A cipher-decipher robust fault-tolerant control method for nonlinear teleoperation system

Abstract

The application discloses a kind of encryption decryption robust fault-tolerant control methods of nonlinear teleoperation system, the method first selects multiple degrees of freedom master-slave teleoperation system model, and is rewritten into multiple linear system, and then is discretized and is solved together.Second, the communication between master-slave robot is introduced encryption decryption algorithm, and the controller of master-slave robot is designed in combination with T-S fuzzy, and the model of master-slave robot is derived by introducing actuator fault.Then the model controller output of master-slave robot is selected, the controller output is rewritten into matrix form, then the inequality is obtained using free weight matrix, and decoupling and introducing actuator fault.Finally, the matrix obtained after decoupling is divided into two parts, and the controller matrix is solved out.The application introduces encryption decryption algorithm to teleoperation system, solves the communication security of system, and also solves the problem of the influence of encryption decryption and partial actuator fault on system stability.

Description

A robust fault-tolerant control method for encryption and decryption of a nonlinear teleoperation system Technical Field

[0001] This invention belongs to the field of control, specifically relating to a robust fault-tolerant control method for encryption and decryption of a nonlinear teleoperation system. Background Technology

[0002] Because current teleoperation systems use a network for information transmission between the master and slave robots, if vulnerabilities are exposed to attackers during transmission, system performance will degrade or even be compromised. To ensure the communication security of the teleoperation system, an encryption technology is chosen to encrypt the information transmitted between the master and slave robots. Over the past few decades, encryption-decryption algorithms have developed rapidly. Currently, the main popular encryption-decryption algorithms are those based on the Data Encryption Standard (DES) and those based on the Advanced Encryption Standard (AES). DES primarily uses the Feistel encryption system and has been the mainstream symmetric encryption algorithm for many years. Compared to DES, AES has a relatively longer (128-bit) block plaintext, and the key length can be 128 bits, 192 bits, or 256 bits, offering better security.

[0003] In teleoperation systems, the master and slave robots transmit information over a network. If vulnerabilities are exposed to attackers during this process, system performance will degrade or even be compromised. To ensure the communication security of the teleoperation system, this invention employs an encryption technology to encrypt the information transmitted between the master and slave robots. Compared to traditional teleoperation systems, the encrypted teleoperation system can guarantee the security of information transmission, protect the system from attacker interference, and ensure stable system operation. Summary of the Invention

[0004] To address the aforementioned problems, this invention discloses a robust fault-tolerant control method for encryption and decryption in a nonlinear teleoperation system. When a typical nonlinear teleoperation system employs encryption and decryption algorithms to ensure information transmission security, the introduced data distortion and actuator failures due to external conditions negatively impact system stability. The newly designed control algorithm can maintain system stability while ensuring information security under these disturbances, enabling the entire system to operate normally. In other words, it considers fault-tolerant control for the teleoperation system while guaranteeing the security of system information transmission.

[0005] A robust fault-tolerant control method for encryption and decryption of a nonlinear teleoperation system includes the following steps:

[0006] Step 1: Select the following multi-degree-of-freedom master-slave teleoperation system model:

[0007]

[0008] in,

[0009]

[0010] Subscripts m and s represent the master robot and slave robot, respectively, and x m (t),x s (t) represents the state of the corresponding master-slave robot, q m (t),q s (t) represents the joint displacement of the corresponding master and slave robots, where t is the continuous time. M represents the joint velocity of the corresponding master and slave robots. m (q m ),M s (q s ) is the positive definite inertia matrix corresponding to the master and slave robots. It is the matrix of centripetal torque and Coriolis torque, F h (t),F e (t) represent operator force and environmental force, respectively. These are the control outputs from the controller to the master and slave robots, respectively.

[0011] Step two: Using TS fuzzy logic, the multi-degree-of-freedom master-slave teleoperation system is rewritten as a combination of multiple linear systems. Then, each small linear system is discretized and combined to obtain the discretized result.

[0012] The system model of formula (1) is discretized by using TS fuzzy processing, thus the following master-slave robot discrete system model can be obtained:

[0013]

[0014] in, (T is the sampling time, k is the discrete time scale), while A mi A si B mi and B si Then, it represents the original data in each small system derived by TS fuzzy derivation before discretization, where L is the number of fuzzy rules, and h is the number of rules. i (y(k)) and Let y(k) represent the fuzzy coefficients. These represent the prerequisite variables of the discrete master-slave robots, respectively.

[0015] Step 3: After obtaining the discretization result from Step 2, an encryption / decryption algorithm is introduced for communication between the master and slave robots:

[0016] The encryption algorithm for the main robot can be written as:

[0017]

[0018] Similarly, we can derive the robot's encryption algorithm, where, This represents the result of decrypting the encrypted information within the encryption system and... This represents the encrypted information, which will be transmitted to the other system via a network channel. a = m represents the master robot, and a = s represents the slave robot. g(k) is a designed dynamic encryption key. And ξ... m (0)=0 n Represents ξ m The initial value of (k) is an n-dimensional vector of all zeros. Then, the encryption algorithm for the operator force can be obtained:

[0019]

[0020] Similarly, an encryption algorithm for the robot's environmental forces can be obtained, where, This represents the result of decrypting the encrypted information within the encryption system and... The encrypted information will be transmitted to the other system through the network channel. ε = h represents the operator force, ε = e represents the force from the robot environment, and g(k) is still the designed dynamic encryption key. Then it means The initial value is an n-dimensional vector of all zeros. This represents the vector v = [v1, v2, ..., v] n ] T Quantification methods.

[0021] The specific process of the decryption algorithm is as follows:

[0022] The decryption algorithm for the main robot can be written as follows:

[0023]

[0024] The decryption algorithm for operator force can be written as:

[0025]

[0026] Similarly, a decryption algorithm can be obtained from the robot and environmental forces. Where, x sm (k) represents the result obtained by the master robot after decrypting the encrypted information received from the slave robot. Similarly, the encrypted information of the master robot decrypted from the slave robot is x. msg(k) and g(k-1) are the same for encryption and decryption. This represents the operator force obtained from the robot after decryption; similarly, the environmental force obtained from decryption in the main robot is... 0 n It is an n-dimensional zero matrix.

[0027] Step 4: Design the controller for the master-slave robot using TS fuzzy logic:

[0028] The basic model of a master-slave robot controller is as follows:

[0029]

[0030] K mj and K sj This indicates the gain of the designed controller.

[0031] Based on the established model, the following controller design for a master-slave robot can be derived using TS fuzzy logic:

[0032]

[0033] Operator force F on the main robot h (k) Encrypt and transmit to the robot, and obtain the result after decryption by the robot. Similarly, the environmental force F from the robot can be applied. e (k) Obtained after encryption and decryption In x m (k) and x s (k) Provided that it can be measured, time-varying delays can satisfy the following conditions: in t , μ and μ are known constants or scalars.

[0034] Step 5: Introduce actuator faults and derive the model of the master-slave robot.

[0035] In practical applications, actuator failures occur frequently. Fault-tolerant control is introduced into formula (8) to address these problems. The controller for the master-slave robot can then be designed as follows:

[0036]

[0037] in,

[0038]

[0039]

[0040] Where, m i (i = 1, 2, 3, ..., p) represents the fault severity of the actuator, and we have:

[0041]

[0042] and These represent the upper and lower bounds of actuator failure, respectively. These are the indicators used to distinguish the magnitude of the fault; less than The range is the large fault range, greater than represents the small fault interval. diag{} represents the diagonal matrix symbol.

[0043] Then, combining the above steps, the master-slave robot model can be derived:

[0044]

[0045] in,

[0046]

[0047]

[0048]

[0049]

[0050] Step six: After ensuring that the system (10) meets the preset performance requirements, decouple the system matrix (11) and introduce actuator faults:

[0051] By selecting the controller output of the master-slave robot model, and using the Lyapunov function, the controller output is rewritten in matrix form. Then, using the free weight matrix, the inequalities are obtained. By decoupling and introducing actuator faults, the closed-loop system stability of system (10) can be obtained according to the inequality. At the same time, it can be determined that system (10) is mean square stable when the disturbance level of H∞ is γ.

[0052] The above calculations yield the following inequality:

[0053]

[0054] The asterisk (*) indicates that the value at that point is symmetrical to the value at the position above the diagonal.

[0055]

[0056]

[0057]

[0058] I represents the identity matrix, and the elements in the above matrix are obtained by solving a series of equations.

[0059] Subsequently, the matrix in inequality (11) After decoupling, the following inequality holds using Schul complement theorem:

[0060]

[0061] in,

[0062]

[0063]

[0064]

[0065]

[0066] The elements in the above matrix are obtained by solving a series of equations.

[0067] Subsequently in the matrix Introducing actuator faults:

[0068]

[0069] in,

[0070]

[0071]

[0072] Γ m =diag{m 1m ,...,m pm},Γ s =diag{m 1s,...,m ps},

[0073] Step 7: Decouple the resulting matrix The controller matrix is ​​solved in two parts to complete the design of the master-slave robot controller:

[0074] Substitute equation (13) from step six into the matrix. Then, the matrix is ​​divided into two parts. Then Λ can be written in the following form:

[0075]

[0076] in,

[0077]

[0078] The elements in the above matrix are obtained by solving a series of equations.

[0079] ΔΛ represents the uncertain part. After processing ΔΛ using the Schul complement theorem and adding it to matrix Λ, we obtain the following inequality (15):

[0080]

[0081] in,

[0082]

[0083]

[0084] The elements of the above matrix are obtained by solving a series of equations. Then, the controller matrix K is solved using matrix Ω. mj and K sj The value is used to complete the design of the master-slave robot controller.

[0085] The beneficial effects of this invention are as follows: This invention introduces encryption and decryption algorithms into the remote operating system, which solves the communication security problem of the system. At the same time, it also proposes solutions to the problems of encryption and decryption and the impact of some actuator failures on system stability. Attached Figure Description

[0086] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0087] Figure 1 shows the FTC scheme based on encryption and decryption;

[0088] Figure 2 shows the fuzzy function used in this system;

[0089] Figure 3 shows q m1 and q s1 Position tracking comparison;

[0090] Figure 4 shows q m2 and q s2 Position tracking comparison;

[0091] Figure 5 shows the fitting comparison of the main operator's force;

[0092] Figure 6 shows the fitting comparison of environmental forces at the end. Detailed Implementation

[0093] The present invention will now be described in further detail with reference to the examples shown in the accompanying drawings.

[0094] Step 1: Select the following multi-degree-of-freedom master-slave teleoperation system model:

[0095]

[0096] in,

[0097]

[0098]

[0099] The subscripts m and s represent the master robot and slave robot, respectively. m (t),x s (t) represents the state of the corresponding master-slave robot, q m (t),q s (t) represents the joint displacement of the corresponding master and slave robots, where t is the continuous time. M represents the joint velocity of the corresponding master and slave robots. m (q m ),M s (q s ) is the positive definite inertia matrix corresponding to the master and slave robots. It is the matrix of centripetal torque and Coriolis torque, F h (t),F e (t) represent operator force and environmental force, respectively. These are the control outputs from the controller to the master and slave robots, respectively.

[0100] Step two: Using TS fuzzy logic, the multi-degree-of-freedom master-slave teleoperation system is rewritten as a combination of multiple linear systems. Then, each small linear system is discretized and combined to obtain the discretized result of the nonlinear system.

[0101] First, the IF-Then fuzzy rules are as follows:

[0102] IF y1(t)isΨ i1 and...and y p (t)isΨ ip ,

[0103] THEN

[0104] Among them, Ψ i1 ,...,Ψ ip It is a fuzzy set, where L is the number of IF-Then fuzzy rules, y1(t), y2(t), ..., y p (t) is the premise variable. Then, the discrete fuzzy system of the main robot can be derived as follows:

[0105]

[0106] in, (T is the sampling time, k is the discrete time scale), L is the number of fuzzy rules, and A mi A si B mi and B si This represents the original data in each small system derived by TS fuzzy derivation before discretization, and also has y(k)=[y1(k),y2(k),...,y p (k)]. Assume that δ i (y(k))≥0 and definition δ can be deduced i (y(k))≥0, i=1,2,…,L and Similarly, the discrete fuzzy system expression of the robot can be obtained using the above method, where Similar to the properties of y(k) above, With the above h i (y(k)) have the same properties.

[0107] Subsequently, the master-slave robot model, after discretization, can be simply described as follows:

[0108]

[0109] Step 3: After obtaining formula (3) from Step 2, an encryption / decryption algorithm is introduced for communication between the master and slave robots, as shown in Figure 1:

[0110] The encryption algorithm for the main robot can be written as:

[0111]

[0112] Similarly, we can derive the robot's encryption algorithm, where, This represents the result of decrypting the encrypted information within the encryption system and... This represents the encrypted information, which will be transmitted to the other system via a network channel. a = m represents the master robot, and a = s represents the slave robot. g(k) is a designed dynamic encryption key. And ξ... m (0)=0 n Represents ξ m The initial value of (k) is an n-dimensional vector of all zeros. Then, the encryption algorithm for the operator force can be obtained:

[0113]

[0114] Similarly, an encryption algorithm for the robot's environmental forces can be obtained, where, This represents the result of decrypting the encrypted information within the encryption system and... The encrypted information will be transmitted to the other system through the network channel. ε = h represents the operator force, ε = e represents the force from the robot environment, and g(k) is still the designed dynamic encryption key. Then it means The initial value is an n-dimensional vector of all zeros. This represents the vector v = [v1, v2, ..., v] n ] T The quantification method is as follows:

[0115]

[0116] in, These are the given quantization parameters.

[0117] The specific process of the decryption algorithm is as follows:

[0118] The main robot's decryption algorithm can be written as:

[0119]

[0120] The decryption algorithm for the master-side operation force can be written as:

[0121]

[0122] Similarly, a decryption algorithm can be obtained from the robot and environmental forces. Where, x sm (k) represents the result obtained by the master robot after decrypting the encrypted information received from the slave robot. Similarly, the encrypted information of the master robot decrypted from the slave robot is x. ms g(k) and g(k-1) are the same for encryption and decryption. This represents the operator force obtained from the robot after decryption; similarly, the environmental force obtained from decryption in the main robot is...

[0123] Step 4: Design the master-slave controller using TS fuzzy logic:

[0124] The basic model of a nonlinear master-slave controller is as follows:

[0125]

[0126] K mj and K sj This indicates the gain of the designed controller.

[0127] Based on the established model above, we select the following fuzzy controller:

[0128] Fuzzy rule j:

[0129] IF y1(k)isΨ i1 and...and y p (k)isΨ ip ,

[0130] THEN

[0131]

[0132] Among them, Ψ i1 ,...,Ψ ip It is a fuzzy set, where j = 1, 2, ..., L is the number of IF-Then fuzzy rules, y1(t), y2(t), ..., y p (t) is the premise variable. Therefore, we can obtain the following controller design for the master-slave robot:

[0133]

[0134] Using the above method, the operator force F on the main robot h(k) Encrypt and transmit to the robot, and obtain the result after decryption by the robot. Similarly, the environmental force F from the robot can be applied. e (k) Obtained after encryption and decryption In x m (k) and x s (k) Provided that it can be measured, time-varying delays can satisfy the following conditions: in t , μ and μ are known constants or scalars.

[0135] Step 5: Introduce some actuator faults and derive the master-slave robot model.

[0136] In practical applications, some actuator failures occur frequently. Fault-tolerant control is introduced into formula (8) to address these problems. The controller can then be designed as follows:

[0137]

[0138] in,

[0139]

[0140]

[0141] Where, m i (i = 1, 2, 3, ..., p) represents the fault severity of the actuator, and we have:

[0142]

[0143] and These represent the upper and lower bounds of actuator failure, respectively. These are the indicators used to distinguish the magnitude of the fault; less than The range is the large fault range, greater than represents the small fault interval. diag{} represents the diagonal matrix symbol.

[0144] Then, combining the above steps, we can derive the master-slave robot model:

[0145]

[0146] in,

[0147]

[0148]

[0149]

[0150]

[0151] Step six: After ensuring that system (12) meets the preset performance requirements, decouple system matrix (13) and introduce actuator faults:

[0152] First, select the controller output for system (12), then select the Lyapunov function for system (12), and then use the controller output to rewrite the scaled Lyapunov function in matrix form. At the same time, use the method of free weight matrix to obtain inequality (13). According to inequality (13), the closed-loop system of system (12) is stable, and it can be determined that system (12) is mean square stable when the disturbance level of H∞ is γ.

[0153] The above calculations yield the following inequality:

[0154]

[0155] The asterisk (*) indicates that the value at that point is symmetrical to the value at the position above the diagonal.

[0156]

[0157]

[0158]

[0159] I represents the identity matrix, and the elements in the above matrix are obtained by solving a series of equations.

[0160] Subsequently, the matrix in inequality (13) After decoupling, the following inequality holds using Schul complement theorem:

[0161]

[0162] in,

[0163]

[0164]

[0165]

[0166]

[0167] The elements in the above matrix are obtained by solving a series of equations.

[0168] Subsequently in the matrix Introducing actuator faults:

[0169]

[0170] in,

[0171]

[0172]

[0173] Γ m =diag{m 1m ,...,m pm},Γ s =diag{m 1s ,...,m ps},

[0174] Step 7, convert the matrix Divide the problem into two parts and solve for the controller matrix K. mj and K sj The value is used to complete the design of the master-slave robot controller.

[0175] Substitute equation (15) from step six into the matrix. Then, the matrix is ​​divided into two parts. Then Λ can be written in the following form:

[0176]

[0177] in,

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186] ΔΛ represents the uncertain part. After processing ΔΛ using the Schul complement theorem and adding it to matrix Λ, we obtain the following inequality (17):

[0187]

[0188] in,

[0189]

[0190]

[0191] The elements of the above matrix are obtained by solving a series of equations. Then, the controller matrix K is solved using matrix Ω. mj and K sj The value of X is used to complete the design of the master-slave robot controller. Figure 2 shows the TS fuzzy membership function used in the design, displaying X respectively. a1 and X a2 Membership functions for the three different types when the value is between -1.5 and 1.5.

[0192] Figure 2 shows the membership function of the TS fuzzy model used in the design. The graph shows that X... a1 and X a2 The membership functions represent three different types of membership functions when the value is between -1.5 and 1.5.

[0193] Figures 3 and 4 show that when the operator applies a force to the main robot that varies according to a sine function, the main robot produces corresponding displacement and velocity under the action of this force. After simulation using MATLAB software, it can be seen from the figures that the displacement curves of the main robot and the slave robot have a high degree of overlap. Therefore, it can be seen that the slave robot has a good tracking performance for the displacement and velocity made by the main robot.

[0194] Figure 5 shows that when we select an environmental force that varies according to a sinusoidal function, the control signal can be easily observed from the simulation diagram. The curves of the control signal and the environmental force Fe have a high degree of overlap, indicating that the control signal... The fitting effect for environmental forces is relatively good. In Figure 6, when we select an operator force that varies with the sine wave, the control signal is easily seen from the simulation diagram. The curve and the operator force Fh curve have a high degree of overlap, indicating that the control signal... It has a good fit for operator force.

[0195] This invention investigates the fault-tolerant control problem based on encryption / decryption for a class of multi-degree-of-freedom nonlinear bilateral teleoperation systems under fault and time-varying communication delay conditions. To ensure communication security between the master and slave robots, a fault-tolerant control scheme based on encryption / decryption is proposed, modeling the nonlinear system as a TS fuzzy discrete system with multiple time-varying delays. To achieve data privacy protection, the states of the master robot and the operator forces are encrypted into a series of codewords and transmitted to the slave robot for decryption. Similarly, the state and environmental forces of the slave robot are encrypted and transmitted to the master robot. When actuator failures occur in the master and slave robots, a fault-tolerant controller is designed using the free weight matrix method. Finally, the feasibility of the proposed method is verified through numerical examples.

Claims

1. A robust fault-tolerant control method for encryption and decryption of a nonlinear teleoperation system, characterized in that, Includes the following steps: Step 1: Select a multi-degree-of-freedom master-slave teleoperation system model; the multi-degree-of-freedom master-slave teleoperation system model is as follows: （1） in, Subscript These represent the master robot and the slave robot, respectively. Represents the master-slave robot state. This represents the joint displacement of the master and slave robots. For continuous time, Represents the joint speed of the master and slave robots. It is the positive definite inertia matrix of the master-slave robot. It is a matrix of centripetal torque and Coriolis torque. These are operator forces and environmental forces. The controller outputs control to the master and slave robots respectively; Step 2, using TS fuzzy logic, the multi-degree-of-freedom master-slave teleoperation system is rewritten into a combination of multiple linear systems, and then each small linear system is discretized and combined to obtain the discretization result; The discretization result is as follows: Formula (1) is discretized by using TS fuzzy logic, and the following master-slave robot discrete system model is obtained: (2) Among them ， Sampling time, For discrete time scales, ， ， and This represents the original data in each small system derived by TS fuzzy derivation before discretization. It is the number of fuzzy rules. and Represents the fuzzy coefficient. and Let each represent a precondition variable of the master-slave robot after discretization; Step 3: After obtaining the discretization result from Step 2, an encryption / decryption algorithm is introduced for communication between the master and slave robots; The encryption algorithm for the master robot is: (3) Similarly, the encryption algorithm for the robot is obtained, where This represents the result of decrypting the encrypted information within the encryption system and... This means the encrypted information will be transmitted to the other party's system via the network channel. Representing the main robot, Representing robots, It is a designed dynamic encryption key, and has represent The initial value is an n-dimensional vector of all zeros; the encryption algorithm for the operator force is: (4) Similarly, the encryption algorithm for the robot's environmental forces is obtained. This represents the result of decrypting the encrypted information within the encryption system and... This means that the encrypted information will be transmitted to the other party's system through the network channel. Represents operator strength, Represents the environmental forces of robots, It still uses the designed dynamic encryption key; Then it means The initial value is an n-dimensional vector of all zeros; Represents for vector The quantization method; the decryption algorithm of the main robot is: (5) The decryption algorithm for operator power is: (6) Similarly, the decryption algorithm from the robot and environmental forces is obtained; where, This indicates the result obtained by the master robot after decrypting the encrypted information received from the slave robot. Similarly, the encrypted information of the master robot decrypted from the slave robot is... ， Encryption and decryption are the same; This represents the operator force obtained from the robot after decryption; similarly, the environmental force obtained from decryption in the main robot is... Step 4: Design the controller for the master-slave robot using TS fuzzy logic. Step 5: Introduce actuator faults and derive the model of the master-slave robot. Step 6: Select the controller output of the master-slave robot model, rewrite the controller output in matrix form using Lyapunov functions, and then use the free weight matrix to obtain the inequalities. Step 6 involves decoupling and introducing actuator faults; Step 7 involves dividing the matrix obtained after decoupling in Step 6 into two parts, solving for the controller matrix, and completing the design of the master-slave robot controller.

2. The encryption and decryption robust fault-tolerant control method for a nonlinear teleoperation system according to claim 1, characterized in that, In step four, the basic model of the master-slave robot controller is as follows: (7) Among them and Indicate the designed controller gain; utilize TS fuzzy mapping to the following master-slave robot controller design: (8) Operator force on the main robot Encrypt and transmit to the robot, and obtain the data after decryption by the robot. Similarly, regarding environmental forces acting on robots... After encryption and decryption, obtain ;exist and Provided that it can be measured, time-varying time delays satisfy the following conditions: in ， and It is a known constant scalar.

3. The encryption and decryption robust fault-tolerant control method for a nonlinear teleoperation system according to claim 2, characterized in that, Step five involves introducing fault-tolerant control into formula (8), and designing the controller for the master-slave robot as follows: （9） in, in, This represents the severity of actuator failures, and includes: and These represent the upper and lower bounds of actuator failure, respectively. These are the indicators used to distinguish the magnitude of the fault; less than The range is the large fault range, greater than This represents the small fault range; This is a diagonal matrix notation; the master-slave robot model is derived as follows: （10）

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