Joint design method of event driver and DOFFSS controller for nonlinear system

Abstract

The invention discloses a method for jointly designing a nonlinear system event driver and a DOFFSS controller, comprising the following steps: A: establishing a nonlinear object model, an actuator saturation model, and an event driver based on the measured output of the nonlinear object; B: establishing a random deception attack model and a DOFFSS controller model and a closed-loop system model that organically integrates the random deception attack, the event driver, the actuator saturation, and the network-induced delay parameters; C: designing the joint design conditions of the nonlinear system event driver and the DOFFSS controller under the influence of the random deception attack, the actuator saturation, and the network-induced delay, and calculating the event driver parameters and the gain matrix of the equivalent DOFFSS controller, and finally obtaining the event driver and the DOFFSS controller. The invention can solve the problem that the existing nonlinear system cannot be stabilized under the influence of the random deception attack, the actuator saturation, and the network-induced delay.

Description

Technical Field

[0001] The present invention relates to the field of networked control systems, and in particular to a method for jointly designing a nonlinear system event driver and a dynamic output feedback fuzzy saturated security (DOFFSS) controller under random deception attacks. 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 the system dynamics and performs on-time control, the event-driven control strategy performs on-demand control only when the system dynamics meet the event-driven conditions, thereby saving system-limited resources such as network bandwidth. However, existing event drivers usually adopt a continuous-time event-driven mechanism, which requires the addition of dedicated monitoring hardware and complex preliminary calculations to avoid the Zeno phenomenon (i.e., infinitely many drive samples 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 through data tampering. 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-driven mechanisms to save more system resources, and rarely consider the impact of spoofing attacks and network-induced delays at the same time. In addition, existing event-driven control system analysis and synthesis methods usually assume that there is no attack threat, and such methods are usually not directly applicable to the analysis of event-triggered control systems under the influence of spoofing attacks.

[0005] In reality, actuator saturation is a common nonlinear phenomenon in control systems. If the actuator input exceeds the saturation threshold, the actuator enters a saturated state. In the saturated state, further increasing the actuator input has no effect on the actuator output. However, existing results rarely consider the effects of actuator saturation and deception attacks at the same time. In addition, existing results usually assume that the system state is fully measurable and design a state feedback controller, but in reality the system state is usually not directly accessible.

[0006] In order to solve the above problems, the present invention proposes a joint design method of nonlinear system event driver and DOFFSS controller, taking into account the impact of random deception attacks, actuator saturation, network induced delay and the inability to directly measure the object state. Summary of the invention

[0007] The purpose of the present invention is to provide a method for jointly designing a nonlinear system event driver and a DOFFSS controller, which can solve the problem that the existing nonlinear system cannot be stabilized under the influence of random deception attacks, actuator saturation and network induced delay, and can 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 jointly designing a nonlinear system event driver and a DOFFSS controller comprises the following steps:

[0010] A: Establish nonlinear plant model and actuator saturation model, and design event drivers based on nonlinear plant measurement output;

[0011] B: Establish a random deception attack model and a DOFFSS controller model, and establish a closed-loop system model that organically integrates random deception attacks, event drivers, actuator saturation, and network-induced delay parameters;

[0012] C: Design the joint design conditions of nonlinear system event driver and DOFFSS controller under the influence of random deception attack, actuator saturation and network induced delay, and find the event driver parameters that meet the communication and control requirements of nonlinear system and the gain matrix of the equivalent DOFFSS controller Finally, we obtain event drivers and DOFFSS controllers that meet the communication and control requirements of nonlinear systems.

[0013] In the step A, the nonlinear plant model is:

[0014]

[0015] in, is the derivative of x(t), x(t) represents the state of the object, x(t) is an n-dimensional real number, represents the control input affected by actuator saturation, 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 Ci represents the gain matrix; the number of object fuzzy rules is r, i represents the sequence number of the object fuzzy rule; the substitution formula and

[0016] 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.

[0017] In step A, the event driver based on the nonlinear object measurement output is:

[0018]

[0019] Where δ∈(0,1) is the driver threshold parameter, is a positive definite matrix, h represents the sampling period, t k h represents the kth driving moment, t k h is the sampling period t k times, t k+1 h represents the k+1th driving moment, t k+1 h is the sampling period t k+1 times, the subscript k indicates the driving 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 nonlinear object measurement output, min{} represents the minimum function, and the upper right subscript T of the matrix represents the transpose of the matrix.

[0020] In step A, the actuator saturation model is:

[0021]

[0022] in, represents the first dimensional component, u(t) represents the object control input without considering the effect of actuator saturation, and u(t) is n u dimensional real numbers, represents the dimension number of u(t), and Respectively represent the maximum and minimum allowable output values ​​of the actuator, express The corresponding actuator saturation function value, sat( ) represents the actuator saturation function.

[0023] In step B, the random deception attack model is:

[0024]

[0025] in,, represents the deception attack function, a(t)∈{0,1} represents the Bernoulli distribution random variable, when a(t)=1, the deception attack is activated and the controller input is tampered with; when a(t)=0, the deception attack is dormant and the controller input is not tampered with; G is the attack energy limitation matrix;

[0026] y(t-η(t)) represents the measured output of the nonlinear object corresponding to the time t-η(t), t-η(t) = t k h+n k h,e(t)=y(t k h)-y(t k h+n k h), y(t k h+n k h) represents the sampling time t k h+n k h corresponds to the measured output of the nonlinear object.

[0027] In the step B, the DOFFSS controller model is:

[0028]

[0029] in, 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 represents the serial number of the fuzzy rules of the controller, and the substitution formula is and Represents the antecedent variable Belongs to fuzzy sets The membership function of .

[0030] In the step B, the closed-loop system model that organically integrates random deception attack, event driver, actuator saturation and network-induced delay parameters is:

[0031]

[0032] 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, and the substitution and They represent u1, and The corresponding actuator dead zone function value, u1, and They represent the first and second dimensions of u(t) respectively. Peacekeeping u Dimensional component, Represents the actuator deadband function.

[0033] The step C comprises the following specific steps:

[0034] C1: Based on Lyapunov stability theory, determine the asymptotic stability conditions of nonlinear systems under the influence of random spoofing attacks, event-driven, actuator saturation and network-induced delays;

[0035] C2: Based on the asymptotic stability conditions of the nonlinear system obtained in step C1, the linear matrix inequality technique is used to obtain the joint design conditions of the event driver and the DOFFSS controller, that is, to find the event driver parameters that meet the communication and control requirements of the nonlinear system. and the gain matrix of the equivalent DOFFSS controller Finally, we obtain event drivers and DOFFSS controllers that meet the communication and control requirements of nonlinear systems.

[0036] The asymptotic stability condition of the nonlinear system under the influence of random deception attack, event drive, actuator saturation and network induced delay is:

[0037] Given a sampling period h, the network-induced delay lower bound τ and upper bound The actuator saturation parameter ε, the attack energy limit matrix G and the event driver threshold parameter δ∈(0,1), if there exists a positive definite matrix P>0,R>0,S>0,Q1>0,Q2>0,Q3>0, and matrices U2,U3, satisfy as well as

[0038]

[0039] Then the closed-loop system is asymptotically stable under the influence of random deception attacks, event-driven, actuator saturation and network-induced delays; in the above stability conditions, the following substitution is used:

[0040]

[0041] Π 21 =col{η 10 Λ1,η 21 Λ1,η 32 Λ1,η 10 Λ2,η 21 Λ2,η 32 Λ2},Π 31 =C i E1e3+e6,

[0042] Π 51 =G(C i E1e3+e6),

[0043] Π 44 =-ε -1 ,Π 55 =-I,

[0044]

[0045] η 10 =η1-η0,η 21 =η2-η1,η 32 =η3-η2, η0=0, η1=τ, η2=0.5(η3+η1),

[0046]

[0047] in, represents the mathematical expectation of a(t), is the mathematical expectation function. He{} represents the sum of a matrix and its transposed matrix, * represents the symmetric term in a symmetric matrix, represents the zero matrix, the -1 in the upper right corner of the matrix represents the inverse matrix, I is the identity matrix, col{} represents the column matrix, and diag{} represents the diagonal matrix.

[0048] The event driver and DOFFSS controller joint design conditions are:

[0049] Given a sampling period h, the network-induced delay lower bound τ and upper bound The actuator saturation parameter ε and the attack energy limit matrix G, real numbers ∈1>0,∈2>0,∈3>0, if there exists a real number Positive definite matrix

[0050] and matrix satisfy as well as

[0051] Then the closed-loop system is asymptotically stable, and the event driver parameters are obtained and the gain matrix of the equivalent DOFFSS controller as follows

[0052]

[0053] In the above conditions, the substitution formula used is as follows

[0054]

[0055] Ψ1=diag{Φ1,Φ1},

[0056] X>0,Y>0 is a positive definite matrix, and N is an n×n dimensional real matrix.

[0057] The present invention can solve the problem that existing nonlinear systems cannot be stabilized under the influence of random deception attacks, actuator saturation and network-induced delays, can effectively save system limited resources such as network bandwidth, and can remove the assumption that the system state is completely measurable. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of event-driven output feedback control of a nonlinear system under a deception attack in the present invention;

[0059] Figure 2 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0060] The present invention is described in detail below with reference to the accompanying drawings and embodiments:

[0061] Event-driven output feedback control system for nonlinear systems under random deception attacks Figure 1As shown in the figure, the sensor samples the measured output of the nonlinear object periodically, and the sensor sampling data is sent to the event driver. The event driver determines whether the event driving condition is met: if it is met, the sampling data is sent; otherwise, the sampling data is discarded. The event driver sends data to the zero-order holder via the communication network. The communication network is affected by random deception attacks. The DOFFSS controller receives the zero-order holder data and calculates the control signal. The actuator adjusts the object state according to the control signal and considers the influence of actuator saturation.

[0062] like Figure 2 As shown, the joint design method of nonlinear system event driver and DOFFSS controller of the present invention comprises the following steps:

[0063] A: Establish nonlinear plant model and actuator saturation model, and design event drivers based on nonlinear plant measurement output;

[0064] Among them, when the nonlinear plant model is described as a TS (Takagi-Sugeno) fuzzy system:

[0065] Assume that the i-th fuzzy rule of a nonlinear object is expressed as follows: If θ1(t) is for M ig ,but

[0066]

[0067] In the formula, is the derivative of x(t), x(t) represents the state of the object, x(t) is an n-dimensional real number, represents the control input affected by actuator saturation, 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; the number of object fuzzy rules is r, 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 first and gth fuzzy sets.

[0068] Using product fuzzy reasoning, central average defuzzifier and single-point fuzzifier, the nonlinear object model represented by the TS fuzzy system is obtained as follows

[0069]

[0070] In the formula, the substitution formula and Represents the antecedent variable Belongs to fuzzy sets , Σ and Π represent the accumulation and multiplication operations respectively.

[0071] When designing an event driver based on the measured output of a nonlinear object:

[0072] Based on the measured output of the nonlinear object, the event driver is designed as:

[0073]

[0074] Where δ∈(0,1) is the driver threshold parameter, is a positive definite matrix, h represents the sampling period, t k h represents the kth driving moment, t k h is the sampling period t k times, t k+1 h represents the k+1th driving moment, t k+1 h is the sampling period t k+1 times, the subscript k represents the driving 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 nonlinear object measurement output, min{} represents the minimum function, and the upper right subscript T of the matrix represents the transpose of the matrix.

[0075] In the present invention, the event driver judges the event driving condition in formula (3) at each periodic sampling point. If the condition is met, the sampled data is sent; if the condition is not met, the sampled data is discarded. Therefore, the event driver only sends the sampled data that meets the event driving condition, thereby saving system limited resources such as network bandwidth. In addition, the event driver only uses the periodic sampling value of the nonlinear object measurement output, 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.

[0076] The actuator saturation model is established as follows:

[0077]

[0078] In the formula, represents the first dimensional component, u(t) represents the object control input without considering the effect of actuator saturation, and u(t) is n u dimensional real numbers, represents the dimension number of u(t), and Respectively represent the maximum and minimum allowable output values ​​of the actuator, express The corresponding actuator saturation function value, sat( ) represents the actuator saturation function.

[0079] From the actuator saturation model (4), we can see that when When , the actuator saturation function output is the actuator maximum allowable output value, that is, when When , the actuator saturation function output is the actuator minimum allowable output value, that is, when When , the actuator saturation function output is

[0080] Using the actuator saturation model (4), the control input affected by actuator saturation in the nonlinear plant model (2) is It is expressed as:

[0081]

[0082] In the formula, the substitution formula u1 and Respectively represent the first and nth dimensions of u(t) u dimensional components, sat(u1) and They represent u1 and The corresponding actuator saturation function value. and They represent u1, and The corresponding actuator dead zone function value, Represents the actuator deadband function.

[0083] According to the actuator saturation model (4), the following equation holds true:

[0084]

[0085] In the formula, the real number express The maximum value of , max{} represents the maximum value function.

[0086] B: Establish a random deception attack model and a DOFFSS controller model, and establish a closed-loop system model that organically integrates random deception attacks, event drivers, actuator saturation, and network-induced delay parameters;

[0087] First, without considering the influence of random deception attack, under the action of zero-order holder, the DOFFSS controller input Expressed as

[0088]

[0089] 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, τ and denote the lower and upper bounds of the network induced delay, respectively.

[0090] definition The zero-order hold time is divided as follows

[0091]

[0092] Where n k Indicates the sub-interval number. n k Maximum value, ∪ is the union symbol, subinterval It is expressed as follows

[0093]

[0094] In the sub-interval On the top, define the function as follows

[0095] e(t)=y(t k h)-y(t k h+n k h), η(t)=t-(t k h+n k h) (10);

[0096] In the formula, y(t k h+n k h) represents the sampling time t k h+n k h corresponds to the measured output of the nonlinear object.

[0097] Using equation (10), the DOFFSS controller input (7) is expressed as:

[0098]

[0099] In the formula, y(t-η(t)) represents the measured output of the nonlinear object corresponding to the time t-η(t). From (10), we can get t-η(t)=t k h+n k h.

[0100] Secondly, the random deception attack model is established as follows

[0101]

[0102] In the formula, represents the deception attack function, a(t)∈{0,1} represents the Bernoulli distribution random variable, when a(t)=1, the deception attack is activated and the controller input is tampered; when a(t)=0, the deception attack is dormant and the controller input is not tampered; since the attack energy is usually limited in practice, that is, Satisfy the following formula

[0103]

[0104] Where G is the attack energy limitation matrix.

[0105] Using equations (11) and (12), we can obtain the controller input under random deception attack: as follows

[0106]

[0107] Then, the DOFFSS controller model is established as follows:

[0108] Assume that the jth fuzzy rule of the controller is expressed as: If θ1(t) is for M jg ,but

[0109]

[0110] 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 represents the serial number of the controller fuzzy rule, M j1 , and M jg They represent the first and the second fuzzy rules of the controller respectively. The first and gth fuzzy sets.

[0111] Using product fuzzy reasoning, central average defuzzifier and single point fuzzifier, the DOFFSS controller model is obtained as follows

[0112]

[0113] In the formula, the substitution formula and Represents the antecedent variable Belongs to fuzzy sets The membership function of .

[0114] In summary, the nonlinear plant model (2) and the DOFFSS controller model (16) are combined to establish the closed-loop system model as follows:

[0115]

[0116] 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.

[0117] C: Design the joint design conditions of nonlinear system event driver and DOFFSS controller under the influence of random deception attack, actuator saturation and network induced delay, and find the event driver parameters that meet the communication and control requirements of nonlinear system and the gain matrix of the equivalent DOFFSS controller Finally, we obtain event drivers and DOFFSS controllers that meet the communication and control requirements of nonlinear systems.

[0118] The step C comprises the following two specific steps:

[0119] C1: Based on Lyapunov stability theory, determine the asymptotic stability conditions for nonlinear systems under the influence of random spoofing attacks, event-driven systems, actuator saturation, and network-induced delays.

[0120] Given a sampling period h, the network-induced delay lower bound τ and upper bound The actuator saturation parameter ε, the attack energy limit matrix G and the event driver threshold parameter δ∈(0,1), if there exists a positive definite matrix P>0,R>0,S>0,Q1>0,Q2>0,Q3>0, and matrices U2,U3, satisfy as well as

[0121]

[0122] Then the closed-loop system (17) is asymptotically stable under the influence of random deception attacks, event-driven, actuator saturation and network-induced delays.

[0123] In the above stability conditions, the substitution formula used is as follows:

[0124]

[0125] Π 21 =col{η 10 Λ1,η 21 Λ1,η 32 Λ1,η 10 Λ2,η 21 Λ2,η 32 Λ2},Π 31 =C i E1e3+e6,

[0126] Π 51 =G(C i E1e3+e6),

[0127] Π 44 =-ε -1 ,Π 55 =-I,

[0128]

[0129] η 10 =η1-η0,η 21 =η2-η1,η 32 =η3-η2, η0=0, η1=τ, η2=0.5(η3+η1),

[0130]

[0131] in, represents the mathematical expectation of a(t), is the mathematical expectation function. He{} represents the sum of a matrix and its transposed matrix, * represents the symmetric term in a symmetric matrix, represents the zero matrix, the -1 in the upper right corner of the matrix represents the inverse matrix, I is the identity matrix, col{} represents the column matrix, and diag{} represents the diagonal matrix.

[0132] Proof: Construct the Lyapunov functional as follows

[0133]

[0134] In the formula, the substitution formula ρ=0.5(η3-η1),s, 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).

[0135] Taking the derivative of the Lyapunov functional, we get

[0136]

[0137] In the formula, is 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:

[0138]

[0139] In the formula, Represents the integral variable The corresponding closed-loop system state derivative.

[0140] Consider the following two cases:

[0141] (1) If η(t)∈[η1,η2), use the Jünsen inequality for ζ1,ζ2,ζ3 in (21) and use Further using the mutual convex method on ζ2, we get

[0142]

[0143] In the formula, the substitution formula and χ(t-η2) and χ(t-η3) represent the closed-loop system states corresponding to t-η2 and t-η3, respectively.

[0144] (2) If η(t)∈[η2,η3], use the Jensen inequality for ζ1,ζ2,ζ3 in (21) and use Further using the mutual convex method on ζ3, we get

[0145]

[0146] In the formula, the substitution formula is used and

[0147] Using (22) and (23), we can find the mathematical expectation of the derivative of the Lyapunov functional (20) and obtain

[0148]

[0149] In the formula, For alternative.

[0150] Using formula (10), the event driver (3) and the attack energy constraint (13) are obtained:

[0151]

[0152] Using formula (25), we can get from formula (24)

[0153]

[0154] In the formula, the following substitution is used

[0155]

[0156] Using Schur's complement lemma on equation (18) we get

[0157]

[0158] Substituting equation (27) into equation (26), we get According to Lyapunov stability theory, the closed-loop system (17) is asymptotically stable. Proof.

[0159] In the above system stability conditions, there exists an event-driven positive definite matrix The inverse matrix And the DOFFSS controller gain matrix Coupled with the positive definite matrix P, therefore, this condition cannot be directly used for event driver and controller design. In order to solve this problem, the present invention will further provide a joint design method of event driver and DOFFSS controller.

[0160] C2: Based on the asymptotic stability conditions of the nonlinear system obtained in step C1, the linear matrix inequality technique is used to obtain the joint design conditions of the event driver and the DOFFSS controller, that is, to find the event driver parameters that meet the communication and control requirements of the nonlinear system. and the gain matrix of the equivalent DOFFSS controller Finally, we obtain event drivers and DOFFSS controllers that meet the communication and control requirements of nonlinear systems.

[0161] First, the prior art (Theorem 1) used in step C2 is given as follows:

[0162] Theorem 1. If a positive definite matrix Q>0, a matrix L and a real number ∈>0, then the inequality (L-∈Q)Q -1 (L-∈Q)≥0 holds, that is, the inequality -LQ -1 L≤∈ 2 Q-2∈L holds.

[0163] Then, the joint design conditions of the event driver and the DOFFSS controller are given as follows:

[0164] Given a sampling period h, the network-induced delay lower bound τ and upper bound The actuator saturation parameter ε and the attack energy limit matrix G, real numbers ∈1>0,∈2>0,∈3>0, if there exists a real number Positive definite matrix

[0165] and matrix satisfy as well as

[0166]

[0167] Then the closed-loop system (17) is asymptotically stable, and the event driver parameters are obtained and the gain matrix of the equivalent DOFFSS controller (34) as follows

[0168]

[0169] In the above conditions, the substitution formula used is as follows

[0170]

[0171] Ψ1=diag{Φ1,Φ1},

[0172] X>0,Y>0 is a positive definite matrix, and N is an n×n dimensional real matrix.

[0173] Proof: Decompose the positive definite matrix P as follows

[0174]

[0175] 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

[0176] The system stability condition in step C1 is transformed as follows

[0177]

[0178] In the formula, the following substitution is used

[0179] Ψ1=diag{Φ1,Φ1},Ψ2=diag{Φ1,Φ1,Φ1,Φ1,Φ1,I,I,I,Ψ3,I,I,I},

[0180] Ψ3=diag{Φ2,Φ2,Φ2,Φ2,Φ2,Φ2},

[0181]

[0182] For (32) and Using Theorem 1, we can obtain and

[0183] Therefore, if the given conditions are met, the closed-loop system (17) is asymptotically stable. At the same time, the event driver parameters are obtained The gain matrix of the DOFFSS controller (16) is as follows

[0184]

[0185] In order to deal with the unknown matrix N in (33), a linear transformation is used The equivalent DOFFSS controller is obtained as follows

[0186]

[0187] In the formula, Indicates the equivalent DOFFSS controller state, is an n-dimensional real number, for The derivative of represents the equivalent DOFFSS controller state corresponding to t-η(t), and the gain matrix From (29), we get:

[0188] Through the event driver and DOFFSS controller joint design method described in the present invention, the user can determine each parameter one by one in combination with specific design requirements, and obtain the event driver and DOFFSS controller according to the steps. The event driver can reduce the data transmission rate, thereby saving system limited resources such as network bandwidth; the DOFFSS controller enables the nonlinear system to be asymptotically stable under the influence of random deception attacks, event drivers, actuator saturation and network induced delays.

[0189] The present invention is described in detail below with reference to the embodiments:

[0190] Step A: Build a nonlinear plant model and design an event driver based on the measured output of the nonlinear plant:

[0191] Among them, the nonlinear object takes the mass spring damper system as an example, and its dynamic equation is described as

[0192]

[0193] 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 affected by the actuator saturation, c, is a real number. The parameter is set to m = 1 kg, c = 2 N·m / s,

[0194] Defining object states Then the mass-spring-damper system (35) can be described as a nonlinear 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:

[0195] C1=C2=[1 0].

[0196] Design an event driver based on the measured output of a nonlinear object (3), where the sampling period h = 100 milliseconds, the driver threshold parameter δ and the positive definite matrix It is obtained by the joint design conditions of the event driver and the DOFFSS controller in step C2.

[0197] Establish the actuator saturation model (4): where the maximum allowable output value of the actuator is The maximum value of Real Numbers

[0198] Step B: Establish random deception attack and DOFFSS controller models, and establish a closed-loop system model that organically integrates random deception attack, event driver, actuator saturation and network-induced delay parameters;

[0199] First, a random deception attack model is established as

[0200] in, is the deception attack function, tanh represents the nonlinear hyperbolic tangent function, a(t)∈{0,1} is a Bernoulli distribution random variable, and the mathematical expectation is The attack energy limiting matrix is ​​G=0.1 (a one-dimensional matrix is ​​equivalent to a real number).

[0201] Secondly, the DOFFSS controller model (16) is established.

[0202] Then, a closed-loop system model (17) is established that organically integrates random deception attacks, event drivers, actuator saturation, and network-induced delay parameters, where the network-induced delay has a lower bound of τ = 10 milliseconds and an upper bound of

[0203] Step C: Design the joint design conditions of the event driver and DOFFSS controller under the influence of random deception attack, actuator saturation and network-induced delay, and obtain the event driver parameters and the gain matrix of the equivalent DOFFSS controller Finally, we get the event driver and DOFFSS controller that meet the system requirements.

[0204] Among them, the asymptotic stability condition of the nonlinear system is obtained by step C1, and then the joint design condition of the event driver and DOFFSS controller is obtained by step C2, where ∈1=∈2=∈3=1. Solving this joint design condition, the event driver parameters are obtained And the equivalent DOFFSS controller gain matrix is ​​as follows

[0205]

[0206] In this embodiment, under the action of the designed DOFFSS controller, the mass spring damping system can be asymptotically stable under the influence of random deception attacks, event drivers, actuator saturation and network-induced delay. In addition, within the simulation time [0,10 seconds], the sensor periodically samples 100 data, of which the event driver sends 71 ​​data, and the data sending rate is 71%. Compared with the 100% data sending rate of the periodic sampler, the event driver saves 29% of system resources while ensuring system performance. In addition, among the 71 data sent by the event driver, 15 data were tampered with by random deception attacks, with an attack rate of 21%.

[0207] The embodiment shows that, on the one hand, the event driver can reduce the data transmission rate to 71%, saving 29% of the system limited resources such as network bandwidth. On the other hand, although up to 21% of the data sent by the event driver is tampered by random spoofing attacks, the nonlinear system can still be asymptotically stable under the action of the DOFFSS controller. In addition, the method of the present invention is designed based on the measurement output of the nonlinear object, which removes the assumption that the object state is completely measurable in most achievements.

Claims

1. A method for jointly designing a nonlinear system event driver and a DOFFSS controller, characterized in that: The following steps are involved: A: Establish nonlinear plant model and actuator saturation model, and design event drivers based on nonlinear plant measurement output; B: Establish a random deception attack model and a DOFFSS controller model, and establish a closed-loop system model that organically integrates random deception attacks, event drivers, actuator saturation, and network-induced delay parameters; C: Design the joint design conditions of nonlinear system event driver and DOFFSS controller under the influence of random deception attack, actuator saturation and network induced delay, and find the event driver parameters that meet the communication and control requirements of nonlinear system and the gain matrix of the equivalent DOFFSS controller Finally, we obtain event drivers and DOFFSS controllers that meet the communication and control requirements of nonlinear systems; Wherein, in the step B, the random deception attack model is: in, represents the deception attack function, a(t)∈{0,1} represents the Bernoulli distribution random variable, when a(t)=1, the deception attack is activated and the controller input is tampered with; when a(t)=0, the deception attack is dormant and the controller input is not tampered with; G is the attack energy limitation matrix; y(t-η(t)) represents the measured output of the nonlinear object corresponding to the time t-η(t), t-η(t) = t k h+n k h,e(t)=y(t k h)-y(t k h+n k h), y(t k h+n k h) represents the sampling time t k h+n k h corresponds to the nonlinear object measurement output; The DOFFSS controller model is: in, 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 represents the serial number of the fuzzy rules of the controller, and the substitution formula is and Represents the antecedent variable Belongs to fuzzy sets The membership function of The closed-loop system model that organically integrates random deception attacks, event drivers, actuator saturation, and network-induced delay parameters 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, and the substitution and They represent u1, and The corresponding actuator dead zone function value, u1, and They represent the first and second dimensions of u(t) respectively. Peacekeeping u Dimensional component, represents the actuator dead zone function; The step C comprises the following specific steps: C1: Based on Lyapunov stability theory, determine the asymptotic stability conditions of nonlinear systems under the influence of random spoofing attacks, event-driven, actuator saturation and network-induced delays; C2: Based on the asymptotic stability conditions of the nonlinear system obtained in step C1, the linear matrix inequality technique is used to obtain the joint design conditions of the event driver and the DOFFSS controller, that is, to find the event driver parameters that meet the communication and control requirements of the nonlinear system. and the gain matrix of the equivalent DOFFSS controller Finally, we obtain event drivers and DOFFSS controllers that meet the communication and control requirements of nonlinear systems; The asymptotic stability condition of the nonlinear system under the influence of random deception attack, event drive, actuator saturation and network induced delay is: Given a sampling period h, the network-induced delay lower bound τ and upper bound The actuator saturation parameter ε, the attack energy limit matrix G and the event driver threshold parameter δ∈(0,1), if there exists a positive definite matrix P>0,R>0,S>0,Q1>0,Q2>0,Q3>0, and matrices U2,U3 satisfy as well as Then the closed-loop system is asymptotically stable under the influence of random deception attacks, event-driven, actuator saturation and network-induced delays; in the above stability conditions, the following substitution is used: P 21 =col{η 10 L1,h 21 L1,h 32 L1,h 10 L2,h 21 L2,h 32 L2},P 31 =C i E1e3+e6, Π 51 G(C i E1e3+e6), P 44 =-e -1 ,P 55 =-I, or 10 =η1-η0,η 21 =η2-η1,η 32 =η3-η2,η0=0,η1=τ,η2=0.5(η3+η1), in, represents the mathematical expectation of a(t), is the mathematical expectation function; He{} represents the sum of a matrix and its transposed matrix, * represents the symmetric term in a symmetric matrix, represents the zero matrix, the -1 in the upper right corner of the matrix represents the inverse matrix, I is the identity matrix, col{} represents the column matrix, and diag{} represents the diagonal matrix; The event driver and DOFFSS controller joint design conditions are: Given a sampling period h, the network-induced delay lower bound τ and upper bound The actuator saturation parameter ε and the attack energy limit matrix G, real numbers ∈1>0,∈2>0,∈3>0, if there exists a real number Positive definite matrix and matrix satisfy as well as Then the closed-loop system is asymptotically stable, and the event driver parameters are obtained and the gain matrix of the equivalent DOFFSS controller as follows In the above conditions, the substitution formula used is as follows Ψ1=diag{Φ1,Φ1}, X>0,Y>0 is a positive definite matrix, and N is an n×n dimensional real matrix.

2. The method for jointly designing a nonlinear system event driver and a DOFFSS controller according to claim 1, characterized in that: In the step A, the nonlinear plant model is: in, is the derivative of x(t), x(t) represents the state of the object, x(t) is an n-dimensional real number, represents the control input affected by actuator saturation, 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; the number of object fuzzy rules is r, i represents the sequence number of the object fuzzy rule; 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 jointly designing a nonlinear system event driver and a DOFFSS controller according to claim 2, characterized in that: In step A, the event driver based on the nonlinear object measurement output is: Where δ∈(0,1) is the driver threshold parameter, is a positive definite matrix, h represents the sampling period, t k h represents the kth driving moment, t k h is the sampling period t k times, t k+1 h represents the k+1th driving moment, t k+1 h is the sampling period t k+1 times, the subscript k indicates the driving 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 nonlinear object measurement output, min{} represents the minimum function, and the upper right subscript T of the matrix represents the transpose of the matrix.

4. The method for jointly designing a nonlinear system event driver and a DOFFSS controller according to claim 3, characterized in that: In step A, the actuator saturation model is: in, represents the first dimensional component, u(t) represents the object control input without considering the effect of actuator saturation, and u(t) is n u dimensional real numbers, represents the dimension number of u(t), and Respectively represent the maximum and minimum allowable output values ​​of the actuator, express The corresponding actuator saturation function value, sat( ) represents the actuator saturation function.

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