DoS attack-oriented cloud control system fuzzy modeling and event triggering prediction method

Abstract

The invention provides a DoS attack-oriented cloud control system modeling and event triggering prediction method under an interval type-2 T-S fuzzy model framework, and the method specifically comprises the steps: S1, monitoring the conditions of complex information transmission and the like of a cloud end and a physical end in a cloud control network system framework; establishing a cloud control system difference equation taking the interval type-2 T-S fuzzy model as a description language; s2, performing statistics, classification and linearization on the state of the fuzzy cloud control system by adopting a type-2 fuzzy set theory and a time division segmentation analysis method, and giving an attack model and regional parameters; s3, designing a dynamic event triggering mechanism with an exponential decay characteristic, reducing the data transmission quantity, and improving the bandwidth and energy utilization rate; s4, proposing an event type fuzzy prediction controller, and establishing a prediction model, a performance index and a constraint condition; s5, constructing a switching control law and a fuzzy optimization algorithm, and obtaining optimal parameters; and S6, the prediction stability of the interval type-2 T-S fuzzy system is ensured, and time-zone-division modeling and on-demand control are realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of control science and engineering, and particularly relates to a cloud control system fuzzy modeling and event-triggered prediction method for DoS attacks. BACKGROUND

[0002] A cloud control system is a combination of cloud computing and network control systems. The cloud control system places the controller algorithm and massive data in the cloud, thereby forming a "cloud-edge-end" remote control system based on cloud computing. In the process of network transmission and communication, many system security issues cannot be ignored, such as signal delay caused by the network, data packet loss, communication constraints, and malicious attacks. The present application proposes a cloud control system fuzzy modeling and event-triggered prediction method for DoS attacks. DoS (Denial of Service, DoS) attack is a type of network signal attack that affects the implementation of communication rules and thus exhausts network resources, causing the target system to lose its stable running state. DoS attacks can consume system resources or cause system crashes by continuously sending a large number of requests or malicious data packets to the target system. This attack can cause service interruption, network delay, system crash, and other problems, seriously affecting the stability of the system. DoS attacks are usually divided into two types: bandwidth-based attacks and resource consumption-based attacks. Bandwidth-based attacks occupy the network bandwidth of the target system by sending a large amount of data traffic to it, making legitimate users unable to normally access the service; while resource consumption-based attacks consume system resources such as CPU and memory by sending a large number of requests or malicious data packets to the system.

[0003] The interval type-II T-S (IT2 T-S) fuzzy cloud control system based on event triggering not only has the universal approximation property of fuzzy models, but also has strong flexibility and robustness of fuzzy control. It obtains a series of local linear models describing the cloud control system through a set of fuzzy rules, and uses its interval type-II membership function to represent the uncertainty and nonlinearity in the actual model.

[0004] For the field of network security, system model prediction for DoS attacks has become an important topic. IT2 T-S fuzzy systems, as a powerful fuzzy reasoning tool, have shown great potential in this field. IT2 T-S fuzzy systems can effectively handle fuzziness and uncertainty, and have good adaptability and flexibility, making them suitable for complex network environments and attack scenarios. Applying IT2 T-S fuzzy modeling and fuzzy control technology to handling cloud control with DoS attacks can achieve network security defense and model prediction control, which has more research value.

[0005] Dynamic Event-Triggered Mechanism (DETM) is a kind of signal control method based on the idea of on-demand control, which decides when to trigger control action and release data according to the dynamic changes of system state. Compared with periodic time or static event-triggered mechanism, DETM can adaptively generate trigger time sequence according to system performance, avoiding the occupation of network resources by redundant data, thereby realizing efficient control of the system. The trigger mechanism usually depends on the measurement or estimation of system state and the pre-set trigger condition, such as the size of state error or the rate of change of system state. By reasonably designing the dynamic event triggering strategy, accurate on-demand control of cloud control system can be realized, which reduces the burden of cloud computing and the communication cost of ''cloud-edge-end'' network to a certain extent. SUMMARY

[0006] In view of the problem that DoS attack sends a large number of requests or malicious traffic to overload the target system, causing normal users to be unable to access, the application provides a fuzzy modeling and event-triggered prediction method for cloud control system facing DoS attack, so as to improve the security and reliability of ''cloud-edge-end'' network

[0007] Technical scheme: the fuzzy modeling and event-triggered prediction method for cloud control system facing DoS attack provided by the application comprises the following steps:

[0008] S1: monitoring the complex information transmission and the like of the cloud and the physical end in the cloud control network system framework, establishing a differential equation of the cloud control system taking IT2T-S fuzzy model as a description language;

[0009] S2: using the two-type fuzzy set theory and time zone segmentation analysis method to statistically, classify and linearize the system state before and after DOS attack, and giving a mathematical model of attack signal and regional parameters;

[0010] S3: based on the idea of on-demand control, designing a dynamic event-triggered mechanism with exponential decay characteristics, reducing data transmission volume, and improving bandwidth and energy utilization rate;

[0011] S4: proposing an event-type fuzzy predictive controller, establishing a prediction model, performance index and constraint condition;

[0012] S5: constructing a switching control law and a fuzzy optimization algorithm, and obtaining optimal parameters;

[0013] S6: ensuring the prediction stability of the IT2T-S fuzzy system, and being capable of processing the uncertainty with DOS attack, realizing time zone modeling and on-demand control;

[0014] Further, the step S1 specifically comprises:

[0015] S11: The fuzzy rules of the IT2 T-S fuzzy model can be described as:

[0016] System rule i: if f1(x(k)) is ... and f g (x(k)) is then

[0017] x(k+1) = Ax(k) + Bu(k)

[0018] where x(k) e R n is the state vector; u(k) e R n is the control input vector; A is the system matrix;

[0019] S12: After single-point fuzzification, multiple inference, and weighted average defuzzification, the global IT2 T-S fuzzy cloud control system on the given domain can be obtained as:

[0020]

[0021] where

[0022]

[0023] S13: The weighted coefficients c i (α(k)) and are two nonlinear functions that can be adjusted online according to the changes in uncertain parameters and satisfy

[0024]

[0025] S14: Based on interval II-type fuzzy sets, the upper and lower membership functions can effectively capture the parameter uncertainty in the model and can be adjusted appropriately according to the dynamic characteristics. In contrast, c i (α(k)) and depend on the uncertain parameters in the actual system.

[0026] Further, the step S2 specifically comprises:

[0027] S21: Based on the time zone modeling method, the nth cycle attack model considering DoS attacks is as follows:

[0028] k e [(n-1)T+1, nT]

[0029] where T e Z + represents the duration of a cycle, including the working period and the sleep period:

[0030] Attack time: ((n-1)T+t off , nT)

[0031] The sleep time is: ((n-1)T+1, (n-1)T+t off )

[0032] Where t off ∈Z + , t off <T represents the duration of the sleep cycle;

[0033] S22: σ(k) ∈ {1, 2} represents different periods in the nth cycle, σ(k) represents:

[0034]

[0035] Where σ(k) = 1 and σ(k) = 2 represent the sleep period and attack period of the nth cycle, respectively;

[0036] S23: In the sleep period, the DoS generator remains silent to replenish energy, and considers the data packet loss caused by the inherent factors of the wireless channel; In the attack period, the DoS jammer initiates continuous DoS jamming attacks, reducing the communication quality of the wireless measurement channel.

[0037] Combined with the attack strategy of the DoS jammer, θ(σ(k), k) ∈ {0, 1} represents whether the controller successfully receives the data packet at time k:

[0038]

[0039] S24: For the cloud control system subjected to DoS jamming attacks, considering the attack strategy of the DoS jammer and the inherent data packet loss of the measurement channel, the probability of the controller successfully receiving the data packet can be represented as:

[0040]

[0041] Where α σ(k) ∈ [0, 1) is a known constant.

[0042] Further, the step S3 specifically comprises:

[0043] S31: First, considering the definition of the error e(k), which represents the error between the actual output x(k) of the system and the desired output , where is a time delay parameter. Generally, the time delay parameter is considered as a fixed value;

[0044] S32: Considering that the time delay will decay with the advancement of the control process, an exponential decay function is used to define

[0045] S33: Based on the above, we define the system actual output and expected output error model as:

[0046]

[0047] S34: When k = k d , the value of the exponential decay function is 1, i.e. equals 1, and the time lag is 0, i.e. no delay effect;

[0048] S35: When k > k d , the value of the exponential decay function is less than 1, indicating that the time delay factor gradually decreases over time, and the time lag effect gradually weakens;

[0049] S36: The modeling of the error e(k) takes into account the difference between the actual output x(k) and the expected output , and introduces a time delay factor through an exponential decay function, making the model better capture the characteristics of the delay effect changing over time;

[0050] S37: Based on the above state error model, the exponential dynamic event triggering mechanism is as follows:

[0051] S38: t k+1 = inf{k > k d | η(k) + θ(σ||x(k)||Φ - ||e(k)||Φ)≤0} where η(k) is a dynamic variable with an update rate of:

[0052] S39: η(k+1) = η(k) + σ||x(k)|| φ -||e(k)|| φ

[0053] where σ ∈ (0, 1); θ > 1; Φ is a positive definite symmetric matrix; k ∈ N is the current sampling time; η(k) is a dynamic term of the dynamic event triggering mechanism,

[0054] S40: According to Lemma 1:

[0055] If and θ satisfies the dynamic event triggering mechanism, then the auxiliary offset variable satisfies η(k) ≥ 0; the upper bound of the interval [k d , k d+1 ] between two adjacent event triggers (i ∈ 1, 2, 3,...) is denoted as M, and M ∈ Z +

[0056] Further, the step S4 specifically comprises:

[0057] S41: using a quadratic programming optimization method, and the optimization index is:

[0058] min J = min Z T QZ + C T Z

[0059] wherein Z T QZ is a quadratic form, C T Z is linear. If Q is a diagonal matrix, i.e. then the problem is a least square problem;

[0060] S42: defining initial conditions as: x(k|k) = x k ; x(k+1|k) = Ax(k|k) + Bu(k|k) = Ax k + Bu(k|k);

[0061] Recursion can be obtained as:

[0062] x(k+N|k) = A N x k + A N-1 Bu(k|k) + … + Bu(k+N-1|k)

[0063] S43: the matrix obtained by recursion is expressed as:

[0064]

[0065] S44: let

[0066] then

[0067] X k = Mx k + CU k

[0068] wherein x k is an initial state, and 0 in C represents a zero matrix;

[0069] S45: constructing a model prediction controller (MPC), the MPC solves the optimal control signal by solving a cost function J, and the cost function is constructed as follows:

[0070] The prediction range of the MPC control is denoted as N, and two positive definite weight matrices Q and R are given, and F is designed as a terminal weight parameter matrix of the MPC;

[0071] According to the optimal control theory, a performance index (cost function) is proposed as a function of the terminal state variable and the target value, i.e. J = h(x[N] , x d );

[0072] S46: Predict the state x(k+l|k), u(k+l|k) and x(k+N|k) for each state and input by model prediction principle;

[0073] S47: The cost function is defined as follows:

[0074]

[0075] where l = 1, 2,..., N-1,

[0076] S48: Let

[0077]

[0078] Then

[0079]

[0080] S49: Substitute X k = Mx k + CU k into the above equation, eliminate the variable X k and simplify:

[0081]

[0082] S50: Since J is a 1x1 matrix, X k and U k are both n x 1 matrices, and are both n x n matrices, then J T = J

[0083] Since the matrices and are transposes of each other and are both numerical values, the numerical values are equal, i.e.:

[0084]

[0085] Let

[0086]

[0087] Then

[0088]

[0089] Further, the step S5 specifically comprises:

[0090] The calculation formula of the switching controller in step S5 is as follows:

[0091] ControllerA: when σ(k) = 2

[0092] S51: Considering the system dynamics and optimal performance index, the optimal control method is used to obtain the optimal control sequence:

[0093]

[0094] Optimize the control input for the next N steps;

[0095] S52: When the event condition is met, the event is triggered,

[0096] Considering the current time k d and the optimal control sequence U * , the first control quantity u(k) is selected as the control input at the current time, and the optimal control sequence U * can quickly update the control input of the system to respond to the occurrence of events and restore system performance as soon as possible, that is:

[0097]

[0098] S53: When an event occurs in the system and needs to be quickly responded, according to the current time k d and the pre-computed optimal control sequence U * , the first control quantity in the sequence is selected as the control input at the current time, which can quickly respond to the occurrence of events and use the pre-computed optimal control sequence as the input signal to restore system performance as soon as possible and compensate for the data loss caused by DoS attacks;

[0099] ControllerB: when σ(k) = 1:

[0100] S54: When the DoS jammer is in a dormant state, the control strategy switches to the feasibility control:

[0101]

[0102] S55: When there is no DoS attack affecting the system, the system uses the feasibility control strategy to calculate the control input in real time by solving the feedback control gain K, and the controller sequence switching system refers to the system switching according to the actual situation of the network in a specific order, and the sequence switching of the controller is based on the DoS attack switching identifier σ(k) and the dynamic event trigger time sequence;

[0103] S56: Considering the time zone non-periodic characteristics of DoS attacks, the following switching controller is proposed based on the on-demand control idea:

[0104]

[0105] where u(k) = u * (k + 1 | k d ) is the control input at time k; K is the control gain matrix, σ(k) = 2, indicating that the DoS jammer is in the active period; σ(k) = 1, indicating that the DoS jammer is in the dormant period; denotes the control input at time k, whose value depends on the state estimate.

[0106] Further, the step S6 specifically comprises:

[0107] S61: Based on the above proposed method, the asymptotic stability of the IT2 T-S fuzzy cloud control system under the proposed switching control strategy is proved:

[0108] Controller A: When σ(k) = 2

[0109] S62: The following Lyapunov function is constructed:

[0110] V k = J k + η k

[0111] S63: Taking the difference of it, we get:

[0112]

[0113]

[0114] S64: According to the dynamic event-triggered mechanism, we get:

[0115]

[0116] S65: Through the definition of η(k) above, we can get (1-μ) and both belong to the range of (0, 1). Since we can get σ|x(k)| Φ +(1-μ)η(k)≤|e(k)| Φ , and further we can get:

[0117]

[0118] S66: For the cost function before, we make the following assumptions, assuming that the terminal cost function satisfies:

[0119]

[0120] where x k ∈X f ;

[0121] S67: Combining the assumption with the Lyapunov function gives:

[0122]

[0123] S68: Since μ∈(0, 1) and according to Lemma 1, it can be concluded that:

[0124]

[0125] S69: According to the Lyapunov stability theory, the IT2 T-S fuzzy cloud control system can guarantee the stability of the system under DoS attack when using the MPC control strategy;

[0126] ControllerB: When σ(k) = 1:

[0127] S70: Case 1: When k∈[k d , k d +1), it can be obtained that:

[0128]

[0129] S71: Case 2: When k = k d+1 , which is the event-triggered moment, it can be seen from the error system that e(k) = 0; therefore:

[0130] S72:

[0131] S73: Case N-1: When k = k d+N-1 , which is the event-triggered moment; similar to Case 2, it can be obtained that:

[0132]

[0133] S74: Case N: When k∈[k d +N, k d +N+1), it can be obtained that:

[0134]

[0135] S75: According to Lemma 2:

[0136] For the event-triggered tuning parameter σ(0, 1), if there exists a matrix and the matrix Y has appropriate dimensions and satisfies the condition:

[0137]

[0138] then the system is asymptotically stable; where

[0139] S76: Based on the IT2 T-S fuzzy system under DoS attack, the following Lyapunov function is constructed:

[0140]

[0141] According to the fuzzy system and the event-triggered mechanism, the V k is differentiated, and we can get

[0142]

[0143] Wherein,

[0144]

[0145]

[0146]

[0147]

[0148] S77: From the above formula,

[0149]

[0150] Then ΔV k < 0, define And

[0151] The left and right sides of the inequality are multiplied by H -1 , so that it becomes a linear matrix inequality. According to the Lyapunov stability theory, when the inequality satisfies the condition , the IT2 T-S fuzzy cloud control system is asymptotically stable under the switching control strategy proposed. BRIEF DESCRIPTION OF DRAWINGS

[0152] Figure 1 The structure block diagram of the IT2 T-S fuzzy cloud control system under DoS attack is shown in Figure 1.

[0153] Figure 2 The schematic diagram of the MPC prediction model introduced in Example 1 of the present application is shown in Figure 2.

[0154] Figure 3 The event model prediction control step flow chart of the IT2-T-S fuzzy cloud control system under DoS attack in Example 1 of the present application is shown in Figure 3.

[0155] Figure 4 The logic of the switching controller designed in Example 1 of the present application is shown in Figure 4.

[0156] Figure 5 The state performance of the cloud control system when the example system is subjected to a non-cyclic DoS attack. DETAILED DESCRIPTION

[0157] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0158] Example 1

[0159] This embodiment provides a fuzzy modeling and event-triggered prediction method for cloud control systems against DoS attacks. This method aims to ensure that the IT2-TS fuzzy cloud control system remains stable under the influence of an MPC controller. The core of this embodiment's solution is to combine DoS attacks with model predictive control, enabling the system to ultimately stabilize after a DoS attack using MPC.

[0160] In order to facilitate the understanding of this embodiment, the basic principle of MPC is first introduced below. Figure 2 As shown in Figure 2, MPC is a rolling optimization control method.

[0161] First, define the prediction interval as: N p , the control interval is defined as N c , let it be N n =N c =5

[0162] The performance indicators of rolling optimization are:

[0163] Assume that the system starts at time k and the initial state is x [k|k] , the rolling optimization control algorithm obtains the optimal control sequence by solving the optimization problem within the prediction interval: y [k|k] ,u [k+1|k] ,u [k+2|k] ,u [k+3|k] ,u [k+4|k] .

[0164] Among them, u [k|k] represents the control strategy at time k+i calculated at time k. [k+i|k] Represents the value of the state variable at time k+i predicted at time k.

[0165] At time k+1, the system will repeat the operation at time k. The system state at this time is the same as the last control u. [k|k] Under the action of x [k+1|k] , x[k+1|k] The initial state at time k+1 is taken as

[0166] The prediction horizon is moved forward by one discrete step and the optimal control sequence is calculated: u [k+1|k+1] , u [k+3|k+1] , u [k+4|k+1] , u [k+5|k+1] The system state value under such control sequence is predicted: x [k+2|k+1] , x [k+3|k+1] , x [k+4|k+1] , x [k+5|k+1] , x [k+6|k+1] .

[0167] Similarly, only the input u [k+1|k+1] is applied to the system at time k+1.

[0168] Such operations are repeated, and the predictive control is constantly repeated and rolled forward with time. At each new time, the situation in the prediction horizon needs to be calculated and analyzed.

[0169] At the beginning of each optimization, the state variables of the system are used as initial conditions for the model prediction of the system, which can also be understood as the feedback term of the system.

[0170] Based on the above-mentioned MPC controller, the improved event model predictive control of IT2-T-S fuzzy system under denial of service attack designed in this embodiment includes: first, modeling the cloud control system as an IT2-T-S fuzzy system.

[0171] Compared with the traditional T-S fuzzy system, the IT2 T-S fuzzy system introduces the II type fuzzy set, which can more accurately model and handle the uncertainty of the system. The IT2 T-S fuzzy system has better performance and robustness when dealing with nonlinear and uncertain systems.

[0172] After introducing the application of MPC, the following will further describe the scheme provided in this embodiment in detail.

[0173] This example provides a cloud control system fuzzy modeling and event triggered prediction method for DoS attack, as shown in Figure 3 , which includes the following steps:

[0174] S1: Monitor the complex information transmission and the like of the cloud and the physical end in the cloud control network system framework, and establish a cloud control system difference equation described by an interval two type T-S fuzzy model;

[0175] S2: Use the two type fuzzy set theory and time zone segmentation analysis method to statistically, classify and linearize the system state before and after the DoS attack, and give the attack model and regional parameters;

[0176] S3: Based on the idea of on-demand control, a dynamic event triggered mechanism with exponential decay characteristics is designed to reduce data transmission and improve bandwidth and energy utilization;

[0177] S4: An event type fuzzy predictive controller is proposed to establish a prediction model, performance index and constraint condition;

[0178] S5: A switching control law and fuzzy optimization algorithm are constructed to obtain the optimal parameters;

[0179] S6: The prediction stability of the interval type-2 T-S fuzzy system is ensured, and the uncertainty with DoS attack is processed to realize time zone modeling and on-demand control;

[0180] In specific implementation, as a preferred embodiment of the application, the step S1 specifically comprises:

[0181] S11: The fuzzy rule of the IT2 T-S fuzzy model can be described as:

[0182] System rule i: if f1(x(k)) is ... and f g (x(k))) is then

[0183] x(k+1)=Ax(k)+Bu(k)

[0184] Wherein, x(k)∈R n is a state vector; u(k)∈R n is a control input vector; A is a system matrix;

[0185] S12: After single-point fuzzification, multiplication reasoning, weighted average defuzzification, the global IT2 T-S fuzzy cloud control system on the given domain can be obtained as:

[0186]

[0187] Wherein

[0188]

[0189] S13: The weighted coefficients c i (α(k)) and are two nonlinear functions, which can be adjusted online according to the change of uncertain parameters

[0190] Satisfy

[0191]

[0192] S14: Based on interval type-2 fuzzy sets, the upper and lower membership functions can effectively capture the parameter uncertainty in the model and can be adjusted appropriately according to the dynamic characteristics; on the contrary, c i (α(k)) and Depend on the uncertain parameters in the actual system.

[0193] In specific implementation, as a preferred embodiment of the present application, the step S2 specifically comprises:

[0194] S21: Based on the time zone modeling method, we consider the nth cycle attack model of DoS attack as follows:

[0195] k∈[(n-1)T+1,nT]

[0196] Where T∈Z + Indicates the duration of a cycle, including the working period and the sleep period:

[0197] Attack time: ((n-1)T+t off , nT)

[0198] Sleep time: ((n-1)T+1, (n-1)T+t off )

[0199] Where t off ∈Z + , t off <T indicates the duration of the sleep cycle;

[0200] S22: σ(k)∈{1,2} indicates in the different periods of the nth cycle, σ(k) is represented as:

[0201]

[0202] Where σ(k)=1 and σ(k)=2 represent the sleep period and the attack period of the nth cycle respectively;

[0203] S23: In the sleep period, the DoS generator keeps silent to replenish energy, and considers the data packet loss caused by the inherent factors of wireless channel; In the attack period, the DoS jammer initiates continuous DoS jamming attack, reduces the communication quality of the wireless measurement channel.

[0204] In the attack period, the DoS jammer initiates continuous DoS jamming attack, reduces the communication quality of the wireless measurement channel.

[0205] Combined with the attack strategy of the DoS jammer, θ(σ(k),k)∈{0,1} indicates whether the controller successfully receives the data packet at time k:

[0206]

[0207] S24: For the cloud control system under DoS jamming attack, the probability of the controller successfully receiving data packets can be expressed as:

[0208]

[0209] where α σ(k) ∈ [0, 1) is a known constant.

[0210] In a specific implementation, as a preferred embodiment of the present application, the step S3 specifically comprises:

[0211] S31: First, considering the definition of the error e(k), the error between the actual output x(k) of the system and the expected output where is a time delay parameter. Generally, the time delay parameter is regarded as a fixed value;

[0212] S32: Considering that the time delay will decay with the advancement of the control process, an exponential decay function is used to define

[0213] S33: Based on the above, we define the error model between the actual output and the expected output of the system as:

[0214]

[0215] S34: When k = k d , the value of the exponential decay function is 1, i.e. is equal to 1, and the time delay is 0, i.e. there is no delay effect;

[0216] S35: When k > k d , the value of the exponential decay function is less than 1, indicating that the time delay factor gradually decreases over time, and the time delay effect gradually weakens;

[0217] S36: The modeling of the error e(k) considers the difference between the actual output x(k) and the expected output , and introduces the time delay factor through the exponential decay function, making the model better capture the characteristics of the delay effect changing over time;

[0218] S37: Based on the above state error model, the exponential dynamic event triggering mechanism is as follows:

[0219] S38: t k+1 = in f(k > k d | η(k) + θ(σ||x(k)|| - ||e(k)||) Φ Φ )≤0} where η(k) is a dynamic variable, and the update rate is:

[0220] S39: η(k+1) = η(k) + σ||x(k)|| - ||e(k)|| φ φ

[0221] where σ ∈ (0, 1); θ > 1; Φ is a positive definite symmetric matrix; k ∈ N is the current sampling time; η(k) is a dynamic term of the dynamic event-triggered mechanism,

[0222] S40: According to Lemma 1:

[0223] If and θ satisfies the dynamic event-triggered mechanism, then the auxiliary offset variable satisfies η(k) ≥ 0; the upper bound of the interval between two adjacent event triggers [k d , k d+1 ](i ∈ 1, 2, 3,...) is denoted as M, and M ∈ Z +

[0224] In the implementation, as a preferred embodiment of the present application, the step S4 specifically comprises:

[0225] S41: An optimal method of quadratic programming is adopted, and the optimization index is:

[0226] min J = min Z T QZ + C T Z

[0227] where Z T QZ is a quadratic form, C T Z is linear. If Q is a diagonal matrix, i.e. then the problem is a least square problem;

[0228] S42: The initial condition is defined as: x(k|k) = x k ; x(k+1|k) = Ax(k|k) + Bu(k|k) = Ax k + Bu(k|k);

[0229] The recursion can be obtained as:

[0230] x(k+N|k) = A N x k + A N-1 Bu(k|k) + … + Bu(k+N-1|k)​​

[0231] S43: The recursive matrix is expressed as:

[0232]

[0233] S44: Let

[0234] Then

[0235] X k = Mx k + CU k

[0236] where x k is the initial state, and 0 in C represents a zero matrix;

[0237] S45: A model predictive controller (MPC) is constructed, which solves the optimal control signal by solving a cost function J, which is constructed as follows:

[0238] The prediction range of the MPC control is denoted as N, and two positive definite weight matrices Q and R are given, and F is designed as the terminal weight parameter matrix of the MPC;

[0239] According to the optimal control theory, the performance index (cost function) is proposed to be a function of the terminal state variable and the target value, i.e., J = h(x [N] , x d );

[0240] S46: By the MPC prediction method, each state and input, and the terminal state x(k+l|k), u(k+l|k) and x(k+N|k) are predicted;

[0241] S47: The cost function is defined as follows:

[0242]

[0243] where l = 1, 2,..., N-1,

[0244] S48: Let

[0245]

[0246] Then

[0247]

[0248] S49: Substitute X k = Mx k + CU k into the above formula, eliminate the variable X k and simplify:

[0249]

[0250] S50: Because J is a 1x1 matrix X k and U k are both n x 1 matrices, and are both n x n matrices, then J T = J

[0251] Since the matrices and are transposes of each other and are both numerical values, the numerical values are equal, that is:

[0252]

[0253] Let

[0254]

[0255] then

[0256]

[0257] In a specific implementation, as a preferred embodiment of the present application, the step S5 specifically includes:

[0258] The calculation formula of the switching controller in step S5 is as follows:

[0259] ControllerA: When σ(k) = 2

[0260] S51: Considering the system dynamic characteristics and the optimal performance index, an optimal control method is used to obtain an optimal control sequence:

[0261]

[0262] The control input for the future N steps is optimized;

[0263] S52: When the event condition is met, the event is triggered,

[0264] Considering the current time k d and the optimal control sequence U * , the first control amount u(k) is selected as the control input at the current time, and the optimal control sequence U * can quickly update the control input of the system to respond to the occurrence of the event and restore the system performance as soon as possible, that is:

[0265]

[0266] S53: When an event occurs in the system and needs to be quickly responded, according to the current time k dand the pre-computed optimal control sequence U * selecting the first control amount in the sequence as the control input at the current time, so that the system can quickly respond to the occurrence of an event and use the pre-computed optimal control sequence to control the system to recover system performance as soon as possible to compensate for data loss caused by the DoS attack;

[0267] ControllerB: when σ(k) = 1:

[0268] S54: When the DoS jammer is in the dormant state, the control strategy is switched to the feasibility control:

[0269]

[0270] S55: When the system is not affected by the DoS attack, the system adopts the feasibility control strategy, and the control input is calculated in real time by solving the feedback control gain K. The sequence switching system refers to the system switching according to the actual situation of the network in a specific sequence, and the sequence switching of the controller is performed according to the DoS attack switching identifier σ(k) and the dynamic event trigger time sequence;

[0271] S56: Considering the time zone non-periodic characteristics of the DoS attack, the following switching controller is proposed based on the on-demand control idea:

[0272]

[0273] wherein u(k) = u * (k+l|k d ) is the control input at time k; K is the control gain matrix, σ(k) = 2, indicating that the DoS jammer is in the working period; σ(k) = 1, indicating that the DoS jammer is in the dormant period; , which indicates that the value of the control input at time k depends on the state estimation value.

[0274] In specific implementation, as a preferred embodiment of the present application, the step S6 specifically comprises:

[0275] S61: Based on the above proposed method, the asymptotic stability of the IT2 T-S fuzzy cloud control system under the switching control strategy is proved:

[0276] ControllerA: when σ(k) = 2

[0277] S62: The following Lyapunov function is constructed:

[0278] V k = J k +η k

[0279] S63: The difference is obtained for it:

[0280]

[0281] S64: According to the dynamic event-triggered mechanism, we have:

[0282]

[0283] S65: Through the definition of η(k), we can get (1-μ) and Both belong to the range of (0, 1). Since We can get σ|x(k)| Φ +(1-μ)η(k)≤|e(k)| Φ , and then we can get:

[0284]

[0285] S66: For the previous cost function, we make the assumption that the terminal cost function satisfies:

[0286]

[0287] Where x k ∈X f ;

[0288] S67: Combining the assumption with the Lyapunov function, we get:

[0289]

[0290] S68: Since μ∈(0, 1) and according to Lemma 1, we can get:

[0291]

[0292] S69: According to the Lyapunov stability theory, under the MPC control strategy adopted in this paper, the IT2 T-S fuzzy cloud control system can guarantee the stability of the system under DoS attacks;

[0293] ControllerB: When σ(k) = 1:

[0294] S70: Case 1: When k∈[k d , k d +1), we can get:

[0295]

[0296] S71: Case 2: When k = k d+1 , which is the event-triggered moment, we can see from the error system that e(k) = 0; therefore:

[0297] S72:

[0298] S73: Case N-1: when k = k d+N-1 This is the event-triggering moment; similar to Case 2, we can get

[0299]

[0300] S74: Case N: when k ∈ [k d +N, k d +N+1), we can get

[0301]

[0302] S75: According to Lemma 2:

[0303] For the event-triggering tuning parameter σ(0, 1), if there exists a matrix and the matrix Y has appropriate dimensions and satisfies the condition:

[0304]

[0305] then the system is asymptotically stable; where

[0306] S76: Based on the IT2 T-S fuzzy system under DoS attacks, the following Lyapunov function is constructed:

[0307]

[0308] According to the fuzzy system and the event-triggering mechanism, the difference of V k is taken, we can get

[0309] ΔV k = V k+1 -V k

[0310]

[0311] where,

[0312]

[0313]

[0314]

[0315]

[0316] S77: From the above formula,

[0317]

[0318] then AV k <0, define and

[0319] Multiply both sides of the inequality by H -1 , it becomes a linear matrix inequality, according to Lyapunov stability theory, when the inequality satisfies the condition , the IT2 T-S fuzzy cloud control system is asymptotically stable under the proposed switching control strategy.

Claims

1. A Denial of Service (DoS) oriented cloud control system fuzzy modeling and event-triggered prediction method, characterized in that, Comprising the following steps: S1: Monitor the complex information transmission and other conditions in the cloud control network system framework, and establish a cloud control system differential equation described by an interval type-2 (IT2) T-S fuzzy model as a description language; S2: Use the type-2 fuzzy set theory and time zone segmentation analysis method to statistically, classify and linearize the system state before and after the DoS attack, and give the attack model and regional parameters; S3: Based on the on-demand control idea, a dynamic event-triggered mechanism with exponential decay characteristics is designed to reduce data transmission and improve bandwidth and energy utilization; S4: A fuzzy event-based model predictive controller (MPC) is proposed, and a prediction model, performance index and constraint condition are established; S5: A switching control law and fuzzy optimization algorithm are constructed to obtain the optimal parameters; S6: The prediction stability of the interval type-2 T-S fuzzy system is ensured, and the uncertainty with DoS attack is handled, realizing time zone modeling and on-demand control.

2. The method of claim 1, wherein the IT2T-S fuzzy model is a fuzzy system model capable of handling uncertainty and strong nonlinearity, characterized in that: In step S1, S11: The fuzzy rules of the IT2 T-S fuzzy model can be described as: System rule i: if f1(x(k)) is … and f g (x(k))) is then x(k+1)=Ax(k)+Bu(k) where x(k) e R n is the state vector; u(k) e R n is the control input vector; A is the system matrix; S12: After single-point fuzzification, multiplication reasoning, and weighted average defuzzification, the global IT2 T-S fuzzy cloud control system on the given domain can be obtained as: where S13: weighting coefficient c i (α(k)) and are two nonlinear functions, which can be adjusted online according to the change of uncertain parameters, satisfying S14: Based on the interval type-2 fuzzy set, the upper and lower membership functions can effectively capture the parameter uncertainty in the model, and can be adjusted appropriately according to the dynamic characteristics; on the contrary, c i (α(k)) and depending on the uncertain parameters in the actual system.

3. The method of claim 1, wherein the IT2 T-S fuzzy model is a fuzzy system model capable of handling uncertainty and strong nonlinearity, and is characterized in that: In step S2, S21: Based on the time zone modeling method, we consider the nth cycle attack model of DoS attack as follows: k∈[(n-1)T+1,nT] where T e Z + denotes the duration of one cycle, including the working period and the sleep period: Attack time is: ((n-1)T + t off , nT) Sleep time is: ((n-1)T+1, (n-1)T+t off ) where t off ∈ Z + , t off < T denotes the duration of the dormancy period; S22: σ(k)∈{1,2} represents different periods in the nth cycle, and σ(k) represents: where σ(k)=1 and σ(k)=2 represent the sleep period and attack period of the nth cycle, respectively; S23: In the sleep period, the DoS generator remains silent to replenish energy, and the data packet loss caused by the inherent factors of the wireless channel is considered; in the attack period, the DoS generator initiates continuous DoS interference attack, reducing the communication quality of the wireless measurement channel; Combined with the attack strategy of the DoS jammer, θ(σ(k),k)∈{0,1} represents whether the controller successfully receives the data packet at time k: S24: For the cloud control system under DoS interference attack, considering the attack strategy of the DoS jammer and the inherent data packet loss of the measurement channel, the probability of the controller successfully receiving the data packet can be represented as: where a σ(k) ∈ [0, 1) is a known constant.

4. The method of claim 1, wherein the IT2 T-S fuzzy model is a fuzzy system model capable of handling uncertainty and strong nonlinearity, and is characterized in that: In step S3, S31 : First, consider the definition of the error e(k) which represents the error between the actual output x(k) of the system and the desired output where is a time delay parameter. Typically, the time delay parameter is considered as a fixed value; S32: Considering that the time lag will decay along with the advancement of the control process, an exponential decay function is adopted to define S33: Based on the above, we define the system actual output and expected output error model as: S34: when k = k d , the value of the exponential decay function is 1, i.e. equals 1, the time lag is 0, i.e. no delay effect; S35: when k > k d , the value of the exponential decay function is less than 1, indicating that the time delay factor is gradually reduced, and the time lag effect is gradually weakened over time; S36: The modeling of the error e(k) takes into account the difference between the actual output x(k) and the desired output and introduces a time delay factor through an exponential decay function making the model better capture the characteristics of the delay effect changing over time; S37: Based on the above state error model, the exponential dynamic event-triggered mechanism is as follows: S38: t k+1 = in f{{k > k d |η(k)+θ(σ||x(k)|| Φ -||e(k)|| Φ )≤0} where η(k) is a dynamic variable with an update rate of: S39: η(k + 1) = μ·e(k) + σ||x(k)| φ -||e(k)| φ where σ∈(0,1);θ>1;Φ is a positive definite symmetric matrix; k∈N is the current sampling time; η(k) is a dynamic term of the dynamic event triggering mechanism, S40: According to Lemma 1: If And θ satisfies the dynamic event triggering mechanism, then the auxiliary offset variable satisfies η(k)≥0; the interval between two adjacent event triggers [k d , k d+1 The upper bound of (i∈1,2,3,…) is denoted as M, and M∈Z + .

5. The method of claim 1, wherein the IT2 T-S fuzzy model is a fuzzy system model capable of handling uncertainty and strong nonlinearity, and is characterized in that: In step S4 according to the optimal control theory, S41: The optimization method of quadratic programming is used, and the optimization index is: min J = min Z T QZ + C T Z where Z T QZ is quadratic, C T Z is linear. If Q is diagonal, i.e. then the problem is a least squares problem; S42: define initial conditions as: x(k|k) = x k ; x(k+1|k) = Ax(k|k) + Bu(k|k) = Ax k + Bu(k|k); Recursion can be obtained as: x(k + N \ k) = A N x k +A N-1 Bu(k \ k) +... + Bu(k + N - 1 \ k) S43: The matrix obtained by recursion is represented as: then X k = Mx k + CU k where x k is the initial state, and 0 in C represents a zero matrix. S45: Construct the model predictive controller, MPC solves the optimal control signal by solving the cost function J, the construction of the cost function is as follows: The prediction range of MPC control is denoted as N, and two positive definite weight matrices Q and R are given, and F is designed as the terminal weight parameter matrix of MPC; According to the optimal control theory, the performance index (cost function) is proposed as a function of the terminal state variable and the target value, i.e. J = h(x [N] , x d ) S46: By MPC prediction method, the state and input of each state and input, and the terminal state x(k+l|k), u(k+l|k) and x(k+N|k) are predicted; S47: The cost function is defined as follows: Where l=1, 2, …, N-1, S48: Let Then S49: Substitute X k = Mx k + CU k into the equation, eliminating the variable X k and simplifying: S50: Because J is a 1 x 1 matrix X k and U k are n x 1 matrices, and are n x n matrices, then J T = J Since matrices and are transposes of each other and are both numeric, the numeric values are equal, i.e.: Let Then 6. The DoS attack-oriented cloud control system fuzzy modeling and event-triggered prediction method according to claim 1, the IT2 T-S fuzzy model is a fuzzy system model capable of handling uncertainty and strong nonlinearity, characterized in that: The switching controller in step S5 is designed as follows: Controller A: When σ(k)=2 S51: Considering the system dynamic characteristics and optimal performance index, the optimal control method is used to obtain the optimal control sequence: Optimize the control input for the next N steps; S52: When the event condition is met, the event is triggered, considering the current time k d and the optimal control sequence U * , the first control amount u(k) is selected as the control input at the current time, and the optimal control sequence U * The control input of the system can be quickly updated to respond to the occurrence of the event and restore the system performance as soon as possible, that is: S53: When an event occurs in the system that requires a quick response, according to the current time k d and the pre-computed optimal control sequence U * select the first control quantity in the sequence as the control input at the current time, so that the occurrence of the event can be quickly responded to, and the pre-computed optimal control sequence is used to control the system to recover the system performance as soon as possible and compensate for the data loss caused by the DoS attack; Controller B: When σ(k)=1 S54: When the DoS jammer is in a dormant state, the control strategy switches to the feasibility control: S55: When there is no DoS attack affecting the system, the system uses the feasibility control strategy, and the control input controller sequence is calculated in real time by solving the feedback control gain K. The controller sequence switching system refers to the system switching according to the actual situation of the network in a specific order, and the controller sequence switching is performed according to the DoS attack switching identifier σ(k) and the dynamic event-triggered time sequence; S56: Considering the time zone non-periodic characteristics of DoS attacks, the following switching controller is proposed based on the on-demand control idea: where u(k) = u * (k + 1 | k d ) is the control input at time k; K is the control gain matrix, σ(k) = 2, indicating that the DoS jammer is in the active period; σ(k) = 1, indicating that the DoS jammer is in the dormant period; denotes the control input at time k, whose value depends on the state estimation value.

7. The method of claim 1, wherein the IT2 T-S fuzzy model is a fuzzy system model capable of handling uncertainty and strong nonlinearity, and is characterized in that, In step S6: S61: Based on the method proposed above, the asymptotic stability of the IT2 T-S fuzzy cloud control system under the switching control strategy proposed is proved: Controller A: When σ(k)=2 S62: The Lyapunov function is constructed as follows: V k =J k +η k S63: Taking the difference of it can be obtained: S64: According to the dynamic event-triggered mechanism, we can get: S65: By the definition of η(k) above, we can obtain (1 - μ) and all belong to the range of (0, 1). Since we can obtain σ|x(k)| Φ + (1 - μ) η(k) ≤ |e(k)| Φ and further we can obtain: S66: For the cost function before, we make an assumption, assuming that the terminal cost function satisfies: where x k ∈ X f ; S67: Combine the assumption with the Lyapunov function to get: S68: Since μ∈(0, 1) and according to Lemma 1, we can get: S69: According to the Lyapunov stability theory, under the MPC control strategy in this paper, the IT2 T-S fuzzy cloud control system can guarantee the stability of the system under DoS attack; Controller B: When σ(k)=1: S70: Case 1: when k ∈ [k d , k d +1) can be obtained: S71 : Case 2: when k = k d+1 This is the event-triggering moment, from the error system, we can see that e(k) = 0; therefore: S72： S73: Case N-1: when k = k d+N-1 This is the event-triggering moment; similar to Case 2, we have: S74: Case N: when k∈[k d +N, k d +N+1), we have: S75: According to Lemma 2: For event-triggered tuning parameters σ(0,1), if there exists a matrix and matrix Y has appropriate dimensions and satisfies the condition: then the system is asymptotically stable; where S76: Based on the IT2 T-S fuzzy system under DoS attack, the following Lyapunov function is constructed: According to the fuzzy system and event triggering mechanism, the V k Performing the difference, we can get wherein, S77: From the above formula, ΔV = V - V k <0, defined and Multiplying both sides of the inequality by H -1 , it becomes a linear matrix inequality. According to Lyapunov stability theory, the inequality is satisfied when the matrix inequality The IT2 T-S fuzzy cloud control system is asymptotically stable under the proposed switching control strategy.

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