant matrix, and GB≠0; K represents the state feedback gain matrix; S23, according to the sliding surface, obtain the sliding condition s(k)=s(k+1)=0; In step S3: (1) The equivalent control law of the system is expressed as: in, represents the equivalent control law of the system; (2) The sliding mode dynamics of the system is expressed as: Among them, the matrix Y2=IB(GB) -1 G, I represent the unit matrix; e(k) represents the state vector x(k) at the current moment and the state observation value at the current moment The difference, that is e y (k) represents the difference between y(k) and y(k s ), that is, e y (k) = y(k) - y(k s ); (3) The system error dynamics is expressed as: in, Represents the nonlinear true value of the system g(x(k)) and the nonlinear observed value of the system The difference, that is The augmented closed-loop system is expressed as: in, Represents the state observation value at the current moment; The adaptive sliding mode controller based on the system equivalent control law is expressed as: Where u(k) represents the input of the actuator when it is not attacked; Indicates the probability of a DoS attack; It indicates the probability of being attacked by FDI; represents the measured output observation value at the current moment; s(k) represents the sliding mode function at the current moment; K represents the state feedback gain matrix; L represents the state observation gain matrix; G represents the constant matrix, and GB≠0; κ and ι both represent positive scalars; represents the adaptive parameters; represents the adaptive parameter variable value; Π(k) and All represent intermediate parameter variables; y(ks) represents the measurement output at the most recent triggering moment.

2. The event-triggered adaptive sliding mode control method for cyber-physical systems under hybrid network attacks according to claim 1 is characterized in that: The hybrid network attack mode is expressed as: in, represents the input of the actuator when attacked; u(k) represents the input of the actuator when not attacked; γ(k) represents the false data signal injected by the attacker; α(k) and β(k) both represent random variables that obey the Bernoulli distribution and satisfy And there is Indicates the probability of a DoS attack; represents the probability of suffering an FDI attack; pr{.} represents the probability of an event occurring.

3. The event-triggered adaptive sliding mode control method for cyber-physical systems under hybrid network attacks according to claim 1 is characterized in that: The adaptive event-triggered communication mechanism is expressed as: Where ψ(k) represents the adaptive event-triggered communication mechanism; e y (k) represents the difference between y(k) and y(k s ), that is, e y (k) = y(k) - y(k s ); y(k) represents the measured output at the current moment; y(k s ) represents the measured output at the most recent triggering moment; Ω1 and Ω2 both represent weight matrices, and Ω1>0, Ω2>0; σ(k) represents the trigger threshold parameter, and σ Indicates the lower bound of the trigger threshold parameter; Indicates the upper bound of the trigger threshold parameter.

4. The event-triggered adaptive sliding mode control method for cyber-physical systems under hybrid network attacks according to claim 1 is characterized by: In the process of using the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system, the sufficient condition for the augmented closed-loop system to satisfy asymptotic stability is expressed as: Where: * represents the symmetric terms at the corresponding positions in the matrix; I represents the identity matrix; P and J both represent positive definite matrices; Ω1 and Ω2 both represent weight matrices; U represents the augmented matrix; σ(k) represents the trigger threshold parameter; H1=[C CI]; H2=[HH 0]; H3=[I 2n 0 n-2p ]; n represents the dimension of the state vector; λ=max{λ1(W1)|,|λ2(W1)|,...,|λ n (W1)}+1;λ i (W1) represents the i-th eigenvalue of matrix W1; W2=diag{G1+G2,G1+G2}; represents a diagonal matrix; represents the inverse matrix of the positive definite matrix P; Θ3=D T D-γ 2 I; γ represents disturbance Attenuation level; represents the inverse matrix of the weight matrix Ω1; Z = diag{Z1, Z2, Z2}; ρ = diag{ρ1, ρ2, ρ2}; Z1, Z2, ρ1 and ρ2 are all unknown matrices to be solved; τ1 and All represent positive scalars; C, D and H all represent constant matrices; p represents the dimension of the measurement output; X represents any matrix greater than 0; ε, Y and V all represent augmented matrices; G1 = 0.05I, G2 = 0.1I; A represents a constant matrix.

5. An adaptive sliding mode control device for cyber-physical system event triggering under hybrid network attack, characterized in that: The method according to any one of claims 1 to 4 is applied, wherein the device comprises: A cyber-physical system model building module, used to build a cyber-physical system model for the hybrid network attack mode suffered by the cyber-physical system, and introduce an adaptive event-triggered communication mechanism into the cyber-physical system model; A sliding surface design module is used to construct a state observer according to the cyber-physical system model; establish a sliding function according to the state observer, and obtain a sliding condition; An augmented system model building module is used to obtain the system sliding mode dynamics, system error dynamics and system equivalent control law based on the sliding mode conditions; and to build an augmented closed-loop system according to the system sliding mode dynamics and the system error dynamics; The adaptive sliding mode control module is used to construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform event-triggered adaptive sliding mode control on the augmented closed-loop system.

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