A design method for event-triggered DOFF quantized controller under deception attack

Abstract

The present invention discloses a design method of an event-triggered DOFF quantized controller under a deception attack, comprising the following steps: A: establishing a T-S fuzzy object model, a discrete event trigger model and a logarithmic quantizer model; B: establishing a deception attack model and a DOFF quantized controller model, and establishing a closed-loop T-S fuzzy system augmented model that organically integrates deception attacks, discrete event triggers, logarithmic quantizers and network-induced delay parameters; C: designing design conditions for a DOFF quantized controller that organically integrates deception attacks, discrete event triggers, logarithmic quantizers and network-induced delay parameters, finding a positive definite matrix and a gain matrix, and using threshold parameters to obtain a DOFF quantized controller suitable for a T-S fuzzy system under the influence of deception attacks and event triggers. The present invention can solve the problem that the existing T-S fuzzy system cannot be stabilized under the influence of deception attacks, data quantization and network-induced delays.

Description

Technical Field

[0001] The present invention relates to the field of networked control systems, and in particular to a design method for an event-triggered dynamic output feedback fuzzy (DOFF) quantized controller of a TS (Takagi-Sugeno) fuzzy system under a deception attack. Background Art

[0002] Networked control systems introduce shared communication networks into the control loop, which have the advantages of high flexibility, low cost, and easy installation and maintenance. They are widely used in smart grids, smart transportation and other fields. Networked control systems usually adopt mature periodic sampling control strategies. In order to ensure system performance in the worst case, the sampling rate is usually set high. However, the worst case rarely occurs in practice. The large amount of redundant data generated by the high sampling rate leads to the waste of system limited resources such as network bandwidth, which greatly affects the system performance.

[0003] Unlike the periodic control strategy that ignores system dynamics and performs on-time control, the event-triggered control strategy performs on-demand control only when the system dynamics meet the event triggering conditions, thereby saving system-limited resources such as network bandwidth. However, existing event triggers usually use a continuous-time event trigger mechanism, which requires the addition of dedicated monitoring hardware and complex preliminary calculations to avoid the Zeno phenomenon (i.e., infinitely many trigger samplings in a finite time).

[0004] Although shared communication networks have brought many conveniences to networked control systems, they have also introduced network-induced delays that deteriorate system performance and expose the system to the threat of network attacks. Network attacks are roughly divided into denial of service attacks and spoofing attacks. Denial of service attacks block communication networks so that data packets cannot be delivered; spoofing attacks generate false data packets by tampering with data. Spoofing attacks are highly concealed and harmful, and are the type of attacks studied in this invention. However, existing results focus on how to design event trigger mechanisms to save more system resources, and rarely consider the effects of spoofing attacks and network-induced delays at the same time. In addition, existing event-triggered control system analysis and synthesis methods usually assume that there is no attack threat. Such methods are usually not directly applicable to the analysis of event-triggered control systems under the influence of spoofing attacks. In addition, existing results focus more on linear systems, but less on nonlinear systems. TS fuzzy system is an important model for describing nonlinear systems.

[0005] With the popularization of digital communication networks, data transmission in networked control systems needs to be quantized. Although data quantization helps to efficiently utilize network bandwidth, quantization errors usually lead to deterioration of system performance. However, existing results rarely consider the impact of data quantization and deception attacks at the same time. In addition, existing results usually assume that the system state is fully measurable and design state feedback controllers, but in practice the system state cannot usually be directly obtained.

[0006] In order to solve the above problems, the present invention proposes an event-triggered DOFF quantized controller design method for TS fuzzy systems under deception attacks, taking into account the effects of deception attacks, data quantization, network-induced delays and the inability to measure the object state. Summary of the invention

[0007] The purpose of the present invention is to provide a design method for an event-triggered DOFF quantization controller under deception attacks, which can solve the problem that the existing TS fuzzy system cannot be stabilized under the influence of deception attacks, data quantization and network induced delays, and effectively save system limited resources such as network bandwidth, and can remove the assumption that the system state is completely measurable.

[0008] The present invention adopts the following technical solutions:

[0009] A method for designing an event-triggered DOFF quantization controller under a deception attack, characterized in that it comprises the following steps:

[0010] A: Establish TS fuzzy object model, discrete event trigger model and logarithmic quantizer model;

[0011] B: Establish a deception attack model and a DOFF quantization controller model, and establish a closed-loop TS fuzzy system augmented model that organically integrates deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters;

[0012] C: Design the design conditions of the DOFF quantized controller that organically integrates the deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters, and find the positive definite matrix Ω of the discrete event trigger and the gain matrix of the equivalent DOFF quantized controller By using the discrete event trigger threshold parameter δ, a DOFF quantized controller suitable for TS fuzzy systems under the influence of deception attacks and event triggers is finally obtained.

[0013] In the step A, the TS fuzzy object model is:

[0014]

[0015] In the formula, is the derivative of x(t), x(t) represents the object state, x(t) is an n-dimensional real number, u(t) represents the control input, and u(t) is n u dimensional real number, y(t) represents the measured output, y(t) is n y dimensional real number, t represents time, A i ,B i and C i represents the gain matrix; r is the number of object fuzzy rules, i represents the sequence number of object fuzzy rules, and the substitution formula and

[0016] θ1(t), and θ g (t) represents the first and The first and gth antecedent variables, g represents the number of antecedent variables, Indicates the sequence number of the antecedent variable, Represents the antecedent variable Belongs to fuzzy sets The membership function of , ∑ and Π represent the accumulation and multiplication operations respectively.

[0017] In step A, the discrete event trigger model is:

[0018]

[0019] Where δ∈(0,1) is the trigger threshold parameter, Ω>0 is a positive definite matrix, h represents the sampling period, and t k h represents the kth triggering moment, t k h is the sampling period t k times, t k+1 h represents the k+1th triggering moment, t k+1 h is the sampling period t k+1 times, the subscript k indicates the triggering time sequence number; Indicates the current sampling time. t k h after Sampling period, y(t k h) and Respectively represent t k h and The corresponding object measurement output, min{·} represents the minimum function, and ||·|| represents the Euclidean norm.

[0020] In step A, the logarithmic quantizer model is:

[0021]

[0022] Among them, f1(y1(tk h))、 and They represent y1(t k h), and The corresponding quantized value, y1(t k h), and They represent y(t k,n h)’s first dimension, Peacekeeping y dimensional data, col{} represents a column matrix;

[0023] The logarithmic quantizer model expressed in the form of fan-shaped boundaries is further obtained as:

[0024] f(y(t k h))=(1+Δ)y(t k h);

[0025] Among them, the quantizer diagonal matrix Δ1 and Represents the first dimension and the nth dimension respectively y The diagonal elements corresponding to the dimensional quantization model, Δ satisfies -σI≤Δ≤σI, the substitution formula σ=(1-ρ) / (1+ρ), I is the unit matrix, ρ∈(0,1) represents the quantization density, and diag{} represents the diagonal matrix.

[0026] In step B, the deception attack model is:

[0027]

[0028] in, represents the deception attack function, b(t)∈{0,1} represents the Bernoulli distribution random variable. When b(t)=1, the deception attack is activated and the controller input is tampered with, that is, When b(t) = 0, the spoofing attack is in a dormant state and the controller input has not been tampered with, i.e. is the DOFF quantized controller input under attack influence, is the DOFF quantized controller input under no attack.

[0029] In step B, the DOFF quantization controller model is:

[0030]

[0031] In the formula, For x c The derivative of (t), x c (t) represents the controller state, x c(t) is an n-dimensional real number, x c (t-η(t)) represents the controller state corresponding to t-η(t), and is the gain matrix; the number of fuzzy rules of the controller is r, j = 1, ..., r represents the serial number of the fuzzy rules of the controller, the substitution formula and Represents the antecedent variable Belongs to fuzzy sets The membership function of Indicates the sub-interval division.

[0032] In the step B, the closed-loop TS fuzzy system augmented model that organically integrates deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameter is:

[0033]

[0034] In the formula, is the derivative of χ(t), represents the state of the closed-loop system, χ(t-η(t)) represents the state of the closed-loop system corresponding to t-η(t), and represents the closed-loop system gain matrix, e(t)=y(t k h)-y(t k h+(n k -1)h),y(t k h+(n k -1)h) represents the sampling time t k h+(n k -1)h corresponding to the object measurement output.

[0035] The step C comprises the following specific steps:

[0036] C1: Based on Lyapunov stability theory, determine the asymptotic stability conditions of the system under the influence of spoofing attacks, discrete event triggers, logarithmic quantizers and network-induced delays;

[0037] C2: Based on the asymptotic stability condition of the system obtained in step C1, use the linear matrix inequality technique to find the positive definite matrix Ω of the discrete event trigger and the gain matrix of the equivalent DOFF quantized controller By using the discrete event trigger threshold parameter δ, a DOFF quantized controller suitable for TS fuzzy systems under the influence of deception attacks and event triggers is finally obtained.

[0038] The asymptotic stability conditions of the system under the influence of the deception attack, discrete event trigger, logarithmic quantizer and network-induced delay are:

[0039] Given a sampling period h, the lower bound of network-induced delay is and upper bound Logarithm of the quantizer diagonal matrix Δ, attack energy limit matrix F and event trigger threshold parameter δ∈(0,1), if there exists a positive definite matrix Ω>0, P>0, R>0, S>0, Q1>0, Q2>0, Q3>0, and matrices U2, U3, satisfying the following equation:

[0040]

[0041] Then the TS fuzzy system under the influence of deception attack, discrete event trigger, logarithmic quantizer and network induced delay is asymptotically stable;

[0042] In the above stability conditions, the substitution formula used is as follows:

[0043]

[0044] Π 21 =col{η 10 Λ1,η 21 Λ1,η 32 Λ1},Π 31 =col{η 10 Λ2,η 21 Λ2,η 32 Λ2},Π 41 =col{Λ3,Λ4},

[0045]

[0046]

[0047] Λ3=C i E1e3+e6,Λ4=F(1+Δ)Λ3,

[0048]

[0049] η 10 =η1-η0,η 21 =η2-η1,η 32 =η3-η2,η0=0, η2=0.5(η3+η1),

[0050] He{} represents the sum of a matrix and its transposed matrix, * represents the symmetric term in a symmetric matrix, Represents the zero matrix, and the -1 in the upper right corner of the matrix represents the inverse matrix. represents the mathematical expectation of b(t), is the mathematical expectation function.

[0051] The design conditions of the DOFF quantization controller are:

[0052] Given a sampling period h, the lower bound of network-induced delay is and upper bound Logarithmic quantizer quantization density ρ and real number ∈>0, attack energy limit matrix F and event trigger threshold parameter δ∈(0,1), if there exists a positive definite matrix Ω>0, and matrix satisfy

[0053]

[0054] Then the TS fuzzy system is asymptotically stable, and the equivalent DOFF quantized controller is obtained as follows:

[0055]

[0056] In the formula, represents the equivalent DOFF quantized controller state, is an n-dimensional real number, for The derivative of It represents the equivalent DOFF quantized controller state corresponding to t-η(t), and its gain matrix Obtained by the following formula:

[0057]

[0058] In the above controller design conditions, the substitution formula used is as follows

[0059]

[0060] Π 55 =diag{-∈σ 2 ,-∈},

[0061]

[0062] Ψ1=diag{Φ1,Φ1},

[0063] X>0,Y>0 is a positive definite matrix, and N is an n×n dimensional real matrix.

[0064] The present invention can solve the problem that the existing TS fuzzy system cannot be stabilized under the influence of deception attacks, data quantization and network-induced delays, and effectively saves system limited resources such as network bandwidth, and can remove the assumption that the system state is completely measurable. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a schematic diagram of the TS fuzzy system event trigger output feedback control under a deception attack in the present invention;

[0066] Figure 2 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0067] The present invention is described in detail below with reference to the accompanying drawings and embodiments:

[0068] Event-triggered output feedback control of TS fuzzy system under deception attack Figure 1 As shown in the figure, the sensor samples the measured output of the TS fuzzy object periodically, and the sensor sampling data is sent to the discrete event trigger. The discrete event trigger determines whether the trigger condition is met: if it is met, the sampling data is sent; otherwise, the sampling data is discarded. The quantizer quantizes the data sent by the discrete event trigger, and the quantized data is sent to the zero-order holder via the communication network. The communication network is affected by the spoofing attack. The DOFF quantization controller receives the zero-order holder data and calculates the control signal. The actuator adjusts the state of the TS fuzzy object according to the control signal.

[0069] like Figure 2 As shown, the design method of the event-triggered DOFF quantization controller under a deception attack of the present invention comprises the following steps in sequence:

[0070] A: Establish TS fuzzy object model, discrete event trigger model and logarithmic quantizer model;

[0071] When building a TS fuzzy object model:

[0072] Assume that the i-th fuzzy rule of the TS fuzzy object model is: if θ1(t) is for M ig ,but

[0073]

[0074] Among them, x(t) represents the state of the object, x(t) is an n-dimensional real number, is the derivative of x(t), u(t) represents the control input, and u(t) is n u dimensional real number, y(t) represents the measured output, y(t) is n y dimensional real number, t represents time, A i ,B i and C irepresents the gain matrix; r is the number of object fuzzy rules, i represents the sequence number of object fuzzy rules, θ1(t), and θ g (t) represents the first and The first and gth antecedent variables, g represents the number of antecedent variables, Indicates the sequence number of the antecedent variable, M i1 , and M ig They represent the first and the second fuzzy rules of the object i respectively. the gth and gth fuzzy sets;

[0075] Using product fuzzy reasoning, central average defuzzifier and single point fuzzifier, the TS fuzzy object model is obtained from (1):

[0076]

[0077] In the formula, the substitution formula and Represents the antecedent variable Belongs to fuzzy sets The membership function of , ∑ and Π represent the accumulation and multiplication operations respectively.

[0078] When modeling discrete event triggers:

[0079] Based on the measurement output of the TS fuzzy object, the discrete event trigger model is established as:

[0080]

[0081] Where δ∈(0,1) is the trigger threshold parameter, Ω>0 is a positive definite matrix, h represents the sampling period, t k h represents the kth triggering moment, t k h is the sampling period t k times, t k+1 h represents the k+1th triggering moment, t k+1 h is the sampling period t k+1 times, the subscript k indicates the triggering time sequence number; Indicates the current sampling time. t k h after Sampling period, y(t k h) and Respectively represent t k h and The corresponding object measurement output, min{·} represents the minimum function, and ||·|| represents the Euclidean norm.

[0082] In the present invention, the discrete event trigger judges the trigger condition in formula (3) at each periodic sampling point. If the trigger condition is met, the current sampled data is sent; if the trigger condition is not met, the current sampled data is discarded. Therefore, the discrete event trigger only sends the sampled data that meets the trigger condition, thereby saving system limited resources such as network bandwidth. In addition, the discrete event trigger only uses the periodic sampled data output by the object measurement, which is easy to implement in software, avoids the Zeno phenomenon in principle, and removes the assumption that the object state is completely measurable in most results.

[0083] When building a logarithmic quantizer model:

[0084] Assume that the logarithmic quantizer The dimension quantization model is:

[0085]

[0086] In the formula, represents y(t k h) Dimensional data, represents y(t k h) dimension number, express The corresponding quantized value; when and hour, The corresponding quantization value is Indicates Quantization level, is the quantization level number, ρ∈(0,1) represents the quantization density, Represents ρ Power, quantization level parameter g 0 >0; when hour, The corresponding quantization value is when hour, The corresponding quantization value is express The corresponding quantized value The opposite number of .

[0087] Using (4), we build the logarithmic quantizer model f(y(t k h)) is:

[0088]

[0089] In the formula, f1(y1(t k h)) and They represent y1(t k h) and The corresponding quantized value, y1(t k h) and They represent y(t k h) the first and nth dimensions y dimensional data, col{} represents a column matrix.

[0090] Using (5), we get the logarithmic quantizer model expressed in the form of a sector boundary as follows:

[0091] f(y(t k h))=(1+Δ)y(t k h) (6);

[0092] In the formula, the quantizer diagonal matrix Δ1 and Represents the first dimension and the nth dimension respectively y The diagonal elements corresponding to the dimensional quantization model, Δ satisfies -σI≤Δ≤σI, the substitution formula σ=(1-ρ) / (1+ρ), I is the unit matrix, and diag{} represents the diagonal matrix.

[0093] B: Establish a deception attack model and a DOFF quantization controller model, and establish a closed-loop TS fuzzy system augmented model that organically integrates deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters;

[0094] First, without considering the influence of deception attack, under the action of logarithmic quantizer and zero-order holder, the DOFF quantization controller input Expressed as

[0095] t∈[t k h+τ k ,t k+1 h+τ k+1 ) (7);

[0096] In the formula, [t k h+τ k ,t k+1 h+τ k+1 ) represents the zero-order holder holding time, and Respectively represent t k h and t k+1 h corresponds to the network-induced delay, and denote the lower and upper bounds of the network induced delay, respectively.

[0097] The zero-order hold time is divided as follows

[0098]

[0099] Where n k Indicates the sub-interval number, N k n k Maximum value, ∪ is the union symbol, dividing the subinterval It is expressed as follows

[0100]

[0101] In the sub-interval On the surface, define the functions e(t) and η(t) as follows

[0102] e(t)=y(t k h)-y(t k h+(n k -1)h),η(t)=t-(t k h+(n k -1)h)(9);

[0103] In the formula, y(t k h+(n k -1)h) represents the sampling time t k h+(n k -1)h corresponding to the object measurement output.

[0104] Using (9), the DOFF quantized controller input in (7) without attack is expressed as:

[0105]

[0106] In the formula, y(t-η(t)) represents the object measurement output corresponding to time t-η(t), and from (9) we can get t-η(t)=t k h+(n k -1)h;

[0107] Then, considering the influence of the deception attack, the DOFF quantization controller input under the influence of the attack is obtained from (10): as follows:

[0108]

[0109] In the formula, represents the deception attack model, where represents the deception attack function, b(t)∈{0,1} represents the Bernoulli distribution random variable. When b(t)=1, the deception attack is activated and the controller input is tampered with, that is, When b(t) = 0, the spoofing attack is in a dormant state and the controller input has not been tampered with, i.e.

[0110] Consider the case where the attack energy is limited. Satisfy the following formula

[0111]

[0112] Where F is the attack energy limiting matrix, and the upper right subscript T represents the transpose of the matrix.

[0113] The DOFF quantized controller model is established as:

[0114] Assume that the jth fuzzy rule of the controller is: If θ1(t) is for M jg ,but

[0115]

[0116] In the formula, For x c The derivative of (t), x c (t) represents the controller state, x c (t) is an n-dimensional real number, x c (t-η(t)) represents the controller state corresponding to t-η(t), and is the gain matrix; the number of controller fuzzy rules is r, j = 1,..., r represents the controller fuzzy rule sequence number, M j1 , and M jg They represent the first and the second fuzzy rules of the controller respectively. The first and gth fuzzy sets.

[0117] Using product fuzzy reasoning, central average defuzzifier and single-point fuzzifier, the DOFF quantized controller model is obtained from (13) as follows:

[0118]

[0119] In the formula, the substitution formula and Represents the antecedent variable Belongs to fuzzy sets The membership function of .

[0120] In summary, the TS fuzzy object model (2) and the DOFF quantized controller model (14) are combined to establish the augmented model of the closed-loop TS fuzzy system as follows:

[0121]

[0122] In the formula, Indicates the closed-loop system status, is the derivative of χ(t), χ(t-η(t)) represents the closed-loop system state corresponding to t-η(t), and represents the closed-loop system gain matrix.

[0123] C: Design the design conditions of the DOFF quantized controller that organically integrates the deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters, and find the positive definite matrix Ω of the discrete event trigger and the gain matrix of the equivalent DOFF quantized controller By using the discrete event trigger threshold parameter δ, a DOFF quantized controller suitable for TS fuzzy systems under the influence of deception attacks and event triggers is finally obtained.

[0124] The step C comprises the following two specific steps:

[0125] C1: Based on Lyapunov stability theory, determine the asymptotic stability conditions of the system under the influence of spoofing attacks, discrete event triggers, logarithmic quantizers and network-induced delays.

[0126] Given a sampling period h, the lower bound of network-induced delay is and upper bound Logarithm of the quantizer diagonal matrix Δ, attack energy limit matrix F and event trigger threshold parameter δ∈(0,1), if there exists a positive definite matrix Ω>0, P>0, R>0, S>0, Q1>0, Q2>0, Q3>0, and matrices U2, U3, satisfying the following equation:

[0127]

[0128]

[0129] Then, the TS fuzzy system (15) under the influence of deception attack, discrete event trigger, logarithmic quantizer and network induced delay is asymptotically stable.

[0130] In the above stability conditions, the substitution formula used is as follows:

[0131]

[0132] Π 21 =col{η 10 Λ1,η 21 Λ1,η 32 Λ1},Π 31 =col{η 10 Λ2,η 21 Λ2,η 32 Λ2},Π 41 =col{Λ3,Λ4},

[0133]

[0134]

[0135] Π 44 =diag{-δ -1 Ω -1 ,-I},

[0136] Λ3=C i E1e3+e6,Λ4=F(1+Δ)Λ3,

[0137]

[0138] η 10 =η1-η0,η 21 =η2-η1,η 32 =η3-η2,η0=0, η2=0.5(η3+η1),

[0139] He{} represents the sum of a matrix and its transposed matrix, * represents the symmetric term in a symmetric matrix, Represents the zero matrix, and the -1 in the upper right corner of the matrix represents the inverse matrix. represents the mathematical expectation of b(t), is the mathematical expectation function.

[0140] Proof: Construct the Lyapunov functional as follows

[0141]

[0142] In the formula, replace the formula ζ(s)=col{χ(s-η1),χ(s-η2)}, ρ=0.5(η3-η1), represents the integral variable, χ(s), χ(s-η1) and χ(s-η2) represent the closed-loop system states corresponding to s, s-η1 and s-η2 respectively. represents the derivative of χ(s).

[0143] Taking the derivative of the Lyapunov functional, we get

[0144]

[0145] In the formula, represents the derivative of V(t), and They represent the substitutions corresponding to t and t-ρ respectively. χ(t-η1) represents the closed-loop system state corresponding to t-η1, and the substitution equations ζ1, ζ2, and ζ3 are expressed as follows:

[0146]

[0147] In the formula, Represents the integral variable The corresponding closed-loop system state derivative.

[0148] Consider the following two cases:

[0149] (1) If v(t)∈[η1,η2), use the Jensen inequality for ζ1,ζ2,ζ3 in (20) and the condition in (16) Further using the mutual convex method on ζ2, we get

[0150]

[0151] In the formula, the substitution equations ε1 = [χ(t-η1) - χ(t-η(t))] and ε2 = [χ(t-η(t)) - χ(t-η2)], χ(t-η2) and χ(t-η3) represent the closed-loop system states corresponding to t-η2 and t-η3, respectively.

[0152] (2) If η(t)∈[η2,η3], use the Jensen inequality for ζ1,ζ2,ζ3 in (20) and the condition in (16) Further using the mutual convex method on ζ3, we get

[0153]

[0154] In the formula, the alternative formulas ε3=[χ(t-η2)-χ(t-η(t))] and ε4=[χ(t-η(t))-χ(t-η3)] are used.

[0155] Using (21) and (22), we can find the mathematical expectation of the Lyapunov functional derivative (19) and obtain

[0156]

[0157] In the formula, the substitution formula

[0158] Using (9), we can get from the discrete event trigger (3) and the attack energy constraint (12):

[0159]

[0160] Using (24), we can get from (23)

[0161]

[0162] In the formula, the following substitution is used:

[0163]

[0164] Using Schur's complement lemma on (17) we get

[0165]

[0166] Substituting (26) into (25), we obtain According to Lyapunov stability theory, TS fuzzy system (15) is asymptotically stable. Proof.

[0167] In the above asymptotic stability condition of TS fuzzy system, the DOFF quantized controller gain matrix is Coupled with the positive definite matrix P, it cannot be directly used for controller design. Therefore, the present invention will further provide a DOFF quantization controller design method.

[0168] C2: Based on the asymptotic stability condition of the system obtained in step C1, use the linear matrix inequality technique to find the positive definite matrix Ω of the discrete event trigger and the gain matrix of the equivalent DOFF quantized controller By using the discrete event trigger threshold parameter δ, a DOFF quantized controller suitable for TS fuzzy systems under the influence of deception attacks and event triggers is finally obtained.

[0169] First, the prior art (Theorem 1 and Theorem 2) used in step C2 is given as follows:

[0170] Theorem 1. Given a real number ∈>0, the symmetric matrix matrix and If and only if the inequality When the inequality holds, Established, where the function satisfy

[0171] Theorem 2. Given a positive definite matrix Q>0 and a matrix G, the inequality (GQ)Q -1 (GQ)≥0 holds, that is, the inequality -GQ - 1 G≤Q-2G holds.

[0172] Then, the design conditions of the DOFF quantization controller are given as follows:

[0173] Given a sampling period h, the lower bound of network-induced delay is and upper bound Logarithmic quantizer quantization density ρ and real number ∈>0, attack energy limit matrix F and event trigger threshold parameter δ∈(0,1), if there exists a positive definite matrix Ω>0, and matrix satisfy

[0174]

[0175]

[0176] Then the TS fuzzy system (15) is asymptotically stable, and the equivalent DOFF quantized controller is obtained as follows:

[0177]

[0178] In the formula, represents the equivalent DOFF quantized controller state, is an n-dimensional real number, for The derivative of It represents the equivalent DOFF quantized controller state corresponding to t-η(t), and its gain matrix Obtained by the following formula

[0179]

[0180] In the above controller design conditions, the substitution formula used is as follows

[0181]

[0182] Π 55 =diag{-∈σ 2 ,-∈},

[0183] Ψ1=diag{Φ1,Φ1},

[0184] X>0,Y>0 is a positive definite matrix, and N is an n×n dimensional real matrix.

[0185] Proof: Decompose the positive definite matrix P as follows

[0186]

[0187] In the formula, X>0, Y>0 is a positive definite matrix, and N is an n×n dimensional real matrix. According to Schur's complement lemma, the positive definite matrix P>0 is equivalent to

[0188] Define the matrix as follows

[0189]

[0190] Define the matrices Ψ2 = diag{Φ1,Φ1,Φ1,Φ1,φ1,I,I,Ψ3,I,I}, Ψ3 = diag{Φ2,Φ2,Φ2,Φ2,Φ2,φ2}, ψ1 = diag{φ1,Φ1}, and transform the system stability conditions (16) and (17) as follows

[0191]

[0192]

[0193] In the formula, the following substitutions are used:

[0194]

[0195] Applying Theorem 1 to (34), we obtain the following equation:

[0196]

[0197] Apply Schur's complement lemma to (36) and middle and Π 44 Using Theorem 2, we obtain condition (28).

[0198] Therefore, if the given conditions are met, the TS fuzzy system (15) is asymptotically stable, and the gain matrix of the DOFF quantization controller (14) is obtained as follows:

[0199]

[0200] In order to deal with the unknown matrix N in (37), a linear transformation is used The equivalent DOFF quantized controller (29) is obtained, whose gain matrix is From (30), we get . The proof is complete.

[0201] Through the event-triggered DOFF quantitative controller design method under deception attack described in the present invention, the user can determine each parameter one by one in combination with specific design requirements, and obtain the event-triggered DOFF quantitative controller under deception attack according to the steps, so that the TS fuzzy system can be asymptotically stable under the influence of deception attack, discrete event trigger, logarithmic quantizer and network induced delay, that is, a method for designing an event-triggered DOFF quantitative controller under deception attack is provided.

[0202] Examples of application scenarios of the present invention: In recent years, network attacks on actual industrial control systems have occurred frequently. For the above scenarios, the relevant methods of the present invention are applied to model the centrifuge system and power system of the above nuclear power plant as TS fuzzy objects, design discrete event triggers and logarithmic quantizers, establish deception attack models, DOFF quantitative controller models, and closed-loop TS fuzzy system augmented models that organically integrate deception attacks, discrete event triggers, logarithmic quantizers, and network-induced delay parameters, derive the asymptotic stability conditions of the system, and provide a DOFF quantitative controller design method. The obtained DOFF quantitative controller can ensure the asymptotic stability of the TS fuzzy system, and the designed discrete event trigger can effectively save system-limited resources such as network bandwidth.

[0203] The present invention is described in detail below with reference to the embodiments:

[0204] Step A: Establish TS fuzzy object model and design discrete event triggers:

[0205] Among them, the TS fuzzy object takes the mass spring damping system as an example, and its dynamic equation is described as

[0206]

[0207] In the formula, represents the displacement from the reference point, and Respectively The first and second derivatives of , m is the mass, represents the friction force, represents the spring force, u(t) represents the control input, c, a is a real number. The parameter is set to m = 1 kg, c = 2 N·m / s, a=0.3 m -1 .

[0208] Defining object states Then the mass-spring-damper system (38) can be described as a TS fuzzy object (2), where μ1(θ(t))=-(θ1(t)+8) / 2.88, μ2(θ(t))=1-μ1(θ(t)), r=2,g=1, the gain matrix is ​​as follows:

[0209] C1=C2=[1 0].

[0210] Design a discrete event trigger:

[0211] Based on the periodic sampling value of the measured output of the TS fuzzy object, a discrete event trigger mechanism (3) is designed, where the trigger threshold parameter δ = 0.01, the sampling period h = 100 milliseconds, and the positive definite matrix Ω is obtained by solving the design conditions of the DOFF quantization controller in the subsequent step C2.

[0212] Establish the logarithmic quantizer model (4): where the quantization density ρ = 0.85 and the quantization level parameter g 0 =2.2, real number∈=0.95.

[0213] Step B: Establish a deception attack model and a DOFF quantization controller model, and establish a closed-loop TS fuzzy system augmented model that organically integrates deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters;

[0214] First, establish a deception attack model as

[0215] in, is the deception attack function, tanh represents the nonlinear hyperbolic tangent function, the Bernoulli distribution random variable b(t)∈{0,1}, and the mathematical expectation is The attack energy limiting matrix is ​​F=0.1 (a one-dimensional matrix is ​​equivalent to a real number).

[0216] Establish the DOFF quantized controller model (14).

[0217] A closed-loop TS fuzzy system augmented model (15) is established that organically integrates deception attacks, discrete event triggers, logarithmic quantizers, and network-induced delay parameters, where the lower bound of the network-induced delay is and upper bound

[0218] Step C: Design the design conditions of the DOFF quantized controller that organically integrates the deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters, and find the positive definite matrix Ω of the discrete event trigger and the gain matrix of the equivalent DOFF quantized controller By using the discrete event trigger threshold parameter δ, a DOFF quantized controller suitable for TS fuzzy systems under the influence of deception attacks and event triggers is finally obtained.

[0219] Among them, the asymptotic stability condition of the TS fuzzy system is obtained by step C1, and then the design condition of the DOFF quantized controller is obtained by step C2. Solving the controller design condition, the discrete event trigger positive definite matrix Ω = 11.0792 and the gain matrix of the equivalent DOFF quantized controller (29) are obtained as follows

[0220]

[0221]

[0222] In this embodiment, under the action of the designed DOFF quantization controller, the mass spring damping system under the influence of deception attack, discrete event trigger, logarithmic quantizer and network induced delay can be asymptotically stable. In addition, within the simulation time [0,10 seconds], the sensor periodically samples 100 data, of which the discrete event trigger sends 79 data, and the data sending rate is 79%. Compared with the 100% data sending rate of the periodic sampler, the discrete event trigger saves 21% of system resources while ensuring system performance. In addition, among the 79 data sent by the discrete event trigger, 24 data were tampered with by the deception attack, and the attack rate was as high as 30.4%.

[0223] The examples show that, on the one hand, the discrete event trigger can reduce the data transmission rate to 79%, saving 21% of system limited resources such as network bandwidth. On the other hand, although up to 30.4% of the discrete event trigger sent data was tampered by spoofing attacks, the TS fuzzy system can still be asymptotically stable under the action of the DOFF quantization controller. In addition, the method of the present invention is designed based on the object measurement output, which removes the assumption that the object state is completely measurable in most achievements.

Claims

1. A design method for an event-triggered DOFF quantized controller under a spoofing attack, characterized in that: The following steps are involved: A: Establish TS fuzzy object model, discrete event trigger model and logarithmic quantizer model; B: Establish a deception attack model and a DOFF quantization controller model, and establish a closed-loop TS fuzzy system augmented model that organically integrates deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters; C: Design the design conditions of the DOFF quantized controller that organically integrates the deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameters, and find the positive definite matrix Ω of the discrete event trigger and the gain matrix of the equivalent DOFF quantized controller By using the discrete event trigger threshold parameter δ, the DOFF quantized controller suitable for TS fuzzy systems under deception attacks and event triggers is finally obtained. In step B, the deception attack model is: in, represents the deception attack function, b(t)∈{0,1} represents the Bernoulli distribution random variable. When b(t)=1, the deception attack is activated and the controller input is tampered with, that is, When b(t) = 0, the spoofing attack is in a dormant state and the controller input has not been tampered with, i.e. is the DOFF quantized controller input under attack influence, is the DOFF quantization controller input under no attack; In step B, the DOFF quantization controller model is: In the formula, For x c The derivative of (t), x c (t) represents the controller state, x c (t) is an n-dimensional real number, x c (t-η(t)) represents the controller state corresponding to t-η(t), and is the gain matrix; the number of fuzzy rules of the controller is r, j = 1, ..., r represents the serial number of the fuzzy rules of the controller, the substitution formula and Represents the antecedent variable Belongs to fuzzy sets The membership function of Indicates the division of subintervals; In the step B, the closed-loop TS fuzzy system augmented model that organically integrates deception attack, discrete event trigger, logarithmic quantizer and network-induced delay parameter is: In the formula, is the derivative of χ(t), represents the state of the closed-loop system, χ(t-η(t)) represents the state of the closed-loop system corresponding to t-η(t), and represents the closed-loop system gain matrix, e(t)=y(t k h)-y(t k h+(n k -1)h),y(t k h+(n k -1)h) represents the sampling time t k h+(n k -1)h corresponding to the object measurement output; The step C comprises the following specific steps: C1: Based on Lyapunov stability theory, determine the asymptotic stability conditions of the system under the influence of spoofing attacks, discrete event triggers, logarithmic quantizers and network-induced delays; C2: Based on the asymptotic stability condition of the system obtained in step C1, use the linear matrix inequality technique to find the positive definite matrix Ω of the discrete event trigger and the gain matrix of the equivalent DOFF quantized controller By using the discrete event trigger threshold parameter δ, the DOFF quantized controller suitable for TS fuzzy systems under deception attacks and event triggers is finally obtained. The asymptotic stability conditions of the system under the influence of the deception attack, discrete event trigger, logarithmic quantizer and network-induced delay are: Given a sampling period h, the lower bound of network-induced delay is and upper bound Logarithm of the quantizer diagonal matrix Δ, attack energy limit matrix F and event trigger threshold parameter δ∈(0,1), if there exists a positive definite matrix Ω>0, P>0, R>0, S>0, Q1>0, Q2>0, Q3>0, and matrices U2, U3, satisfying the following equation: Then the TS fuzzy system under the influence of deception attack, discrete event trigger, logarithmic quantizer and network induced delay is asymptotically stable; In the above stability conditions, the substitution formula used is as follows: P 21 =col{η 10 L1,h 21 L1,h 32 L1},P 31 =col{η 10 L2,h 21 L2,h 32 L2},P 41 =col{Λ3,Λ4}, or 10 =η1-η0,η 21 =η2-η1,η 32 =η3-η2,η0=0, η2=0.5(η3+η1), He{} represents the sum of a matrix and its transposed matrix, * represents the symmetric term in a symmetric matrix, Represents the zero matrix, and the -1 in the upper right corner of the matrix represents the inverse matrix. represents the mathematical expectation of b(t), is the mathematical expectation function; The design conditions of the DOFF quantization controller are: Given a sampling period h, the lower bound of network-induced delay is and upper bound Logarithmic quantizer quantization density ρ and real number ∈>0, attack energy limit matrix F and event trigger threshold parameter δ∈(0,1), if there exists a positive definite matrix Ω>0, and matrix satisfy Then the TS fuzzy system is asymptotically stable, and the equivalent DOFF quantized controller is obtained as follows: In the formula, represents the equivalent DOFF quantized controller state, is an n-dimensional real number, for The derivative of It represents the equivalent DOFF quantized controller state corresponding to t-η(t), and its gain matrix Obtained by the following formula: In the above controller design conditions, the substitution formula used is as follows X>0,Y>0 is a positive definite matrix, and N is an n×n dimensional real matrix.

2. The method for designing an event-triggered DOFF quantized controller under a spoofing attack according to claim 1, characterized in that: In the step A, the TS fuzzy object model is: In the formula, is the derivative of x(t), x(t) represents the object state, x(t) is an n-dimensional real number, u(t) represents the control input, and u(t) is n u dimensional real number, y(t) represents the measured output, y(t) is n y dimensional real number, t represents time, A i ,B i and C i represents the gain matrix; r is the number of object fuzzy rules, i represents the sequence number of object fuzzy rules, and the substitution formula and and θ g (t) represents the first and The first and gth antecedent variables, g represents the number of antecedent variables, Indicates the sequence number of the antecedent variable, Represents the antecedent variable Belongs to fuzzy sets , Σ and Π represent the accumulation and multiplication operations respectively.

3. The method for designing an event-triggered DOFF quantized controller under a spoofing attack according to claim 2, characterized in that: In step A, the discrete event trigger model is: Where δ∈(0,1) is the trigger threshold parameter, Ω>0 is a positive definite matrix, h represents the sampling period, t k h represents the kth triggering moment, t k h is the sampling period t k times, t k+1 h represents the k+1th triggering moment, t k+1 h is the sampling period t k+1 times, the subscript k indicates the triggering time sequence number; Indicates the current sampling time. t k h after Sampling period, y(t k h) and Respectively represent t k h and The corresponding object measurement output, min{·} represents the minimum function, and ||·|| represents the Euclidean norm.

4. The method for designing an event-triggered DOFF quantized controller under a spoofing attack according to claim 3, characterized in that: In step A, the logarithmic quantizer model is: Among them, f1(y1(t k h))、 and They represent y1(t k h), and The corresponding quantized value, y1(t k h), and They represent y(t k,n h)’s first dimension, Peacekeeping y dimensional data, col{} represents a column matrix; The logarithmic quantizer model expressed in the form of fan-shaped boundaries is further obtained as: f(y(t k h))=(1+Δ)y(t k h); Among them, the quantizer diagonal matrix Δ1 and Represents the first dimension and the nth dimension respectively y The diagonal elements corresponding to the dimensional quantization model, Δ satisfies -σI≤Δ≤σI, the substitution formula σ=(1-ρ) / (1+ρ), I is the unit matrix, ρ∈(0,1) represents the quantization density, and diag{} represents the diagonal matrix.

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