A multi quadrotor aircraft position consensus control system based on attack isolation and privacy protection

Abstract

The application discloses a position consistent control system of multi-four-rotor aircraft based on attack isolation and privacy protection and belongs to the technical field of industrial process control; the position consistent control system comprises a Liu password system, a network attack detection and isolation system and a consistent control system; the Liu password system performs encrypted transmission on provided leader expected signals and position information and obtains decrypted information; the network attack detection and isolation system detects attacked followers and isolates the attacked followers; input ends of the consistent control system are connected with output ends of an undirected graph G; and output ends of the consistent control system are connected with input ends of the i-th follower. The signal amplification technology of the Liu password system is used to protect the sensitivity of information and reduce errors between plaintext encryption and decryption; the consistent controller is used to compensate unknown dynamics and errors between real signals and decrypted signals through a small number of learning parameters, so that the protection of sensitive information and network security of the multi-four-rotor aircraft during task execution are ensured.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of industrial process control, and particularly relates to a position consistency control system of a multi-quadrotor aircraft based on attack isolation and privacy protection. BACKGROUND

[0002] In modern industry and military fields, multi-quadrotor aircrafts are widely concerned due to their flexibility and versatility. These aircrafts need high consistency and coordination when performing tasks such as reconnaissance, surveillance, cargo transportation, and environmental monitoring. However, with the development of technology and the expansion of application scenarios, multi-quadrotor aircraft systems face new challenges, especially in privacy protection and security.

[0003] Privacy protection becomes increasingly important in the application of multi-quadrotor aircrafts. These aircrafts may collect and transmit sensitive data such as geographic information and image data when performing tasks, and if these data are obtained by unauthorized third parties, it may pose a threat to personal privacy or national security. Therefore, designing a multi-quadrotor aircraft control system that can protect privacy is crucial for ensuring data security and user trust.

[0004] In addition, with the increasing application of quadrotor aircrafts in critical infrastructure and sensitive areas, they have become potential targets of cyber attacks. Attackers may try to interfere or control the aircrafts through various means to steal data, disrupt task execution, or cause physical damage. Therefore, developing a multi-quadrotor aircraft consistency controller that includes attack detection and isolation mechanisms is crucial for improving the security and ability to resist cyber attacks of the system.

[0005] In the research of multi-quadrotor aircraft consistency control, how to design a control system that can protect privacy and resist external attacks is a challenging problem. This requires comprehensive consideration of the dynamics of the aircraft, the security of the control algorithm, the encryption technology of the communication protocol, and the attack detection and response strategy.

[0006] Although there are many achievements related to network attacks, Liu's cryptographic system, and reinforcement learning technology, there are still some technical gaps.

[0007] In real-world situations, nonlinear multi-agent systems are more common. For example, the nonlinear dynamics of a multi-quadrotor aircraft system are unknown, and the network attack detector for linear multi-agent systems is not feasible, requiring additional construction of the nonlinear dynamics of the quadrotor aircraft. There are deficiencies in the processing technology for the nonlinear dynamics of the quadrotor aircraft. In addition, existing attack detectors do not utilize privacy protection information. It is a challenge to construct a network attack detector in the presence of potential decryption errors and noise.

[0008] Existing Liu cryptosystem utilizes a large number of random sequences to create ciphertexts. Although these random numbers enhance privacy, they introduce decryption errors between the plaintext and the decrypted text. This lacks theoretical improvements to mitigate decryption errors caused by random numbers, and further technical progress is needed in this regard.

[0009] Most existing reinforcement learning-based control schemes and network attack detectors utilize neural networks to approximate unknown dynamics. As the number of nodes in the hidden layer increases, the number of weights for a single quadrotor also increases accordingly. More seriously, as the number of quadrotors increases, these numbers will further increase dramatically. This involves a rather large number of orders.

[0010] In summary, how to solve the sensitive protection and network security of multiple quadrotors when performing tasks, thereby improving their stability and reliability in complex environments is a technical problem that the present application wants to solve. SUMMARY

[0011] The purpose of the present application is to provide a position consensus control system for multiple quadrotors based on attack isolation and privacy protection to solve the problems raised in the background art.

[0012] The purpose of the present application is achieved in that the system comprises a Liu cryptosystem, a network attack detection and isolation system, and a consensus control system, the Liu cryptosystem encrypts the transmission of the leader's expected signal and the position information transmitted by the followers, and decrypts the received information at the information receiver to obtain decrypted information;

[0013] The network attack detection and isolation system detects and isolates the attacked followers, and the input ends of the consensus control system are connected to the output ends of the undirected graph G, and the output ends of the consensus control system are connected to the input ends of the i-th follower;

[0014] The Liu cryptosystem comprises a plaintext information acquisition unit, a signal amplification unit, a Liu encryption algorithm, a generated ciphertext transmitted through a network, a follower receiving the ciphertext, a Liu decryption algorithm, a signal reduction unit, and a decrypted information acquisition unit;

[0015] The network attack detection and isolation system includes a finite-time attack detector, an attack detection unit, and an attack isolation unit. The consistency control system includes a first error comparator, a utility function unit, a long-term performance exponential neural network weight update unit, a long-term performance exponential neural network activation function unit, a long-term performance exponential unit, a first nonlinear function unit, a first nonlinear neural network activation function unit, a first nonlinear function neural network weight update unit, a virtual control law unit, a second error comparison unit, a second nonlinear function unit, a first filtering unit, a second nonlinear function neural network activation function unit, a second nonlinear function neural network weight update unit, and a consistency controller.

[0016] Preferably, the input terminals of the first error comparator are respectively connected to the neighbor decryption information after passing through the attack isolation unit. Leaders decrypt information Measurement information from noise measurement sensors for quadcopters

[0017] The input of the utility function unit is connected to the output of the first error comparator. The input of the long-term performance function neural network weight update unit is connected to the output p of the utility function unit. i,c The input of the activation function unit of the long-term performance function neural network is connected to the quadcopter's state information χ. i,1 Long-term performance The inputs of the exponent unit are connected to the outputs Φ of the activation function unit of the long-term performance function neural network. i,c The output of the neural network weight update unit for the long-term performance function;

[0018] The inputs of the first nonlinear function neural network weight update unit are respectively connected to the outputs of the first error comparator. Output of the Long-Term Performance Index Unit The output Φ of the activation function unit of the first nonlinear function neural network i,1 ;

[0019] The input of the activation function unit of the first nonlinear function neural network is connected to the quadcopter's state information χ. i,1 The input terminals of the first nonlinear function unit are respectively connected to the output Φ of the activation function unit of the first nonlinear function neural network. i,1 The output of the first nonlinear function neural network weight update unit

[0020] The input terminals of the virtual control unit are respectively connected to the neighbor decryption information after passing through the attack isolation unit. Leaders decrypt information The output of the first error comparator and the output of the first nonlinear function unit

[0021] The input of the first filter unit is connected to the output α of the virtual control rate unit i,2 The input of the second error comparison unit is connected to the quadrotor state information χ i,2 and the output κ of the first filter unit i,2 The input of the second nonlinear function neural network weight update unit is connected to the output of the long-term performance index unit The output e of the second error comparison unit i,2 and the output Φ of the second nonlinear function neural network activation function unit i,2 ;

[0022] The input of the second nonlinear function neural network activation function unit is connected to the quadrotor state information χ i,1 and χ i,2 The input of the second nonlinear function unit is connected to the output Φ of the second nonlinear function neural network activation function unit i,2 , the output κ of the first filter unit i,2 and the output e of the second error comparison unit i,2 .

[0023] Preferably, the followers are N unknown dynamic quadrotors, the N unknown dynamic quadrotors and the 1 leader are connected through a directed topological graph to form a multi-agent network, and the multi-agent network is the controlled object;

[0024] Up to F followers in the multi-agent network are attacked by the network, and there is communication between at least F followers and the leader, and the communication is represented by a direction;

[0025] The directed graph G=(V, E) is obtained; wherein V={ν1,…,ν N} represents a set of N nodes; ν1,…,ν N represents quadrotor follower 1 to quadrotor follower N;

[0026] represents an edge set, (ν i ,v j ) represents an edge of the topological graph G, ν i ,v j respectively represent the i-th aircraft and the j-th aircraft; if (ν i ,v j ) ∈ E, then ν j is an adjacent node of ν i Ω i ={v j ∈v|(v j ,νi} represents v i ;

[0027] Define the adjacency matrix A = [a ij ] ∈ R N×N , if (v i , v j ) ∈ E, then a ij = 1, otherwise a ij = 0.

[0028] Define the degree matrix D = diag[d1,...,d N ], where,

[0029] Define the Laplacian matrix L = D - A, define the adjacency matrix related to the leader B = diag[b1,...,b N ], if the i-th aerial vehicle can access the information of the leader, then b i = 1, otherwise b i = 0.

[0030] Preferably, the mathematical model of the i-th quadcopter of the follower is:

[0031]

[0032] where x i represents the x-direction coordinate of the i-th quadcopter, y i represents the y-direction coordinate of the i-th quadcopter, and z i represents the z-direction coordinate of the i-th quadcopter; is the x-direction acceleration information, is the y-direction acceleration information, is the z-direction acceleration information; is the x-direction velocity information, is the y-direction velocity information, is the z-direction velocity information; m i is the mass of the i-th quadcopter, represents the x-direction aerodynamic damping coefficient of the i-th quadcopter, represents the y-direction aerodynamic damping coefficient of the i-th quadcopter, represents the z-direction aerodynamic damping coefficient of the i-th quadcopter, g is the acceleration of gravity, and u i is the control force of the i-th quadcopter.

[0033] Let χ i，1 = [χ i,1,x , χ i,1,y , χi,1,z ] T = [x i , y i , z i ] T and is the position system state and u i,x , u i,y , u i,z are virtual control inputs in x, y, z directions respectively;

[0034] Quadrotor position system where u i = [u i,x , u i,y , u i,z ] T is the system input;

[0035] F i,f = f i + g i is the system unknown dynamics, where g i,χ = diag [1 / m i , 1 / m i , 1 / m i ];

[0036] The sensor input with noisy measurement is the system state χ i,1 of the quadrotor, and the output of the sensor with noisy measurement is

[0037] Preferably, the Liu encryption algorithm comprises three parts, the first part is that the input of the signal amplification unit in the encryption algorithm is the sensor output information of the quadrotor The output is calculated by the following formula

[0038]

[0039] where k p is the amplification factor;

[0040] The second part is to generate four random numbers r i , q i , t i and s i , i = 1, …, M, to form the private key K (M) = {(q1, r1, t1), …, (q M , r M , t M )};

[0041] The third part is to obtain the ciphertext by the following formula

[0042] c1=q1t1m A +s1r M +q1(r1-r M-1 ),

[0043] c i =q i t i m A +s i r M +q i (r i -r i-1 ), i = 2, ..., M-1;

[0044] c M =(q M s M t M )r M

[0045] The ciphertext is output after calculation. And transmit it over the network.

[0046] Preferably, the Liu decryption algorithm is ciphertext. The ciphertext is received by the receiving end via network transmission. The input to Liu's decryption algorithm is the ciphertext. The following calculations were performed to obtain...

[0047]

[0048] The input of the signal reduction unit is the output of the improved Liu decryption algorithm. The decryption information is obtained through the following calculations.

[0049]

[0050] Where, k p This is the magnification factor.

[0051] Preferably, the input terminals of the attack detection unit and the attack isolation unit are decrypted information output through the Liu cryptographic system. Encrypted and decrypted leader information With sensor output information The output ε of the attack detection error unit is obtained by calculating using the following formula. i :

[0052]

[0053] The input of the limited-time attack detector is connected to the output of the attack detection error unit i The output of the attack detector is obtained by the following formula:

[0054]

[0055] Wherein, μ is the activation function center value, ξ is the activation function width; c i is the limited-time attack detector correction term gain, c i > 0; Γ i is the limited-time attack detector weight gain, Γ i > 0; α i is the Young's inequality parameter, α i > 0;

[0056] The input of the attack detection error comparison unit is connected to the output of the attack detector And the attack detection error unit ε i The output of the attack detection error comparison unit is obtained by the following calculation

[0057]

[0058] The attack detection process is as follows:

[0059] Firstly, define: state index Q i = 1 indicates that there is an attacked intelligent agent in the subnet, otherwise Q i = 0 indicates that there is no;

[0060] The counter W i indicates the sum of Q j = 1, j∈J i ;

[0061] The security index H i = 1 indicates that the intelligent agent is attacked, otherwise H i = 0 indicates that the intelligent agent is not attacked;

[0062] The isolation index P i = 1 indicates that the attacked intelligent agent is successfully isolated, otherwise P i = 0 isolation fails;

[0063] When the output of the attack detection error comparison unit is Wherein, is the set detection threshold, the state index Q i = 1, the counter W i = 1; the intelligent agent i transmits its state index Q iAnd query the state index Q of the neighboring agents. j ,j∈J i If Q j =1, then the counter W i Add 1; if W i =|J i | So, the safety index H i =1 indicates that an attacked agent has been detected;

[0064] The specific operation process of the attack isolation unit is as follows:

[0065] The security index H is obtained after the attack detection unit. i Query the safety index H of its neighbors j ,j∈J i If H j =1, then a ij =0, Ultimately, if a ij =0, then P i =1.

[0066] Preferably, the input of the first error comparator in the consistency control system is connected to the attack isolation unit and then output. and sensor output information The output of the first error comparison unit is obtained through the following calculations.

[0067] The input of the utility function unit is the output of the first error comparison unit. The output p of the utility function unit is obtained through the following calculations. i,c :

[0068]

[0069] Where γ is the discount factor, 0 < γ < 1; T is a small integral reinforcement interval, T > 0;

[0070] The input to the activation function unit of the long-term performance function neural network is the state information χ of the quadcopter. i,1 The long-term performance function, the output Φ of the neural network activation function unit, is obtained through the following formula. i,c :

[0071]

[0072] These are the long-term performance functions of the neural network and the activation functions in the x, y, and z directions, respectively; x i,1 y i,1 and z i,1Let ξ represent the system state in the x, y, and z directions, respectively, where μ is the center value of the activation function and ξ is the width of the activation function.

[0073] The final output is:

[0074] The input to the weight update unit of the long-term performance function neural network is the output p of the utility function. i,c The long-term performance function is calculated using the following formula, which yields the output of the neural network weight update unit.

[0075]

[0076] in, Γ represents the activation function of the neural network in the x, y, and z directions, respectively, and is the long-term performance function in those directions. i,c For the weighted gain of the long-term performance function, Γ i,c >0; σ i,c For the gain of the long-term performance function correction term, σ i,c >0; p i,c,x p i,c,y and p i,c,z The outputs of the utility function units in the x, y, and z directions are p, respectively. i,c The elements in the text are then used to obtain the output.

[0077] The inputs to the long-term performance index unit are the outputs Φ of the long-term performance function neural network activation function unit. i,c and the output of the weight update unit The long-term performance index unit output is obtained by multiplying all inputs.

[0078] Preferably, the input to the first nonlinear neural network activation function unit in the consistency control system is the state information χ of the quadcopter. i,1 The activation function unit Φ of the first nonlinear neural network is obtained through calculation using the following formula. i,1 :

[0079]

[0080] These are the activation functions of the first nonlinear neural network in the x, y, and z directions, respectively; x i,1 y i,1 and z i,1 Let μ be the system state in the x, y, and z directions, ξ be the center value of the activation function, and ξ be the width of the activation function; finally, the output is obtained.

[0081] The input of the first nonlinear neural network weight updating unit is the output Φ of the first nonlinear neural network activation function unit i,1 and the long-term performance index unit output The output of the first nonlinear neural network weight updating unit is calculated by the following formula

[0082]

[0083] wherein, ||φ i,1,x ||, ||φ i,1,y || and ||φ i,1,z are the outputs of the first nonlinear neural activation function unit in the x, y and z directions, respectively, and are elements in the output Φ i,1 ; and are elements of the first error comparison unit in the x, y and z directions, respectively, and are elements in the output , Γ i,c is the long-term performance function weight gain, Γ i,c > 0; σ i,c is the long-term performance function correction term gain, σ i,c > 0; and finally the output

[0084] The input of the first nonlinear operation unit is the output Φ of the first nonlinear neural network activation function unit i,1 and the output of the weight updating unit The output of the first nonlinear operation unit is calculated by multiplying all the inputs

[0085] The input of the virtual control rate unit is the output of the first nonlinear operation unit the output of the first error comparison unit and the output after the attack isolation algorithm and The output of the virtual control rate unit is calculated by the following formula i,2 :

[0086]

[0087] wherein, k i,1 is the virtual control rate parameter, k i,1 > 0,

[0088] The input of the first filter unit is the output of the virtual control rate unit i,2 , and the output of the first filter unit is calculated by the following formula i,2 :

[0089]

[0090] where θ i,2 is the time constant of the filter, θ i,2 > 0;

[0091] The input of the second error comparison unit is the output of the first filter unit κ i,2 and the state information of the quadrotor χ i,2 , and the output of the second error comparison unit e i,2 is obtained by the following calculation:

[0092] e i,2 = χ i,2 - κ i,2 ;

[0093] The input of the second nonlinear neural network activation function unit is the state information of the quadrotor χ i,1 and χ i,2 , and the output of the second nonlinear neural network activation function unit Φ i,2 is obtained by the following calculation:

[0094]

[0095] are the second nonlinear neural network activation functions in the x, y and z directions respectively, and x i,1 , y i,1 and z i,1 are the x, y and z direction information respectively, and are the x, y and z direction velocity information respectively, μ is the activation function center value, and ξ is the activation function width; and finally the output is obtained

[0096] The input of the second nonlinear neural network weight update unit is the output of the second nonlinear neural network activation function unit Φ i,2 and the long-term performance index unit output and the output of the second nonlinear neural network weight update unit is obtained by the following calculation:

[0097]

[0098] wherein, and are the outputs of the second nonlinear neural activation function unit in the x, y and z directions respectively, and are all elements in Φ i,2 , e i,2,x , e i,2,y and e i,2,zThese are the elements of the second error comparison unit in the x, y, and z directions, respectively, all of which are e. i,2 The elements in Γ i,2 Γ represents the weight gain of the long-term performance function of the second nonlinear neural network. i,2 >0; σ i,2 σ is the gain of the correction term in the long-term performance function of the second nonlinear neural network. i,2 >0, finally get the output

[0099] The input terminals of the second nonlinear operation unit are the output Φ of the second nonlinear neural network activation function unit. i,2 Output of weight update unit The output of the second nonlinear operation unit is obtained by multiplying all inputs.

[0100] The inputs of the consistency controller are respectively the outputs of the second nonlinear operation unit. The output e of the second error comparison unit i,2 and the output κ of the first filter unit i,2 The output u of the virtual control unit is obtained through calculation using the following formula. i :

[0101]

[0102] Where, k i,2 For controller parameters, k i,2 >0; For the weight update unit output, This is the output derivative of the first filter unit.

[0103] Compared with the prior art, the present invention has the following improvements and advantages:

[0104] 1. By improving the signal amplification technology of the Liu cryptographic system, the sensitivity of information is protected and the decryption error between plaintext encryption and decryption is reduced, ensuring privacy protection and satisfactory recovery of plaintext information; the consistency controller based on privacy protection reinforcement learning compensates for the unknown dynamics and errors between the real signal and the decrypted signal with a small number of learning parameters, ensuring the protection of sensitive information and network security of multi-quadrotor aircraft when performing missions.

[0105] 2. By using a network attack detection and isolation system, the number of learning parameters for the neural network used to approximate unknown dynamics in the attack detector and reinforcement learning-based controller is reduced, and the number of learning parameters is significantly reduced. It also ensures that other normal aircraft are not affected when an aircraft is under network attack. Attached Figure Description

[0106] Figure 1 is a structural schematic diagram of the system of the present application.

[0107] Figure 2 is a flow chart of the Liu cryptosystem.

[0108] Figure 3 is a flow chart of the attack check quarantine.

[0109] Figure 4 is a topology diagram of twelve normal quadrotors, two attacked quadrotors and a leader.

[0110] Figure 5 is a consistency trajectory 3D schematic diagram of twelve normal quadrotors, two attacked quadrotors and a leader.

[0111] Figure 6 is a consistency trajectory 2D schematic diagram of twelve normal quadrotors, two attacked quadrotors and a leader.

[0112] Figure 7 is a safety index schematic diagram of attack detection of twelve normal quadrotors, two attacked quadrotors.

[0113] Figure 8 is a quarantine index schematic diagram of attack detection of twelve normal quadrotors, two attacked quadrotors.

[0114] Figure 9 is a comparison curve comparison diagram of the y-axis direction information encryption and decryption information of the first quadrotor.

[0115] Figure 10 is a comparison curve comparison diagram of the y-axis direction information decryption error of the first quadrotor.

[0116] Figure 11 is a comparison curve comparison diagram of the x-axis direction attack detector of the third attacked quadrotor.

[0117] Figure 12 is a comparison curve comparison diagram of the x-axis direction attack detector of the seventh normal quadrotor. DETAILED DESCRIPTION

[0118] The present application is further described below in conjunction with the accompanying drawings.

[0119] As Figure 1As shown, a multi quadrotor aircraft position consistent control system based on attack isolation and privacy protection, the system comprises a Liu cipher system, a network attack detection and isolation system and a consistency control system, the Liu cipher system provides encrypted transmission of leader expectation signal and position information transmitted by followers to the leader, and decrypts the received information to obtain decrypted information at the information receiver;

[0120] The network attack detection and isolation system detects and isolates the attacked followers, the input ends of the consistency control system are connected with the output ends of the undirected graph G, and the output ends of the consistency control system are connected with the input ends of the i th follower;

[0121] The followers are N unknown dynamic quadrotor aircrafts, the N unknown dynamic quadrotor aircrafts and the 1 leader are connected through a directed topological graph to form a multi-agent network, and the multi-agent network is a controlled object.

[0122] Further, the mathematical model of the i th quadrotor aircraft of the follower is:

[0123]

[0124] Wherein, x i represents the x direction coordinate of the i th quadrotor aircraft, y i represents the y direction coordinate of the i th quadrotor aircraft, and z i represents the z direction coordinate of the i th quadrotor aircraft; is x direction acceleration information, is y direction acceleration information, is z direction acceleration information; is x direction velocity information, is y direction velocity information, is z direction velocity information; m i is the mass of the i th quadrotor aircraft, represents the x direction aerodynamic damping coefficient of the i th quadrotor aircraft, represents the y direction aerodynamic damping coefficient of the i th quadrotor aircraft, represents the z direction aerodynamic damping coefficient of the i th quadrotor aircraft, and g is the acceleration of gravity, u i is the control force of the i th quadrotor aircraft;

[0125] Let χ i，1 =[χ i,1,x ,χ i,1,y ,χ i,1,z ] T =[x i ,y i ,z i ]T and is the position system state and u i,x , u i,y , u i,z are virtual control inputs in x, y, z directions respectively;

[0126] quadrotor position system where u i = [u i,x , u i,y , u i,z ] T is the system input;

[0127] F i,f = f i + g i is the system unknown dynamics, where g i,χ = diag [1 / m i , 1 / m i , 1 / m i ];

[0128] sensor input containing noisy measurement is the system state χ i,1 of the quadrotor, and the output of the measured sensor with noisy measurement is

[0129] Liu decryption algorithm is ciphertext transmitted through the network, and the receiving end receives the ciphertext The input end of the Liu decryption algorithm is ciphertext obtained through the following calculation

[0130]

[0131] The input end of the signal reduction unit is the output of the improved Liu decryption algorithm obtain decryption information through the following calculation

[0132]

[0133] where k p is the amplification factor.

[0134] Improved Liu cipher system for privacy protection: signal amplification is to reduce the error between encryption and decryption. The amplification operation is performed on the plaintext before the encryption process, increasing its proportion in the ciphertext. According to the decryption algorithm, the decrypted plaintext is composed of two parts: one is the original plaintext, and the other is composed of a random number and a public key 0. The amplification of the plaintext causes the proportion of the part composed of a random number and a public key 0 to decrease. Therefore, by reducing the impact of the error between encryption and decryption on the plaintext, a satisfactory recovery of the plaintext information is achieved.

[0135] The network attack detection and isolation system comprises a finite-time attack detector, an attack detection unit and an attack isolation unit;

[0136] The input end of the attack detection unit and the attack isolation unit is the decrypted information output by the Liu cipher system The leader information after encryption and decryption And the sensor output information The output ε of the attack detection error unit is obtained by the following formula calculation i :

[0137]

[0138] The output of the attack detection error unit is connected to the input end of the finite-time attack detector i , and the output of the attack detector is obtained by the following formula calculation:

[0139]

[0140] wherein, μ is the center value of the activation function, ξ is the width of the activation function; c i is the gain of the finite-time attack detector correction term, c i > 0; Γ i is the weight gain of the finite-time attack detector, Γ i > 0; α i is the Young's inequality parameter, α i > 0;

[0141] The output of the attack detector is connected to the input end of the attack detection error comparison unit and the attack detection error unit ε i , and the output of the attack detection error comparison unit is obtained by the following calculation

[0142]

[0143] The specific process of attack detection is as follows:

[0144] Firstly, define: state index Qi = 1 means that there is an attacked agent in the subnet, otherwise Q i = 0 means that there is not;

[0145] Counter W i means that Q j = 1, j e J i The sum of;

[0146] Security index H i = 1 means that the agent is attacked, otherwise H i = 0 means that the agent is not attacked;

[0147] Isolation index P i = 1 means that the attacked agent is successfully isolated, otherwise P i = 0 means that the isolation fails;

[0148] When the output of the attack detection error comparison unit Where, is the set detection threshold, its state index Q i = 1, the counter W i = 1; the agent i transmits its state index Q i to its neighbors and queries the state index Q j of the neighbor agents, j e J i If Q j = 1, then the counter W i is incremented by 1; if W i = |J i |, then the security index H i = 1 means that the attacked agent is detected;

[0149] The attack isolation unit specifically operates as follows:

[0150] After the attack detection unit obtains the security index H i , it queries the security index H j of its neighbors, j e J i If H j = 1, then a ij = 0, Finally, if a ij = 0, then P i = 1.

[0151] Furthermore, the consistency control system includes an evaluation network and an execution network. The evaluation network includes a first error comparator, a utility function unit, a long-term performance index neural network weight update unit, a long-term performance index neural network activation function unit, and a long-term performance index unit. The execution network includes a first nonlinear function unit, a first nonlinear neural network activation function unit, a first nonlinear function neural network weight update unit, a virtual control law unit, a second error comparison unit, a second nonlinear function unit, a first filtering unit, a second nonlinear function neural network activation function unit, a second nonlinear function neural network weight update unit, and a consistency controller.

[0152] The inputs of the first error comparator are respectively connected to the neighbor's decrypted information after passing through the attack isolation unit. Leaders decrypt information Measurement information from noise measurement sensors for quadcopters

[0153] The input of the utility function unit is connected to the output of the first error comparator. The input of the long-term performance function neural network weight update unit is connected to the output p of the utility function unit. i,c The input of the activation function unit of the long-term performance function neural network is connected to the quadcopter's state information χ. i,1 Long-term performance The inputs of the exponent unit are connected to the outputs Φ of the activation function unit of the long-term performance function neural network. i,c The output of the neural network weight update unit for the long-term performance function;

[0154] The inputs of the first nonlinear function neural network weight update unit are respectively connected to the outputs of the first error comparator. Output of the Long-Term Performance Index Unit The output Φ of the activation function unit of the first nonlinear function neural network i,1 ;

[0155] The input of the activation function unit of the first nonlinear function neural network is connected to the quadcopter's state information χ. i,1 The input terminals of the first nonlinear function unit are respectively connected to the output Φ of the activation function unit of the first nonlinear function neural network. i,1 The output of the first nonlinear function neural network weight update unit

[0156] The input terminals of the virtual control unit are respectively connected to the neighbor decryption information after passing through the attack isolation unit. Leaders decrypt information The output of the first error comparator and the output of the first nonlinear function unit

[0157] The input of the first filter unit is connected to the output α of the virtual control rate unit i,2 ; the input of the second error comparison unit is connected to the state information χ of the quadrotor aircraft respectively i,2 and the output κ of the first filter unit i,2 ; the input of the second nonlinear function neural network weight update unit is connected to the output of the long-term performance index unit respectively The output e of the second error comparison unit i,2 and the output Φ of the second nonlinear function neural network activation function unit i,2 ;

[0158] The input of the second nonlinear function neural network activation function unit is connected to the state information χ of the quadrotor aircraft i,1 and χ i,2 ; the input of the second nonlinear function unit is connected to the output Φ of the second nonlinear function neural network activation function unit respectively i,2 , the output κ of the first filter unit i,2 and the output e of the second error comparison unit i,2 .

[0159] The design of the evaluation network is as follows:

[0160] The input of the first error comparator is connected to the output after the attack isolation unit and the sensor output information The output of the first error comparison unit is obtained by the following calculation

[0161]

[0162] The input of the utility function unit is the output of the first error comparison unit The output p of the utility function unit is obtained by the following calculation i,c :

[0163]

[0164] Wherein, γ is the discount factor, 0<γ<1; T is a small integral reinforcement interval, T>0;

[0165] The input of the long-term performance function neural network activation function unit is the state information X of the quadrotor aircraft i,1 , and the output Φ of the long-term performance function neural network activation function unit is obtained by the following formula i,c :

[0166]

[0167] are the activation functions of the long-term performance function neural network in x, y and z directions respectively; x i,1 , y i,1 and z i,1 are the system states in x, y and z directions respectively, μ is the center value of the activation function, and ξ is the width of the activation function;

[0168] The output is finally obtained as

[0169] The input of the long-term performance function neural network weight updating unit is the output p i,c of the utility function, and the output of the long-term performance function neural network weight updating unit is obtained through the following formula

[0170]

[0171] wherein, are the activation functions of the long-term performance function neural network in x, y and z directions respectively, Γ i,c is the long-term performance function weight gain, Γ i,c > 0; σ i,c is the long-term performance function correction term gain, σ i,c > 0; p i,c,x , p i,c,y and p i,c,z are the outputs of the utility function unit in x, y and z directions respectively, which are all elements in p i,c , and the output is finally obtained as

[0172] The input of the long-term performance index unit is the output Φ i,c of the long-term performance function neural network activation function unit and the output of the weight updating unit The output of the long-term performance index unit is obtained by multiplying all the inputs

[0173] The design of the execution network is as follows:

[0174] The input of the first nonlinear neural network activation function unit is the state information X i,1 of the quadcopter, and the output of the first nonlinear neural network activation function unit Φ i,1 is obtained through the following formula:

[0175]

[0176] are the activation functions of the first nonlinear neural network in x, y and z directions respectively; x i,1 , y i,1 and z i,1Let μ be the system state in the x, y, and z directions, ξ be the center value of the activation function, and ξ be the width of the activation function; finally, the output is obtained.

[0177] The input to the first nonlinear neural network weight update unit is the output Φ of the first nonlinear neural network activation function unit. i,1 and long-term performance index unit output The output of the first nonlinear neural network weight update unit is obtained through calculation using the following formula.

[0178]

[0179] Where, ||φ i,1,x ||、||φ i,1,y ||and||φ i,1,z || These are the outputs of the first nonlinear neural activation function unit in the x, y, and z directions, respectively, and are all outputs Φ. i,1 Elements in; and These are the elements of the first error comparison unit in the x, y, and z directions, respectively, and are all outputs. The elements in Γ i,c For the weighted gain of the long-term performance function, Γ i,c >0; σ i,c For the gain of the long-term performance function correction term, σ i,c >0; finally, the output is obtained.

[0180] The input terminals of the first nonlinear operation unit are the output terminals Φ of the first nonlinear neural network activation function unit. i,1 and the output of the weight update unit The output of the first nonlinear operation unit is obtained by multiplying all inputs.

[0181] The input terminals of the virtual control unit are respectively the output terminals of the first nonlinear operation unit. Output of the first error comparison unit Output after attack isolation algorithm and The output α of the virtual control unit is obtained by calculation using the following formula. i,2 :

[0182]

[0183] Where, k i,1 k is the virtual control law parameter. i,1 >0,

[0184] The input of the first filter unit is the output α of the virtual control rate unit i,2 The output κ of the first filter unit is calculated by the following formula i,2 :

[0185]

[0186] Where θ i,2 is the time constant of the filter, and θ i,2 > 0

[0187] The input of the second error comparison unit is the output κ of the first filter unit i,2 and the state information χ of the quadcopter i,2 The output e of the second error comparison unit is calculated by the following formula i,2 :

[0188] e i,2 = χ i,2 - κ i,2 ;

[0189] The input of the second nonlinear neural network activation function unit is the state information χ of the quadcopter i,1 and χ i,2 The output Φ of the second nonlinear neural network activation function unit is calculated by the following formula i,2 :

[0190]

[0191]

[0192] are the second nonlinear neural network activation functions in the x, y, and z directions, respectively i,1 , y i,1 , and z i,1 are the x, y, and z direction information, respectively and are the x, y, and z direction velocity information, respectively, μ is the activation function center value, and ξ is the activation function width

[0193] The input of the second nonlinear neural network weight update unit is the output Φ of the second nonlinear neural network activation function unit i,2 and the output of the long-term performance index unit The output of the second nonlinear neural network weight update unit is calculated by the following formula

[0194]

[0195] Where and are the outputs of the second nonlinear neural activation function unit in x, y and z directions, respectively, both are Φ i,2 are the elements in e i,2,x , e i,2,y and e i,2,z are the elements of the second error comparison unit in x, y and z directions, respectively, both are e i,2 are the elements in Γ i,2 is the second nonlinear neural network long-term performance function weight gain, Γ i,2 > 0; σ i,2 is the second nonlinear neural network long-term performance function correction term gain, σ i,2 > 0, and finally the output is obtained

[0196] The input ends of the second nonlinear operation unit are the outputs of the second nonlinear neural network activation function unit Φ i,2 and the output of the weight update unit The product of all input ends is calculated to obtain the output of the second nonlinear operation unit

[0197] The input ends of the consistency controller are the output of the second nonlinear operation unit The output of the second error comparison unit e i,2 and the output of the first filter unit κ i,2 ; the output of the virtual control rate unit u i is obtained by the following formula:

[0198]

[0199] where k i,2 is the controller parameter, k i,2 > 0; is the output of the weight update unit, is the derivative of the output of the first filter unit.

[0200] As shown in Figure 4 , the system selects a multi-four-rotor aircraft system of fourteen followers and one leader as an example to verify the effect of the system:

[0201] Among them, the mathematical model of the fourteen four-rotor aircraft is:

[0202]

[0203] where x i represents the x-direction coordinate of the i-th four-rotor aircraft, y i represents the y-direction coordinate of the i-th four-rotor aircraft, and z idenotes the z-direction coordinate of the i-th quadrotor; is the x-direction acceleration information, is the y-direction acceleration information, is the z-direction acceleration information; is the x-direction velocity information, is the y-direction velocity information, is the z-direction velocity information; m i is the mass of the i-th quadrotor, denotes the x-direction aerodynamic damping coefficient of the i-th quadrotor, denotes the y-direction aerodynamic damping coefficient of the i-th quadrotor, denotes the z-direction aerodynamic damping coefficient of the i-th quadrotor, g is the gravitational acceleration, u i is the control force of the i-th quadrotor;

[0204] Let χ i，1 = [χ i,1,x , χ i,1,y , χ i,1,z ] T = [x i , y i , z i ] T and is the position system state and u i,x , u i,y , u i,z are the virtual control inputs in the x, y, z directions, respectively;

[0205] Quadrotor position system where u i = [u i,x , u i,y , u i,z ] T is the system input;

[0206] F i,f = f i + g i is the system unknown dynamics, where g i,χ = diag [1 / m i , 1 / m i , 1 / m i ];

[0207] The sensor input with noisy measurements is the system state χ i,1 of the quadrotor, and the output of the sensor with noisy measurements is

[0208] Four quadrotor model parameters are chosen: gravitational acceleration g = 9.8 m / s 2 , mass m = 2 kg, aerodynamic drag coefficient Vehicle control parameters are chosen: k i,1 = diag[55, 55, 55], k i,2 = diag[5, 5, 1], Γ i,c = 10, Γ i,1 = 1.2, Γ i,2 = 1.2, σ i,c = 0.5, σ i,1 = 0.2, σ i,2 = 0.2, c pi = 0.01, γ i = 0.6, p i = 0.6, attack detector parameters are chosen: Γ i,a = 10, a i = 15, c i,a = 10, β i = 0.99 All parameters i = 1, 2, …, 14;

[0209] Leader signal χ d (t) = [cos(0.3t), sin(0.3t), 0.5t] T (m);

[0210] 1st vehicle initial position χ 1,1 (0) = (0.51, 0.03, 0) (m); 2nd vehicle initial position χ 2,1 (0) = (1.33, 0.05, 0) (m);

[0211] 3rd vehicle initial position χ 3,1 (0) = (-0.49, 0.02, 0) (m); 4th vehicle initial position χ 4,1 (0) = (1.28, -0.1, 0) (m);

[0212] 5th vehicle initial position χ 5,1 (0) = (0.17, -0.08, 0) (m); 6th vehicle initial position χ 6,1 (0) = (1.17, -0.08, 0) (m);

[0213] 7th vehicle initial position χ 7,1 (0) = (-1.17, -0.08, 0) (m); 8th vehicle initial position χ 8,1 (0) = (1.17, -0.08, 0) (m);

[0214] 9th vehicle initial position χ9,1 (0) = (1.18, -0.08, 0) (m); 10th machine initial position χ 10,1 (0) = (1.3, -0.08, 0) (m);

[0215] 11th machine initial position χ 11,1 (0) = (1.3, -0.08, 0) (m); 12th machine initial position χ 12,1 (0) = (0.3, -0.08, 0) (m);

[0216] 13th machine initial position χ 13,1 (0) = (1.3, -0.08, 0) (m); 14th machine initial position χ 14,1 (0) = (0.3, -0.08, 0) (m).

[0217] As shown in Figure 5 , 6 , fourteen quadcopters and leaders achieve consensus while isolating the attacked quadcopter; as Figure 7 and Figure 8 give the curve of safety index P i , isolation index H i , it can be seen that the attacked 3rd and 5th machines are attacked with safety index 1 and successfully isolated; Figure 9 , 10 show the difference between the y direction state information of the 1st machine and the Liu cipher system and the improved Liu cipher system, it can be seen that the decrypted information of the improved Liu cipher system is closer to the real information and the decryption error tends to 0.

[0218] Figure 11 show that the attack detector cannot estimate the attack detection error when the 3rd machine is attacked, thus the error generated by the subsequent attack detection and isolation algorithm. Figure 12 show that the attack detector accurately estimates the attack detection error of the 7th machine.

[0219] The above only describes the embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the scope of claims of the present application.

Claims

1. A multi quadrotor aircraft position consensus control system based on attack isolation and privacy protection, characterized in that: The system comprises a Liu cipher system, a network attack detection and isolation system and a consistency control system, the Liu cipher system provides encrypted transmission of leader expectation signals and position information transmitted by followers, and decryption is performed at the information receiving end to obtain decrypted information; The network attack detection and isolation system detects and isolates an attacked follower, the input ends of the consistency control systems are connected with the output ends of the undirected graph , and the output ends of the consistency control systems are connected with the input ends of the first follower. The Liu cipher system comprises a plaintext information acquisition unit, a signal amplification unit, a Liu encryption algorithm, generated ciphertext transmitted through a network, a follower receiving the ciphertext, a Liu decryption algorithm, a signal reduction unit and a decrypted information acquisition unit; The Liu encryption algorithm includes three parts, the first part is the input end of the signal amplification unit in the encryption algorithm is the sensor output information of the quadrotor aircraft , the output is calculated by the following formula : ； wherein is the magnification factor; The second part is to generate four random numbers , , With , , constitutes a private key ; The third part is ciphertext obtained by calculating the following formula : ； Computing an output ciphertext and transmitting over a network; The Liu decryption algorithm is a ciphertext Through network transmission, the receiving end receives the ciphertext The input end of the Liu decryption algorithm is a ciphertext The following calculations are performed : ； The input end of the signal reduction unit is the output of the improved Liu decryption algorithm The decryption information is obtained through the following calculation : ； wherein is the magnification factor; The network attack detection and isolation system comprises a finite time attack detector, an attack detection unit and an attack isolation unit, and the consistency control system comprises a first error comparator, an utility function unit, a long-term performance index neural network weight update unit, a long-term performance index neural network activation function unit, a long-term performance index unit, a first nonlinear function unit, a first nonlinear neural network activation function unit, a first nonlinear function neural network weight update unit, a virtual control rate unit, a second error comparison unit, a second nonlinear function unit, a first filter unit, a second nonlinear function neural network activation function unit, a second nonlinear function neural network weight update unit and a consistency controller.

2. The multi quadrotor aircraft position consensus control system based on attack isolation and privacy protection of claim 1, wherein: The inputs of the first error comparator are respectively connected to the neighbor decryption information after passing through the attack isolation unit. Leaders decrypt information Measurement information from noise measurement sensors for quadcopters ; An input terminal of the utility function unit is connected to an output of the first error comparator An input terminal of the long-term performance function neural network weight update unit is connected to an output of the utility function unit An input terminal of the long-term performance function neural network activation function unit is connected to the quadcopter state information An input terminal of the long-term performance An input terminal of the long-term performance function neural network activation function unit is connected to the quadcopter state information An input terminal of the long-term performance function neural network weight update unit is connected to an output of the utility function unit The input end of the first non-linear function neural network weight updating unit is connected with the output of the first error comparator , the output of the long-term performance index unit , and the output of the first non-linear function neural network activation function unit ​ An input end of the first nonlinear function neural network activation function unit is connected with the quadrotor state information An input end of the first nonlinear function unit is respectively connected with an output of the first nonlinear function neural network activation function unit and an output of the first nonlinear function neural network weight updating unit ​ The input terminals of the virtual control rate unit are connected to the neighbor decryption information and the leader decryption information after passing through the attack isolation unit The output of the first error comparator and the output of the first nonlinear function unit ;​​ The input of the first filter unit is connected to the output of the virtual control rate unit ; the input of the second error comparison unit is respectively connected to the quadrotor state information and the output of the first filter unit ; the input of the second nonlinear function neural network weight update unit is respectively connected to the output of the long-term performance index unit , the output of the second error comparison unit and the output of the second nonlinear function neural network activation function unit ; An input terminal of the second nonlinear function neural network activation function unit is connected to the quadcopter state information With An input terminal of the second nonlinear function unit is connected to an output of the second nonlinear function neural network activation function unit , an output of the first filter unit , and an output of the second error comparison unit .

3. The position consensus control system for multiple quad-rotor aircraft based on attack isolation and privacy protection of claim 2, wherein: The followers are N unknown dynamic quadrotors, the N unknown dynamic quadrotors and the 1 leader are connected through a directed topological graph to form a multi-agent network, and the multi-agent network is a controlled object; The maximum number of followers in a multi-agent network is attacked by a network attack and at least There is communication between at least one follower and the leader, and the communication is represented by a direction; directed graph ; wherein, , denotes a set of four nodes; denotes quadcopter follower 1 to quadcopter follower ; denotes a set of edges, denotes a topological graph of edges, denotes the ith aircraft and the jth aircraft, respectively; if then is an adjacent node of denotes an adjacent node of define the adjacency matrix if then else ; defining a degree matrix wherein, ; define the Laplacian matrix , define the adjacency matrix related to the leader , if the i-th aircraft has access to the leader's information, , otherwise .

4. The multi quadcopter aircraft position consensus control system based on attack isolation and privacy protection of claim 3, wherein: The mathematical model of the fourth quadcopter of the follower is: ​ ； wherein, represents an x-direction coordinate of the i-th quadcopter, represents a y-direction coordinate of the i-th quadcopter, represents a z-direction coordinate of the i-th quadcopter; is x-direction acceleration information, is y-direction acceleration information, is z-direction acceleration information; is x-direction velocity information, is y-direction velocity information, is z-direction velocity information; is the mass of the i-th quadcopter, represents an x-direction air-dynamic damping coefficient of the i-th quadcopter, represents a y-direction air-dynamic damping coefficient of the i-th quadcopter, represents a z-direction air-dynamic damping coefficient of the i-th quadcopter, is the gravitational acceleration, is the control force of the i-th quadcopter; Let and be the position system states and , , , be the virtual control inputs in the directions of , , , respectively. Quadcopter position system wherein is the system input; unknown dynamics to the system, where , ; Sensor inputs containing noisy measurements for system states of a quadrotor , the outputs of the sensors with measured noisy measurements are .

5. The multi quadcopter aircraft position consensus control system based on attack isolation and privacy protection of claim 4, wherein: The input of the attack detection unit and attack isolation unit is the decrypted information output from the Liu cryptosystem , the decrypted leader information and the sensor output information The output of the attack detection error unit is obtained by the following formula : ； The input of the finite-time attack detector is connected to the output of the attack detection error unit The output of the attack detector is obtained by calculation of the following equation: ； wherein, , ; , ; is an activation function center value, is an activation function width; is a finite-time attack detector correction term gain, ; is a finite-time attack detector weight gain, ; is a Young’s inequality parameter, ; The input of the attack detection error comparison unit is connected to the output of the attack detector The attack detection error comparison unit is connected to the attack detection error unit The output of the attack detection error comparison unit is obtained by the following calculation : ； The attack detection specific process is as follows: First, define: state index denotes that there is an attacked agent in the subnet, otherwise denotes no; counter representing sums Security Index represents that the agent is under attack, otherwise represents that it is not under attack; Isolation Index Indicates that the attacked agent was successfully isolated, otherwise Isolation failed; When the attack detection error comparison unit outputs ,in, To set the detection threshold, its state index ,calculator intelligent agent Transmit its status index to neighbors And query the state index of neighboring agents. ,if Then the counter Add 1; if So, what is the safety index? This indicates that an attacked agent has been detected; The attack isolation unit has the following specific operation process: obtaining a security index by an attack detection unit , querying the security index of its neighbors , if , then , ; finally, if , then .

6. The multi quadcopter aircraft position consensus control system based on attack isolation and privacy protection of claim 5, wherein: The input terminals of the first error comparator in the consistency control system are respectively connected to the output after the attack isolation unit , and the sensor output information , and the first error comparator unit output is obtained through the following calculation : ； The utility function unit input is the output of the first error comparison unit The output of the utility function unit is obtained by the following calculation : ； wherein is a discount factor, ; is a small interval of integration, ; An input end of the long-term performance function neural network activation function unit is state information of the quadrotor aircraft The long-term performance function neural network activation function unit outputs, through calculation of the following formula : , , are activation functions of long-term performance function neural networks in x, y and z directions, respectively; , and are system states in x, y and z directions, respectively, is a center value of activation function, is a width of activation function; Finally the output is obtained: ; The input of the long-term performance function neural network weight updating unit is the output of the utility function The output of the long-term performance function neural network weight updating unit is obtained by the following formula : ； ； ； wherein, , , are activation functions of the long-term performance function neural network in x, y and z directions, respectively, is a long-term performance function weight gain, ; is a long-term performance function correction term gain, ; , and are outputs of the utility function units in x, y and z directions, respectively, are elements in , which then results in the output ; The input end of the long-term performance index unit is respectively the output of the long-term performance function neural network activation function unit and the output of the weight updating unit ; the long-term performance index unit output is obtained by multiplying all the input ends .

7. The multi quadcopter aircraft position consensus control system based on attack isolation and privacy protection of claim 6, wherein: The input end of the first nonlinear neural network activation function unit in the consistency control system is state information of the quadrotor aircraft The first nonlinear neural network activation function unit is obtained through the following formula : , , are the first non-linear neural network activation functions in x, y and z directions, respectively; , and are the system states in x, y and z directions, respectively, is the activation function center value, is the activation function width; and finally the output is obtained. An input of the first nonlinear neural network weight update unit is an output of the first nonlinear neural network activation function unit and the long-term performance index unit output ; The first non-linear neural network weight update unit output is obtained by calculation of the following formula : 、 、 ； wherein, , and are the outputs of the first non-linear neural activation function units in the x, y and z directions, respectively, and are elements of the output ; , and are elements of the first error comparison units in the x, y and z directions, respectively, and are elements of the output , is the long-term performance function weight gain, ; is the long-term performance function correction term gain, ; and the output ; The input ends of the first nonlinear operation unit are respectively the outputs of the first nonlinear neural network activation function unit and the weight update unit ; and the product of all the input ends is the output of the first nonlinear operation unit ; The input terminals of the virtual control rate unit are respectively the output of the first non-linear operation unit , the output of the first error comparison unit and the output after the attack isolation algorithm and ; the output of the virtual control rate unit is obtained through the following formula : ； wherein is a virtual control rate parameter, , ; The input of the first filter unit is the output of the virtual control rate unit The output of the first filter unit is calculated by the following equation : ； wherein is a time constant of the filter, ; An input of the second error comparison unit is an output of the first filter unit state information of the quadcopter The output of the second error comparison unit is obtained by the following calculation : ； An input end of the second nonlinear neural network activation function unit is state information of the quadcopter With The second nonlinear neural network activation function unit is calculated by the following formula : , , are the second nonlinear neural network activation functions in x, y and z directions respectively; , and are the x, y and z direction information respectively, , and are the x, y and z direction velocity information respectively, is the activation function center value, is the activation function width; finally the output is obtained. An input of the second nonlinear neural network weight update unit is an output of the second nonlinear neural network activation function unit and the long-term performance index unit output The second nonlinear neural network weight update unit output is calculated by the following equation : ； ； ； wherein, , and are the outputs of the second non-linear neural activation function unit in the x, y and z directions, respectively, and are elements of , , and are the elements of the second error comparison unit in the x, y and z directions, respectively, and are elements of , is the second non-linear neural network long-term performance function weight gain, ; is the second non-linear neural network long-term performance function correction term gain, , and the output is finally obtained. The input ends of the second nonlinear operation unit are respectively the outputs of the second nonlinear neural network activation function units and the weight update unit output ; and the product of all the input ends is calculated to obtain the output of the second nonlinear operation unit ; The input of the consistency controller is the output of the second non-linear operation unit , the output of the second error comparison unit , and the output of the first filter unit ; the output of the virtual control rate unit is calculated by the following formula : ； wherein is a controller parameter, ; is a weight update unit output, is an output derivative of the first filter unit.

Images