Position consistency control system of multi-four-rotor aircraft based on attack isolation and privacy protection

Abstract

The invention discloses a multi-four-rotor aircraft position consistency control system based on attack isolation and privacy protection, and belongs to the technical field of industrial process control. Comprising a Liu password system, a network attack detection and isolation system and a consistency control system, and the Liu password system carries out encryption transmission on a provided leader expected signal and position information and obtains decryption information; the network attack detection and isolation system detects and isolates attacked followers, the input end of the consistency control system is connected with the output end of the undirected graph G, and the output end of the consistency control system is connected with the input end of the ith follower. Through the signal amplification technology of the Liu password system, the sensitivity of information is protected, and the error between plaintext encryption and decryption is reduced; and the consistent controller compensates unknown dynamic states and errors between real signals and decryption signals through a small number of learning parameters, and ensures protection of sensitive information and network security when the multi-four-rotor aircraft executes tasks.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial process control, and in particular relates to a position consistency control system for multiple quad-rotor aircraft based on attack isolation and privacy protection. Background Art

[0002] In modern industrial and military fields, multi-quadrotor aircraft have attracted widespread attention due to their flexibility and versatility. These aircraft require a high degree of 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 terms of privacy protection and security.

[0003] Privacy protection is becoming increasingly important in the application of multi-quadrotors. These aircraft may collect and transmit sensitive data, such as geographic information, image data, etc. when performing their missions. If these data are obtained by unauthorized third parties, they may pose a threat to personal privacy or national security. Therefore, designing a multi-quadrotor control system that can protect privacy is crucial to ensure data security and user trust.

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

[0005] In the study of consistency control of multiple quadrotors, how to design a control system that can both protect privacy and resist external attacks is a challenging problem. This requires comprehensive consideration of the dynamic characteristics of the aircraft, the security of the control algorithm, the encryption technology of the communication protocol, and the attack detection and response strategy.

[0006] Despite the fruitful results related to cyber attacks, Liu cryptographic systems, and reinforcement learning techniques, some technical gaps still exist.

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

[0008] The existing Liu cryptosystem utilizes a large number of random sequences to create ciphertext. While these random numbers enhance privacy, they introduce decryption errors between plaintext and decrypted text. There is a lack of theoretical improvements to mitigate the decryption errors caused by random numbers, and further technological advances are needed in this regard.

[0009] Most existing reinforcement learning-based control schemes and cyber 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 increases accordingly. More seriously, these numbers will further grow dramatically as the number of quadrotors increases. This involves a considerable order of magnitude.

[0010] In summary, how to solve the sensitive protection and network security of multiple quadrotor aircraft when performing tasks, thereby improving their stability and reliability in complex environments is the technical problem that the present invention aims to solve. Summary of the invention

[0011] The object of the present invention is to provide a position consistency control system for multiple quadrotor aircraft based on attack isolation and privacy protection to solve the problems raised in the above background technology.

[0012] The object of the present invention is achieved as follows: the system includes a Liu cryptographic system, a network attack detection and isolation system, and a consistency control system. The Liu cryptographic system encrypts and transmits the leadership expectation signal provided by the leader and the location information transmitted by the follower, and decrypts the information at the information receiving end to obtain the decrypted information;

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

[0014] The Liu cryptographic system obtains a plaintext information unit, a signal amplification unit, a Liu encryption algorithm, generates ciphertext, transmits the ciphertext to a follower through a network, receives the ciphertext, the Liu decryption algorithm, a signal reduction unit, and obtains a decrypted information 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 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 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 ends of the first error comparator are respectively connected to the neighbor decrypted information after passing through the attack isolation unit Leaders Decrypt Information and quadrotor aircraft noise measurement sensor measurement information

[0017] The input terminal of the utility function unit is connected to the output of the first error comparator The input of the weight update unit of the long-term performance function neural network is connected to the output p of the utility function unit i,c , the input end of the activation function unit of the long-term performance function neural network is connected to the state information of the quadrotor aircraft χ i,1 ; Long-term performance The input of the index unit is connected to the output of the long-term performance function neural network activation function unit Φ i,c and the output of the neural network weight update unit of the long-term performance function;

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

[0019] The input end of the first nonlinear neural network activation function unit is connected to the quadrotor state information χ i,1 ; The input ends of the first nonlinear function unit are respectively connected to the output Φ of the first nonlinear function neural network activation function unit i,1 and the output of the first nonlinear function neural network weight update unit

[0020] The input end of the virtual control rate unit is connected to the neighbor decrypted 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 end of the first filter unit is connected to the output α of the virtual control rate unit i,2 The input ends of the second error comparison unit are connected to the quadrotor status information x i,2 and the output κ of the first filter unit i,2 The input ends of the second nonlinear function neural network weight update unit are respectively connected to the output ends of the long-term performance index unit The output of the second error comparison unit i,2 and the output Φ of the second nonlinear neural network activation function unit i,2 ;

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

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

[0024] In a multi-agent network, at most F followers are attacked by the network and at least F followers communicate with the leader, where the communication is represented by directed;

[0025] Directed graph G = (V, E); where V = {ν 1 ,…,ν N}, represents a set of N nodes; ν 1 ,…,ν N Indicates quadrotor follower 1 to quadrotor follower N;

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

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

[0028] Define the degree matrix D = diag[d 1 ,...,d N ],in,

[0029] Define the Laplacian matrix L = DA, and define the adjacency matrix associated with the leader B = diag[b 1 ,…,b N ], if the i-th aircraft can access the leader's information, then b i =1, otherwise b i =0.

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

[0031]

[0032] Among them, x i represents the x-direction coordinate of the i-th quadrotor, y i represents the y-direction coordinate of the i-th quadrotor, z i represents the z-direction coordinate of the i-th quadrotor; is the acceleration information in the x direction, is the direction acceleration information, is the acceleration information in the z direction; is the x-direction velocity information, is the velocity information in the y direction, is the velocity information in the z direction; m i is the mass of the ith quadrotor, represents the aerodynamic damping coefficient in the x direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the y direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the z direction of the i-th quadrotor, g is the gravitational acceleration, u i is the control force of the ith quadrotor;

[0033] Let xi，1 =[χ i,1,x ,x i,1,y ,x i,1,z ] T =[x i ,y i ,z i ] T and for the location system status and u i,x 、u i,y 、u i,z They are the virtual control inputs in the x, y, and z directions respectively;

[0034] Quadcopter Positioning System where u i =[u i,x ,u i,y ,u i,z ] T Input for the system;

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

[0036] The sensor input containing the noisy measurement is the system state χ of the quadrotor i,1 , the output of the sensor after measuring the noisy measurement is

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

[0038]

[0039] Among them, k p is the magnification;

[0040] The second part is to generate four random numbers r i ,q i ,t i With s i , i = 1, ..., M, forming a private key K(M) = {(q 1 ,r 1 ,t 1 ),…,(qM ,r M ,t M )};

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

[0042] c 1 =q 1 t 1 m A +s 1 r M +q 1 (r 1 -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] After calculation, the output ciphertext and transmitted on the network.

[0046] Preferably, the Liu decryption algorithm is a ciphertext Transmitted over the network, the receiving end receives the ciphertext The input of Liu decryption algorithm is ciphertext The following calculations are obtained

[0047]

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

[0049]

[0050] Among them, k p is the magnification.

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

[0052]

[0053] The input of the finite time attack detector is connected to the output ε of the attack detection error unit i , the output of the attack detector is obtained by calculating the following formula:

[0054]

[0055] in, μ is the center value of the activation function, ξ is the width of the activation function; c i is the finite time attack detector correction gain, 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;

[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 through the following calculation

[0057]

[0058] The specific process of attack detection is as follows:

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

[0060] Counter W i Indicates Q j =1, j∈J i of and;

[0061] Safety Index H i =1 means the agent is attacked, otherwise H i =0 means no attack;

[0062] Isolation Index P i =1 means the attacked agent is successfully isolated, otherwise P i=0 Isolation failed;

[0063] When the output of the attack detection error comparison unit in, To set the detection threshold, its state index Q i =1, calculator W i =1; Agent i transmits its state index Q to its neighbors i And query the state index Q of the neighboring agent j , j∈J i , if Q j =1, then the counter W i Add 1; if W i =|J i |, then the safety index H i =1 means that an attacked agent is detected;

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

[0065] The security index H is obtained through 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, Finally, if a ij =0, then P i =1.

[0066] Preferably, the input end of the first error comparator in the consistency control system is respectively connected to the attack isolation unit and the output And sensor output information The output of the first error comparison unit is obtained by the following calculation

[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 by the following calculation 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 of the activation function unit of the long-term performance function neural network is the state information of the quadrotor aircraft χ i,1 , the long-term performance function neural network activation function unit output Φ is calculated by the following formula i,c :

[0071]

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

[0073] Finally, the output is:

[0074] The input of 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 neural network weight update unit output is obtained by calculating the following formula

[0075]

[0076] in, are the activation functions of the neural network for the long-term performance function in the x, y and z directions, Γ i,c is the weight gain of the long-term performance function, Γ i,c >0;σ i,c is the gain of the correction term of the long-term performance function, 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 the x, y and z directions, all p i,c The elements in the output are

[0077] The input of the long-term performance index unit is the output of the long-term performance function neural network activation function unit Φ i,c and the output of the weight update unit The long-term performance index unit output is calculated by multiplying all input terminals.

[0078] Preferably, the input end of the first nonlinear neural network activation function unit in the consistency control system is the state information x of the quadrotor aircraft. i,1 , the first nonlinear neural network activation function unit Φ is obtained by calculating the following formula i,1 :

[0079]

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

[0081] The input end of 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 by calculating the following formula:

[0082]

[0083] Among them, ||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 all output Φ i,1 Elements in and They are the elements of the first error comparison unit in the x, y and z directions, and are output The elements in Γ i,c is the weight gain of the long-term performance function, Γ i,c >0;σ i,c is the gain of the correction term of the long-term performance function, σ i,c >0; finally get the output

[0084] The input ends of the first nonlinear operation unit are the output Φ of the first nonlinear neural network activation function unit. i,1 and the output of the weight update unit All inputs are multiplied to obtain the output of the first nonlinear operation unit.

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

[0086]

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

[0088] The input end 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 :

[0089]

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

[0091] The input end of the second error comparison unit is the output κ of the first filtering unit. i,2 The status information of the quadrotor i,2 , the output e of the second error comparison unit is obtained through the following calculation i,2 :

[0092] e i,2 = x i,2 -κ i,2 ;

[0093] The input end of the second nonlinear neural network activation function unit is the state information χ of the quadrotor i,1 With χ i,2 , the second nonlinear neural network activation function unit Φ is calculated by the following formula i,2 :

[0094]

[0095] 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 x, y and z direction information respectively, and are the speed information in the x, y and z directions respectively, μ is the center value of the activation function, ξ is the width of the activation function; finally, the output is

[0096] The input end 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 long-term performance index unit output The output of the second nonlinear neural network weight update unit is obtained by calculating the following formula:

[0097]

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

[0099] The input ends of the second nonlinear operation unit are respectively the output Φ of the second nonlinear neural network activation function unit i,2 And the weight update unit output All inputs are multiplied to obtain the output of the second nonlinear operation unit.

[0100] The input terminals of the consistency controller are the output terminals of the second nonlinear operation unit The output 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 rate unit is calculated by the following formula: i :

[0101]

[0102] Among them, k i,2 is the controller parameter, k i,2 >0; is the output of the weight update unit, is the output derivative of the first filtering 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 consistent controller based on privacy-preserving reinforcement learning compensates for the unknown dynamics and errors between the real signal and the decrypted signal through a smaller number of learning parameters, ensuring the protection of sensitive information and network security of multi-quadrotors when performing missions.

[0105] 2. Through the network attack detection and isolation system, the number of learning parameters of the neural network used to approximate unknown dynamics in the attack detector and the reinforcement learning-based controller is significantly reduced, and it is ensured that other normal aircraft are not affected when the aircraft is attacked by the network. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 It is a schematic diagram of the structure of the system of the present invention.

[0107] Figure 2 This is the flow chart of Liu's cryptographic system.

[0108] Figure 3 Check the Isolation Flowchart for the attack.

[0109] Figure 4 The topological structure diagram of twelve normal quadrotors, two attacked quadrotors and the leader.

[0110] Figure 5 3D schematic diagram of the consistent trajectories of twelve normal quadrotors, two attacked quadrotors and the leader.

[0111] Figure 6 2D schematic diagram of the consensus trajectories of twelve normal quadrotors, two attacked quadrotors, and the leader.

[0112] Figure 7 Schematic diagram of the safety index for attack detection of twelve normal quadrotors and two attacked quadrotors

[0113] Figure 8 Schematic diagram of the isolation index for attack detection of twelve normal quadrotors and two attacked quadrotors.

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

[0115] Fig.10 This is a comparison curve of the y-axis information decryption error of the first quadrotor aircraft.

[0116] Fig.11 This is a comparison chart of the attack detector comparison curves in the x-axis direction of the third attacked quadrotor.

[0117] Fig.12 This is a comparison chart of the attack detector comparison curves of the seventh normal quadrotor in the x-axis direction. DETAILED DESCRIPTION

[0118] The present invention is further summarized below with reference to the accompanying drawings.

[0119] like Figure 1 As shown, a position consistency control system for multiple quad-rotor aircraft based on attack isolation and privacy protection, the system includes a Liu cryptographic system, a network attack detection and isolation system, and a consistency control system. The Liu cryptographic system encrypts and transmits the leadership expectation signal provided by the leader and the position information transmitted by the follower, and decrypts the information at the information receiver to obtain the decrypted information;

[0120] The network attack detection and isolation system detects the attacked follower and isolates it. The input ends of the consistency control system are all connected to the output ends of the undirected graph G, and the output ends of the consistency control system are all connected to the input ends of the i-th follower.

[0121] The followers are N quadrotors with unknown dynamics. The N quadrotors with unknown dynamics and one leader are connected through a directed topological graph to form a multi-agent network, and the multi-agent network is the controlled object.

[0122] Furthermore, the mathematical model of the i-th quadrotor aircraft is:

[0123]

[0124] Among them, x i represents the x-direction coordinate of the i-th quadrotor, y i represents the y-direction coordinate of the i-th quadrotor, z i represents the z-direction coordinate of the i-th quadrotor; is the acceleration information in the x direction, is the direction acceleration information, is the acceleration information in the z direction; is the x-direction velocity information, is the velocity information in the y direction, is the velocity information in the z direction; m i is the mass of the ith quadrotor, represents the aerodynamic damping coefficient in the x direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the y direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the z direction of the i-th quadrotor, g is the gravitational acceleration, u i is the control force of the ith quadrotor;

[0125] Let x i，1 =[χ i,1,x ,x i,1,y ,x i,1,z ] T =[x i,y i ,z i ] T and for the location system status and u i,x 、u i,y 、u i,z They are the virtual control inputs in the x, y, and z directions respectively;

[0126] Quadcopter Positioning System where u i =[u i,x ,u i,y ,u i,z ] T Input for the system;

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

[0128] The sensor input containing the noisy measurement is the system state χ of the quadrotor i,1 , the output of the sensor after measuring the noisy measurement is

[0129] Liu decryption algorithm for ciphertext Transmitted over the network, the receiving end receives the ciphertext The input of Liu decryption algorithm is ciphertext The following calculations are obtained

[0130]

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

[0132]

[0133] Among them, k p is the magnification.

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

[0135] The network attack detection and isolation system includes a limited time attack detector, an attack detection unit and an attack isolation unit;

[0136] The input of the attack detection unit and the attack isolation unit is the decrypted information output by the Liu cryptographic system Encrypted and decrypted leader information Sensor output information The output ε of the attack detection error unit is obtained by calculating the following formula: i :

[0137]

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

[0139]

[0140] in, μ is the center value of the activation function, ξ is the width of the activation function; c i is the finite time attack detector correction gain, 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 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 through the following calculation

[0142]

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

[0144] First define: state index Qi =1 means there is an attacked agent in the subnet, otherwise Q i =0 means no;

[0145] Counter W i Indicates Q j =1, j∈J i of and;

[0146] Safety Index H i =1 means the agent is attacked, otherwise H i =0 means no attack;

[0147] Isolation Index P i =1 means the attacked agent is successfully isolated, otherwise P i =0 Isolation failed;

[0148] When the output of the attack detection error comparison unit in, To set the detection threshold, its state index Q i =1, calculator W i =1; Agent i transmits its state index Q to its neighbors i And query the state index Q of the neighboring agent j , j∈J i , if Q j =1, then the counter W i Add 1; if W i =|J i |, then the safety index H i =1 means that an attacked agent is detected;

[0149] The specific operation process of the attack isolation unit is as follows:

[0150] The security index H is obtained through 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, Finally, if a ij =0, then P i =1.

[0151] Further, 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 rate 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 input ends of the first error comparator are respectively connected to the neighbor decrypted information after passing through the attack isolation unit Leaders Decrypt Information and quadrotor aircraft noise measurement sensor measurement information

[0153] The input terminal of the utility function unit is connected to the output of the first error comparator The input of the weight update unit of the long-term performance function neural network is connected to the output p of the utility function unit i,c , the input end of the activation function unit of the long-term performance function neural network is connected to the state information of the quadrotor aircraft χ i,1 ; Long-term performance The input of the index unit is connected to the output of the long-term performance function neural network activation function unit Φ i,c and the output of the neural network weight update unit of the long-term performance function;

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

[0155] The input end of the first nonlinear neural network activation function unit is connected to the quadrotor state information χ i,1 ; The input ends of the first nonlinear function unit are respectively connected to the output Φ of the first nonlinear function neural network activation function unit i,1 and the output of the first nonlinear function neural network weight update unit

[0156] The input end of the virtual control rate unit is connected to the neighbor decrypted 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 end of the first filter unit is connected to the output α of the virtual control rate unit i,2 The input ends of the second error comparison unit are connected to the quadrotor status information x i,2 and the output κ of the first filter unit i,2 The input ends of the second nonlinear function neural network weight update unit are respectively connected to the output ends of the long-term performance index unit The output of the second error comparison unit i,2 and the output Φ of the second nonlinear neural network activation function unit i,2 ;

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

[0159] The design of the evaluation network is:

[0160] The input terminals of the first error comparator are connected to the attack isolation unit and the output ... And 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] Where γ is the discount factor, 0<γ<1; T is a small integral reinforcement interval, T>0;

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

[0166]

[0167] are the long-term performance functions in the x, y and z directions respectively, and the neural network activation functions; i,1 ,y i,1 and z i,1 are the system states in the 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] Finally, the output is:

[0169] The input of 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 neural network weight update unit output is obtained by calculating the following formula

[0170]

[0171] in, are the activation functions of the neural network for the long-term performance function in the x, y and z directions, Γ i,c is the weight gain of the long-term performance function, Γ i,c >0;σ i,c is the gain of the correction term of the long-term performance function, 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 the x, y and z directions, all p i,c The elements in the output are

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

[0173] The execution network is designed as follows:

[0174] The input end of the first nonlinear neural network activation function unit is the state information X of the quadrotor aircraft i,1 , the first nonlinear neural network activation function unit Φ is obtained by calculating the following formula i,1 :

[0175]

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

[0177] The input end of 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 by calculating the following formula:

[0178]

[0179] Among them, ||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 all output Φ i,1 Elements in and They are the elements of the first error comparison unit in the x, y and z directions, and are output The elements in Γ i,c is the weight gain of the long-term performance function, Γ i,c >0;σ i,c is the gain of the correction term of the long-term performance function, σ i,c >0; finally get the output

[0180] The input ends of the first nonlinear operation unit are the output Φ of the first nonlinear neural network activation function unit. i,1 and the output of the weight update unit All inputs are multiplied to obtain the output of the first nonlinear operation unit.

[0181] The input ends of the virtual control rate unit are the output of the first nonlinear operation unit The output of the first error comparison unit Output after attack isolation algorithm and The output α of the virtual control rate unit is calculated by the following formula: i,2 :

[0182]

[0183] Among them, k i,1 is the virtual control rate parameter, k i,1 >0,

[0184] The input end 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] Among them, θ i,2 is the time constant of the filter, θ i,2 >0;

[0187] The input end of the second error comparison unit is the output κ of the first filtering unit. i,2 The status information of the quadrotor i,2 , the output e of the second error comparison unit is obtained through the following calculation i,2 :

[0188] e i,2 = x i,2 -κ i,2 ;

[0189] The input end of the second nonlinear neural network activation function unit is the state information χ of the quadrotor aircraft i,1 With χ i,2 , the second nonlinear neural network activation function unit Φ 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 x, y and z direction information respectively, and are the speed information in the x, y and z directions respectively, μ is the center value of the activation function, ξ is the width of the activation function; finally, the output is

[0193] The input end 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 long-term performance index unit output The output of the second nonlinear neural network weight update unit is obtained by calculating the following formula:

[0194]

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

[0196] The input ends of the second nonlinear operation unit are respectively the output Φ of the second nonlinear neural network activation function unit i,2 and the output of the weight update unit All inputs are multiplied to obtain the output of the second nonlinear operation unit.

[0197] The input terminals of the consistency controller are the output terminals of the second nonlinear operation unit The output 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 rate unit is calculated by the following formula: i :

[0198]

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

[0200] like Figure 4 As shown, this system takes a multi-quadrotor system with fourteen followers and one leader as an example to verify the effect of this system:

[0201] The mathematical models of the fourteen quadrotor aircraft are:

[0202]

[0203] Among them, x i represents the x-direction coordinate of the i-th quadrotor, y i represents the y-direction coordinate of the i-th quadrotor, z irepresents the z-direction coordinate of the i-th quadrotor; is the acceleration information in the x direction, is the direction acceleration information, is the acceleration information in the z direction; is the x-direction velocity information, is the velocity information in the y direction, is the velocity information in the z direction; m i is the mass of the ith quadrotor, represents the aerodynamic damping coefficient in the x direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the y direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the z direction of the i-th quadrotor, g is the gravitational acceleration, u i is the control force of the ith quadrotor;

[0204] Let x i，1 =[χ i,1,x ,x i,1,y ,x i,1,z ] T =[x i ,y i ,z i ] T and for the location system status and u i,x 、u i,y 、u i,z They are the virtual control inputs in the x, y, and z directions respectively;

[0205] Quadcopter Positioning System where u i =[u i,x ,u i,y ,u i,z ] T Input for the system;

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

[0207] The sensor input containing the noisy measurement is the system state χ of the quadrotor i,1 , the output of the sensor after measuring the noisy measurement is

[0208] Fourteen quadrotor model parameter selections: Gravity acceleration g = 9.8 m / s 2 , mass m = 2kg, aerodynamic damping coefficient Aircraft control parameter selection: 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,ρ i =0.6, attack detector parameter selection: Γ i,a =10, α i =15, c i,a =10, β i = 0.99 for all parameters i = 1, 2, …, 14;

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

[0210] Initial position of machine 1 1,1 (0) = (0.51, 0.03, 0) (m); starting position of machine 2 χ 2,1 (0) = (1.33, 0.05, 0) (m);

[0211] Unit 3 initial position χ 3,1 (0) = (-0.49, 0.02, 0) (m); Starting position of machine 4 χ 4,1 (0) = (1.28, -0.1, 0) (m);

[0212] Unit 5 initial position χ 5,1 (0) = (0.17, -0.08, 0) (m); Starting position of machine 6 χ 6,1 (0) = (1.17, -0.08, 0) (m);

[0213] Initial position of unit 7 7,1 (0) = (-1.17, -0.08, 0) (m); starting position of machine 8 χ 8,1 (0) = (1.17, -0.08, 0) (m);

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

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

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

[0217] like Figure 5 , 6 As shown, fourteen quadrotors and the leader achieved consensus while isolating the attacked quadrotor; Figure 7 and Figure 8 The safety index P is given i , Isolation index H i From the curve chart, we can see that the attacked machines 3 and 5 have their attack safety index set to 1 and are successfully isolated; Fig. 9 , 10 The figure shows the difference between the improved Liu cryptographic system and the Liu cryptographic system in the y-direction state information of machine 1. It can be seen that the decrypted information of the improved Liu cryptographic system is closer to the real information and the decryption error tends to 0.

[0218] Fig.11 This indicates that the attack detector cannot estimate the attack detection error when machine 3 is attacked, resulting in an error in the subsequent judgment of the attack detection isolation algorithm. Fig.12 It means that the attack detector accurately estimates the attack detection error of machine 7.

[0219] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A position consistency control system for multiple quadrotors based on attack isolation and privacy protection, characterized by: The system includes the Liu cryptographic system, the network attack detection and isolation system, and the consistency control system. The Liu cryptographic system encrypts and transmits the leadership expectation signal provided by the leader and the location information transmitted by the followers, and decrypts the information at the receiving end to obtain the decrypted information. The network attack detection and isolation system detects the attacked follower and isolates it. The input ends of the consistency control system are all connected to the output ends of the undirected graph G, and the output ends of the consistency control system are all connected to the input ends of the i-th follower. The Liu cryptographic system obtains a plaintext information unit, a signal amplification unit, a Liu encryption algorithm, generates ciphertext, transmits the ciphertext to a follower through a network, receives the ciphertext, the Liu decryption algorithm, a signal reduction unit, and obtains a decrypted information unit; 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 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 filtering unit, a second nonlinear function neural network activation function unit, a second nonlinear function neural network weight update unit and a consistency controller.

2. A position consistency control system for multiple quadrotor aircraft based on attack isolation and privacy protection according to claim 1, characterized in that: The input ends of the first error comparator are respectively connected to the neighbor decrypted information after passing through the attack isolation unit Leaders Decrypt Information and quadrotor aircraft noise measurement sensor measurement information The input terminal of the utility function unit is connected to the output of the first error comparator The input of the weight update unit of the long-term performance function neural network is connected to the output p of the utility function unit i,c , the input end of the activation function unit of the long-term performance function neural network is connected to the state information of the quadrotor aircraft χ i,1 ; Long-term performance The input of the index unit is connected to the output of the long-term performance function neural network activation function unit φ i,c and the output of the neural network weight update unit of the long-term performance function; The input ends of the first nonlinear function neural network weight updating unit are respectively connected to the output of the first error comparator Output of the Long-Term Performance Index Unit and the output of the first nonlinear neural network activation function unit φ i,1 ; The input end of the first nonlinear neural network activation function unit is connected to the quadrotor state information X i,1 The input ends of the first nonlinear function unit are respectively connected to the output φ of the first nonlinear function neural network activation function unit i,1 and the output of the first nonlinear function neural network weight update unit The input end of the virtual control rate unit is connected to the neighbor decrypted 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 The input end of the first filter unit is connected to the output α of the virtual control rate unit i,2 The input ends of the second error comparison unit are connected to the quadrotor status information x i,2 and the output κ of the first filter unit i,2 The input ends of the second nonlinear function neural network weight update unit are respectively connected to the output ends of the long-term performance index unit The output of the second error comparison unit i,2 and the output φ of the second nonlinear neural network activation function unit i,2 ; The input end of the second nonlinear neural network activation function unit is connected to the quadrotor state information X i,1 With χ i,2 The input ends of the second nonlinear function unit are respectively connected to the output Φ of the second nonlinear function neural network activation function unit i,2 , the output of the first filter unit κ i,2 and the output e of the second error comparison unit i,2 .

3. A position consistency control system for multiple quadrotors based on attack isolation and privacy protection according to claim 1, characterized in that: The followers are N quadcopters with unknown dynamics, and the N quadcopters with unknown dynamics and one leader are connected through a directed topological graph to form a multi-agent network, and the multi-agent network is the controlled object; In a multi-agent network, at most F followers are attacked by the network and at least F followers communicate with the leader, where the communication is represented by directed; Directed graph G = (V, E); Where V = {v1,…,v N }, represents a set of N nodes; v1,…,v N Indicates quadrotor follower 1 to quadrotor follower N; represents the edge set, (v i ,v j ) represents the edge of the topological graph G, v i ,v j represent the i-th aircraft and the j-th aircraft respectively; if (v i ,ν j )∈E then ν j ν i The adjacent nodes of i = {v j ∈ν|(ν j ,ν i )∈E} represents v i The adjacent nodes of Define the adjacency matrix A = [a ij ]∈R N×N , if (v i ,v j )∈E then a ij =1, otherwise a ij =0; Define the degree matrix D = diag[d1,…,d N ],in, Define the Laplacian matrix L = DA, and define the adjacency matrix B = diag[b1,…,b N ], if the i-th aircraft can access the leader's information, then b i =1, otherwise b i =0.

4. A position consistency control system for multiple quadrotors based on attack isolation and privacy protection according to claim 3, characterized in that: The mathematical model of the follower's i-th quadrotor is: Among them, x i represents the x-direction coordinate of the i-th quadrotor, y i represents the y-direction coordinate of the i-th quadrotor, z i represents the z-direction coordinate of the i-th quadrotor; is the acceleration information in the x direction, is the direction acceleration information, is the acceleration information in the z direction; is the x-direction velocity information, is the velocity information in the y direction, is the velocity information in the z direction; m i is the mass of the ith quadrotor, represents the aerodynamic damping coefficient in the x direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the y direction of the i-th quadrotor, represents the aerodynamic damping coefficient in the z direction of the i-th quadrotor, g is the gravitational acceleration, u i is the control force of the ith quadrotor; Let x i，1 =[χ i,1,x ,x i,1,y ,x i,1,z ] T =[x i ,y i ,z i ] T and for the location system status and u i,x 、u i,y 、u i,z They are the virtual control inputs in the x, y, and z directions respectively; Quadcopter Positioning System where u i =[u i,x ,u i,y ,u i,z ] T Input for the system; F i,f =f i +g i is the unknown dynamics of the system, where g i,χ =diag[1 / m i ,1 / m i ,1 / m i ]; The sensor input containing the noisy measurement is the system state χ of the quadrotor i,1 , the output of the sensor after measuring the noisy measurement is 5. The position consistency control system for multiple quadrotors based on attack isolation and privacy protection according to claim 1, characterized in that: The Liu encryption algorithm consists of three parts. The first part is the input end of the signal amplification unit in the encryption algorithm, which is the sensor output information of the quadrotor aircraft. The output is calculated by the following formula Among them, k p is the magnification; The second part is to generate four random numbers r i ,q i ,t i With s i , i=1,…,M, forming the private key K(M)={(q1,r1,t1),…,(q M ,r M ,t M )}; The third part is to obtain the ciphertext by the following formula c1=q1t1m A +s1r M +q1(r1-r M-1 ), c i =q i t i m A +s i r M +q i (r i -r i-1 ),i=2,…,M-1; c M =(q M s M t M )r M After calculation, the output ciphertext and transmitted on the network.

6. A position consistency control system for multiple quadrotors based on attack isolation and privacy protection according to claim 1, characterized in that: The Liu decryption algorithm is a ciphertext Transmitted over the network, the receiving end receives the ciphertext The input of Liu decryption algorithm is ciphertext The following calculations are obtained The input end of the signal reduction unit is the output of the improved Liu decryption algorithm The decrypted information is obtained through the following calculation Among them, k p is the magnification.

7. A position consistency control system for multiple quadrotors based on attack isolation and privacy protection according to claim 1, characterized in that: The input end of the attack detection unit and the attack isolation unit is to output the decrypted information through the Liu cryptographic system Encrypted and decrypted leader information Sensor output information The output ε of the attack detection error unit is obtained by calculating the following formula: i : The input of the finite time attack detector is connected to the output ε of the attack detection error unit i , the output of the attack detector is obtained by calculating the following formula: in, μ is the center value of the activation function, ξ is the width of the activation function; c i is the finite time attack detector correction gain, 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; 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 through the following calculation The specific process of attack detection is as follows: First define: state index Q i =1 means there is an attacked agent in the subnet, otherwise Q i =0 means no; Counter W i Indicates Q j =1, j∈J i of and; Safety Index H i =1 means the agent is attacked, otherwise H i =0 means no attack; Isolation Index P i =1 means the attacked agent is successfully isolated, otherwise P i =0 Isolation failed; When the output of the attack detection error comparison unit in, To set the detection threshold, its state index Q i =1, calculator W i =1; Agent i transmits its state index Q to its neighbors i And query the state index Q of the neighboring agent j , j∈J i , if Q j =1, then the counter W i Add 1; if W i =|J i |, then the safety index H i =1 means that an attacked agent is detected; The specific operation process of the attack isolation unit is as follows: The security index H is obtained through 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, Finally, if a ij =0, then P i =1.

8. The position consistency control system for multiple quadrotors based on attack isolation and privacy protection according to claim 1, characterized in that: The input ends of the first error comparator in the consistency control system are respectively connected to the output of the attack isolation unit And sensor output information The output of the first error comparison unit is obtained by the following calculation 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 : Where γ is the discount factor, 0<γ<1; T is a small integral reinforcement interval, T>0; The input of the activation function unit of the long-term performance function neural network is the state information of the quadrotor aircraft χ i,1 , the long-term performance function neural network activation function unit output Φ is calculated by the following formula i,c : are the long-term performance functions in the x, y and z directions respectively, and the neural network activation functions; i,1 ,y i,1 and z i,1 are the system states in the x, y and z directions respectively, μ is the center value of the activation function, and ξ is the width of the activation function; Finally, the output is: The input of 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 neural network weight update unit output is obtained by calculating the following formula in, are the activation functions of the neural network for the long-term performance function in the x, y and z directions, Γ i,c is the weight gain of the long-term performance function, Γ i,c >0;σ i,c is the gain of the correction term of the long-term performance function, 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 the x, y and z directions, all p i,c The elements in the output are The input of the long-term performance index unit is the output of the long-term performance function neural network activation function unit Φ i,c and the output of the weight update unit The long-term performance index unit output is calculated by multiplying all input terminals.

9. The position consistency control system for multiple quadrotors based on attack isolation and privacy protection according to claim 1, characterized in that: The input end of the first nonlinear neural network activation function unit in the consistency control system is the state information x of the quadrotor aircraft. i,1 , the first nonlinear neural network activation function unit Φ is obtained by calculating the following formula i,1 : are the first nonlinear neural network activation functions in the x, y and z directions respectively; i,1 ,y i,1 and z i,1 is the system state in the x, y and z directions, μ is the activation function center value, ξ is the activation function width; finally, the output is The input end of 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 by calculating the following formula: Among them, ||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 all output Φ i,1 Elements in and They are the elements of the first error comparison unit in the x, y and z directions, and are output The elements in Γ i,c is the weight gain of the long-term performance function, Γ i,c >0;σ i,c is the gain of the correction term of the long-term performance function, σ i,c >0; finally get the output The input ends of the first nonlinear operation unit are the output Φ of the first nonlinear neural network activation function unit. i,1 and the output of the weight update unit All inputs are multiplied to obtain the output of the first nonlinear operation unit. The input ends of the virtual control rate unit are the output of the first nonlinear operation unit The output of the first error comparison unit Output after attack isolation algorithm and The output α of the virtual control rate unit is calculated by the following formula: i,2 : Among them, k i,1 is the virtual control rate parameter, k i,1 >0, The input end 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 : Among them, θ i,2 is the time constant of the filter, θ i,2 >0; The input end of the second error comparison unit is the output κ of the first filtering unit. i,2 The status information of the quadrotor i,2 , the output e of the second error comparison unit is obtained through the following calculation i,2 : e i,2 =x i,2 -k i,2 ; The input end of the second nonlinear neural network activation function unit is the state information v of the quadrotor aircraft i,1 With χ i,2 , the second nonlinear neural network activation function unit Φ is calculated by the following formula i,2 : 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 x, y and z direction information respectively, and are the speed information in the x, y and z directions respectively, μ is the center value of the activation function, ξ is the width of the activation function; finally, the output is The input end 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 long-term performance index unit output The output of the second nonlinear neural network weight update unit is obtained by calculating the following formula: in, and are the outputs of the second nonlinear neural activation function unit in the x, y and z directions, all of which are Φ i,2 The element in e i,2,x 、e i,2,y and e i,2,z are the elements of the second error comparison unit in the x, y and z directions, all of which are e i,2 The elements in Γ i,2 is the weight gain of the second nonlinear neural network long-term performance function, Γ i,2 >0;σ i,2 is the gain of the correction term of the second nonlinear neural network long-term performance function, σ i,2 >0, and finally get the output The input ends of the second nonlinear operation unit are respectively the output Φ of the second nonlinear neural network activation function unit i,2 And the weight update unit output All inputs are multiplied to obtain the output of the second nonlinear operation unit. The input terminals of the consistency controller are the output terminals of the second nonlinear operation unit The output 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 rate unit is calculated by the following formula: i : Among them, k i,2 is the controller parameter, k i,2 >0; is the output of the weight update unit, is the output derivative of the first filtering unit.

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