An unmanned system cooperative privacy protection method based on multi-scale control technology

Abstract

The application discloses a kind of based on multi-scale control technology's unmanned system cooperation privacy protection method, belong to unmanned system safety cooperation control field.This method solves the ill-conditioned numerical problem in the cooperative control of unmanned system with fast-slow coupling characteristics, and the state privacy leakage problem caused by communication eavesdropping.Scheme includes: establishing system dynamic model;Design the differential privacy leader-following multi-scale cooperative controller containing attenuation noise;Obtain the standard singular perturbation form of error system through matrix transformation;Based on multi-scale control theory, solve the state control gain that guarantees mean square consistency;Determine the noise control gain and privacy parameter in combination with probability theory and matrix spectral theory.The present application avoids the ill-conditioned numerical problem, and the controller is robust, while achieving accurate cooperative control, provides verifiable differential privacy protection for the initial state of the system, significantly improves the safety and reliability of unmanned system in the hostile environment.

Description

Technical Field

[0001] This invention relates to the field of unmanned system safety and collaborative control technology, and in particular to a method for protecting the collaborative privacy of unmanned systems based on multi-scale control technology. Background Technology

[0002] With the widespread application of unmanned systems in national defense, logistics, disaster relief, and other fields, their cooperative control technology has become a core support for intelligent warfare and autonomous operation. Unmanned systems (such as multiple unmanned surface vessels and multi-rotor drones) typically exhibit significant multi-timescale characteristics, meaning that the system state can be divided into slowly changing states (such as position and velocity) and rapidly changing states (such as attitude and angular rate), with a strong coupling relationship between the two. If traditional cooperative control algorithms are directly applied to such systems, the numerical solution process will suffer from "illness" due to the timescale differences, making controller design difficult and system stability hard to guarantee.

[0003] Furthermore, unmanned systems often rely on open communication networks for state interaction and collaborative decision-making, making them highly vulnerable to eavesdropping attacks during information transmission. By intercepting communication data between drones, attackers can deduce the system's initial state, control strategies, and even mission intentions, potentially launching more destructive attacks (such as deception interference and replay attacks), ultimately paralyzing the entire collaborative system. Therefore, while achieving efficient collaborative control, effectively protecting the state privacy of each unit within the system and preventing the leakage of sensitive information has become a critical issue that urgently needs to be addressed in the field of unmanned system security control.

[0004] Currently, research on collaborative control and privacy protection for unmanned systems still faces the following challenges:

[0005] 1. Control challenges caused by multi-timescale coupling: Existing cooperative control methods often do not fully consider the dynamic separation characteristics of fast and slow states of unmanned systems. Direct application can easily lead to ill-conditioned numerical problems, limiting the feasibility and robustness of the controller.

[0006] 2. Privacy leakage risk in open communication environment: Traditional security mechanisms focus on communication encryption or authentication, lacking privacy protection for the initial state and dynamic information of the system at the control level, making it difficult to deal with the threat of eavesdroppers inferring the internal state of the system through long-term listening.

[0007] Therefore, there is an urgent need to propose a control method that can simultaneously handle multi-timescale characteristics, avoid ill-conditioned numerical problems, and embed privacy protection mechanisms during collaborative processes, in order to improve the survivability and mission reliability of unmanned systems in open and hostile environments. Against this backdrop, this invention proposes a collaborative privacy protection method for unmanned systems that integrates multi-scale control and differential privacy mechanisms. Summary of the Invention

[0008] The purpose of this invention is to overcome the problems in the prior art and provide a collaborative privacy protection method for unmanned systems based on multi-scale control technology. By designing a leader-follower multi-scale collaborative controller with noise feedback, combined with a differential privacy mechanism, the method achieves mean-square consistency and initial state privacy protection of the system while avoiding ill-conditioned numerical problems, effectively resisting eavesdropping attacks.

[0009] To achieve the aforementioned objectives, the present invention employs the following technical solution: a collaborative privacy protection method for unmanned systems based on multi-scale control technology, comprising the following steps:

[0010] S1: Establish a dynamic model based on the fast and slow coupling characteristics of unmanned systems.

[0011] S2: Follower in unmanned systems Design a differential privacy leader-follower multi-scale collaborative controller with noise feedback.

[0012] S3: Obtain the distributed singular perturbation standard form of the leader-follower dynamic error system model through matrix transformation;

[0013] S4: Based on the dynamic error system model in step S3, solve the fast and slow state control gain in the multi-scale cooperative controller in step S2 using multi-scale control technology.

[0014] S5: Based on probability theory and the properties of the correlation matrix spectrum, solve for the specific forms of noise control gain and differential privacy parameters in the multi-scale cooperative controller in step S2.

[0015] Furthermore, in step S1, establishing a dynamic model based on the fast-slow coupling characteristics of the unmanned system specifically includes the following steps:

[0016] S1.1: The dynamic model of a leader with fast-slow coupling characteristics is established as follows:

[0017] ,

[0018] in, and These represent the superscripts for the slow and fast states, respectively. Indicates the time step. and Leaders at any time Slow and fast states; The dimension is unit array, , , and Given a known parameter matrix with compatible dimensions, These are perturbation parameters, which describe the variables. and The dynamics of separation on fast and slow time scales.

[0019] S1.2: Establishing a follower with fast-slow coupling characteristics The dynamic model is as follows:

[0020] ,

[0021] in, The number representing the follower. and Followers At any moment The slow state and the fast state, For followers At any moment Control input; and It is a known parameter matrix with compatible dimensions.

[0022] S1.3: Expand the number of leaders and followers respectively. The dynamic equations are as follows:

[0023] ,

[0024] in, and These represent the augmented forms of the leader's fast and slow states, and the followers, respectively. Augmented forms of fast and slow states, Represents the transpose of a vector or matrix. and Let represent the system state matrix and input matrix, respectively; based on the specific form of the augmented matrix, we obtain... The requirements must be controllable.

[0025] Furthermore, the specific content of step S2 is as follows:

[0026] S2.1: Design Differential Privacy Noise The specific form; defining the direction for each follower Injected Laplace noise in The value at time ,in, Represented as:

[0027] ,

[0028] in, Indicates follower Dimensions Represents the transpose of a vector or matrix; design probability density for: ,in, The mathematical expectation is expressed as The variance is expressed as , For time An exponentially decaying function, its specific form is: ,in, for initial value, Given the base of the exponentially decaying term, it is required that... .

[0029] S2.2: Design a differential privacy leader-follower consensus multi-scale collaborative controller with noise feedback as follows:

[0030] ,

[0031] It can be transformed into:

[0032] ,

[0033] in , and These represent the control gains for the slow and fast states in a multi-scale cooperative controller, respectively. , and These represent the control gains for noise injected into the slow and fast states in the multi-scale cooperative controller, respectively. Indicates follower Neighborhood set, Indicates follower With followers The adjacency coefficient, Indicates follower Adjacency coefficient with the leader; Followers At any moment Used to transmit the status data of other followers. Followers At any moment Receive neighbor follower The state in which, , and They are followers At any moment Used for slow and fast states in data transmission. , and They are followers At any moment Slow and fast states are used for data transmission.

[0034] Furthermore, the specific content of step S3 is as follows:

[0035] S3.1: Through leaders and followers The dynamic equations yield the following error system model for a single follower:

[0036] ,

[0037] in, For followers Error of the leader's state at time The value, The specific form of expression is ,in, , .

[0038] S3.2: Augment the error vector of each follower in S3.1 into a dynamic error system model with N followers:

[0039] ,

[0040] in, This represents the augmentation of the error vector for each follower. This represents the operation of the Crodic product. express An identity matrix of dimensions , For a multi-follower system, the Laplace matrix is ​​shown in the diagram. For leaders and every follower The adjacency diagonal matrix; This represents the combined term of all noise. The specific form of expression is: .

[0041] S3.3: Define the transformation matrix , This is an elementary matrix with two rows swapped. Based on the properties of the transformation matrix, the left and right sides of the dynamic error system model with N followers in step S3.2 are multiplied by the transformation matrix, thus grouping its odd-numbered rows and columns together, and even-numbered rows and columns together, resulting in a dynamic error system model with the standard form of distributed singular perturbations, specifically:

[0042] ,

[0043] The correlation matrix is ​​defined as follows:

[0044]

[0045]

[0046]

[0047] .

[0048] Furthermore, the specific content of step S4 is as follows:

[0049] S4.1: Based on the dynamic error system model with distributed singular perturbation standard form established in step S3, construct a system containing multi-scale control techniques. Lyapunov function : ,in, The specific form is: .

[0050] S4.2: By modifying the structure constructed in step S4.1, which contains... By performing finite difference operations on the Lyapunov equations and calculating their expected values, and utilizing the Schur complement principle and scaling properties, we derive the LMIs that ensure mean-square leader-follower consistency in unmanned systems. Specifically:

[0051]

[0052]

[0053] ,

[0054] in, It is to satisfy Given parameters, , , and It is a symmetric matrix with compatible dimensions. , , and It is a matrix with compatible dimensions. , , , , , , and For a matrix with a certain dimension, its specific form is:

[0055]

[0056] .

[0057] S4.3: Obtained by solving the matrix inequality equation in S4.2 , , and Solve for the fast and slow state control gain. and Specifically:

[0058] .

[0059] Furthermore, the specific content of step S5 is as follows:

[0060] S5.1: Define a set - Initial state of adjacent followers and ,satisfy:

[0061] , ,

[0062] Among them, there are followers. The initial state relationship satisfies , for One component is 0, and all other components are 0. There are two initial states. and The error vector between them.

[0063] Define the initial state and The two corresponding times are 0 to 1. Noise sequence:

[0064]

[0065] ,

[0066] in, Initial state At that time The value of the noise vector injected at time 1. Initial state Time from time 0 to time 1 The augmentation of the noise vector, Initial state At that time The value of the noise vector injected at time 1. Initial state Time from time 0 to time 1 Augmentation of the noise vector.

[0067] S5.2: Assumptions - Initial state of adjacent followers and To ensure that the corresponding output sequence sets are identical, noise is designed according to the definition in S5.1. and satisfy:

[0068] .

[0069] S5.3: Based on probability theory and the random noise variable in step S5.2 and Based on the relationship, derive the initial state of the final unmanned system. Able to achieve Differential privacy, where each follower Privacy level It can be represented as: ,in, , and A constant that satisfies certain conditions, namely: satisfy , satisfy , satisfy , Representation matrix The spectrum, This represents the decay rate of the added Laplace noise with attenuation characteristics. express The minimum value, express The minimum value, This represents the initial value of the added Laplace noise with attenuation characteristics.

[0070] S5.4: Based on the properties of the spectrum and the requirements of the differential privacy parameter in step S5.3, the noise control gain in the multi-scale cooperative controller is obtained. ,satisfy:

[0071] .

[0072] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0073] This invention effectively solves the ill-conditioned numerical problems commonly found in the cooperative control of unmanned systems with fast-slow coupling characteristics by introducing multi-scale control technology. Traditional control methods, due to their failure to consider the time-scale separation of state variables, often lead to unstable system solutions, slow convergence, or even failure to achieve the desired control. This invention establishes a dynamic error model including the perturbation parameter ε, constructs a matching Lyapunov function, and derives ε-independent linear matrix inequalities (LMIs) to solve for the control gain. This method not only avoids the numerical singularity problem caused by the minima of ε but also makes the designed controller highly robust to system parameter perturbations, significantly improving the reliability and feasibility of cooperative control of unmanned systems in complex dynamic environments.

[0074] Regarding privacy protection, this invention innovatively embeds a differential privacy mechanism into a multi-scale cooperative control structure, achieving effective protection of the initial state of the unmanned system. By injecting Laplace noise with exponential decay characteristics into the state feedback of each follower and co-designing the noise gain and spectrum, the data trajectories transmitted by the system are statistically difficult to distinguish between different initial states. This method, without affecting the system's convergence performance, strictly satisfies the ε-differential privacy definition, ensuring that even if an eavesdropper obtains all communication data, they cannot accurately infer the initial state information of any individual unmanned platform, thus fundamentally enhancing the system's anti-eavesdropping capability and information security in open network environments.

[0075] The proposed method achieves mean-square leader-follower consistency while possessing good engineering applicability and adjustable privacy protection strength. Through theoretical proof and simulation verification, the system can still ensure that the state exponents of all followers converge to the leader's trajectory even under noise injection, and the privacy protection level can be flexibly adjusted by the initial amplitude and decay rate of the noise. Simulation results show that this method can effectively balance control accuracy and privacy protection requirements in typical multi-UAV scenarios, not only avoiding the ill-conditioned numerical defects of traditional methods but also providing a systematic solution for cooperative tasks with high security requirements, demonstrating significant military and civilian application value. Attached Figure Description

[0076] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0077] Figure 1 This is a control structure block diagram of a collaborative privacy protection method for unmanned systems based on multi-scale control technology provided by the present invention.

[0078] Figure 2This is a schematic diagram of the communication topology between a leader and three followers in an embodiment of the present invention.

[0079] Figure 3 This is a mean square error curve obtained by three followers conducting one thousand Monte Carlo experiments in an embodiment of the present invention.

[0080] Figure 4 This is a trajectory tracking diagram of two slow states of three followers and one leader in an embodiment of the present invention.

[0081] Figure 5 This is a trajectory tracking diagram of two fast states of three followers and one leader in an embodiment of the present invention.

[0082] Figure 6 This is the trajectory of follower 2 transmitting data to neighboring followers in two initial states in this embodiment of the invention.

[0083] Figure 7 The privacy level parameters in the embodiments of this invention are and Relationship diagram. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0085] like Figures 1 to 7 As shown in the figure, this embodiment provides a collaborative privacy protection method for unmanned systems based on multi-scale control technology, which specifically includes the following steps.

[0086] Step S1: Establish a dynamic model based on the common fast-slow coupling characteristics of unmanned systems.

[0087] S1.1, First, establish the dynamic model of the leader with fast-slow coupling characteristics as follows: In this context, the subscript 0 represents the leader's number. and These represent the superscripts for the slow and fast states, respectively. Indicates the time step. and Leaders at any time Slow and fast states; This indicates the dimension of the corresponding matrix. The dimension is unit array, , , and Given a known parameter matrix with compatible dimensions, These are perturbation parameters, which describe the variables. and The dynamics of separation on fast and slow time scales.

[0088] S1.2 Then establish a follower with fast and slow coupling characteristics. The dynamic model is as follows: ,in, The number representing the follower. and Followers At any moment The slow state and the fast state, For followers At any moment The control input, and It is a known parameter matrix with compatible dimensions.

[0089] S1.3 Finally, expand the ranks of leaders and followers separately. The dynamic equations can be written in the following form: ,in, and These represent the augmented forms of the leader's fast and slow states, and the followers, respectively. Augmented forms of fast and slow states, The transpose of a matrix, representing a vector or matrix. and Let these represent the system state matrix and the input matrix, respectively. These are perturbation parameters; here they are matrix indices, indicating whether the matrix contains... Furthermore, based on the specific form of the augmented matrix, we can obtain... The requirements must be controllable.

[0090] Step S2: For each follower Design a differential privacy leader-follower consensus multi-scale collaborative controller with noise feedback.

[0091] S2.1, First, design differential privacy noise. The specific form. Defined for each follower. Injected Laplace noise in The value at time ,in, It can be represented as: ,in, Indicates follower Dimensions To represent the transpose of a vector or matrix, design probability density for: ,in, The mathematical expectation is expressed as The variance is expressed as , For time An exponentially decaying function, specifically in the form of: ,in, for initial value, Given the base of the exponentially decaying term, it is required that... .

[0092] S2.2 Then, based on the designed differential privacy noise, a differential privacy leader-follower consensus multi-scale collaborative controller with noise feedback is designed, the specific form of which is as follows:

[0093] ,

[0094] Its compact form can be rewritten as:

[0095] ,

[0096] in, , and These represent the control gains for the slow and fast states in a multi-scale cooperative controller, respectively. , and These represent the control gains for noise injected into the slow and fast states in the multi-scale cooperative controller, respectively. Indicates follower Neighborhood set, Indicates follower With followers The adjacency coefficient, Indicates follower The adjacency coefficient with the leader. Furthermore, Followers At any moment Used to transmit the status data of other followers. Followers At any moment Receive neighbor follower The state in which, , and They are followers At any moment Used for slow and fast states in data transmission. , and They are followers At any moment Slow and fast states are used for data transmission.

[0097] Step S3: Based on linear algebra theory and through matrix transformations, obtain the leader and followers. The standard form of distributed singular perturbation for dynamic error system models.

[0098] S3.1, First, through leaders and followers The dynamic equations yield the following error system model for a single follower: ,in, For followers Error of the leader's state at time The value, The specific form of expression is that it can be written as ,in , .

[0099] S3.2, then, the error vector of each follower is augmented into a dynamic error system model of N followers: ,in, This represents the augmentation of the error vector for each follower. This represents the operation of the Crodic product. express An identity matrix of dimensions , For a multi-follower system, the Laplace matrix is ​​shown in the diagram. For leaders and every follower The adjacency diagonal matrix, This represents the combined term of all noise. The specific form of expression is: .

[0100] S3.3 Finally, first define the transformation matrix. , This involves swapping two rows of an elementary matrix. Then, based on the properties of the transformation matrix, the left and right sides of the dynamic error system model with N followers from step S3.2 are multiplied by the transformation matrix. This groups the odd rows and odd columns together, and the even rows and even columns together, resulting in a dynamic error system model with the standard form of distributed singular perturbations:

[0101] ,

[0102] The correlation matrix is ​​defined as follows:

[0103]

[0104]

[0105]

[0106] .

[0107] Step S4: Based on the dynamic error system model in Step S3, solve the fast and slow state control gain in the multi-scale consensus controller in Step S2 using multi-scale control technology.

[0108] S4.1 First, based on the dynamic error system model with distributed singular perturbation standard form established in step S3, a multi-scale control technique is used to construct a system containing... Lyapunov function : ,in, The specific form is: .

[0109] S4.2, then, by modifying the structure constructed in step S4.1 containing... By performing finite difference operations on the Lyapunov equations and calculating their expected values, and utilizing the Schur complement principle and some scaling properties, we derive the LMIs that ensure mean-square leader-follower consistency in unmanned systems as follows:

[0110]

[0111]

[0112] ;

[0113] in, It is to satisfy Given parameters, , , and It is a symmetric matrix with appropriate dimensions. , , and It is a matrix with appropriate dimensions; , , , , , , and For a matrix with a certain dimension, its specific form is:

[0114]

[0115] .

[0116] S4.3 Finally, based on the matrix inequality equations obtained in S4.2, , , and Solve for the fast and slow state control gain. and for: .

[0117] Step S5: Based on probability theory and the properties of the correlation matrix spectrum, solve for the noise control gain and differential privacy parameter in the multi-scale consensus controller in step S2.

[0118] S5.1, First, define a set - Initial state of adjacent followers and ,satisfy: , Among them, there are followers. The initial state relationship satisfies , for One component is 0, and all other components are 0. There are two initial states. and The error vector between them.

[0119] Define the initial state and The two corresponding times are 0 to 1. Noise sequence:

[0120]

[0121] ,

[0122] in, Initial state At that time The value of the noise vector injected at time 1. Initial state Time from time 0 to time 1 The augmentation of the noise vector, Initial state At that time The value of the noise vector injected at time 1. Initial state Time from time 0 to time 1 Augmentation of the noise vector.

[0123] S5.2, then, assuming - Initial state of adjacent followers and To make the corresponding output sequence sets the same, then, according to Design noise and satisfy:

[0124] .

[0125] S5.3, following this, based on probability theory and random noise variables... and The relationship can be used to deduce the initial state of the final unmanned system. It can be achieved Differential privacy, where each follower Privacy level It can be represented as: ,in, , and A constant that satisfies certain conditions. satisfy , satisfy , satisfy , Representation matrix The spectrum, This represents the decay rate of the added Laplace noise with attenuation characteristics. express The minimum value, express The minimum value, This represents the initial value of the added Laplace noise with attenuation characteristics.

[0126] S5.4 Finally, based on the properties of the spectrum and the requirements of the differential privacy parameter in step S5.3, the noise control gain in the multi-scale cooperative controller is obtained. satisfy: .

[0127] In this embodiment, four followers are selected as an example, and their communication topology is as follows: Figure 2 As shown, number 0 is the leader, and numbers 1-3 are followers. The perturbation parameters are selected. Define the system dynamic model parameters for the four followers as follows:

[0128]

[0129] Based on the system equations, find the matrix that satisfies the requirements and is under control. Then we have:

[0130]

[0131] Assumption The minimum attenuation rate of the injected noise is designed to be Based on the multi-scale cooperative controller design criteria in steps 4 and 5, the control gain can be obtained:

[0132] .

[0133] In consensus analysis, it is assumed that noise is injected. ,in Define the initial state of the leader and 3 followers as follows:

[0134] ,

[0135] .

[0136] In privacy analytics, two sets are defined. - Adjacent initial state vectors , Define two types , The state information of followers 1 and 3 is exactly the same as the initial state in the above formula analysis. We designed the injected Laplace noise as... ,in .

[0137] The simulation results are as follows: Figure 3 – Figure 7 As shown, Figure 3 The mean square error variation curves of three followers after 1000 Monte Carlo trials are presented. Figure 4 and Figure 5 The simulation results show the trajectory tracking results of three followers and one leader under a random single trial condition in two slow states and two fast states, respectively, in an embodiment of the present invention. The simulation results show that the unmanned system can achieve consistency with the leader's state in both fast and slow states. Furthermore, the mean square error curves obtained through 1000 Monte Carlo trials all exhibit absolute convergence characteristics, indicating that the multi-scale cooperative controller designed in step 2 achieves mean square leader-follower consistency between the leader and followers.

[0138] Figure 6 The data trajectory transmitted by follower 2 to its neighboring followers under two different initial states is shown. It can be seen that, in this scenario, despite the different initial states, follower 2 maintains a consistent data transmission trajectory, making it difficult for eavesdroppers to infer its true initial state information, thus effectively meeting the system's privacy protection requirements. Figure 7The relationship curves between the privacy level parameter and the noise attenuation parameter and their initial values ​​in embodiments of the present invention are presented. The results show that in step 2, the greater the attenuation rate and initial value of the noise injected by the multi-scale cooperative controller, the higher the corresponding privacy level parameter of the system, and the stronger the privacy protection performance.

[0139] In summary, simulation results verify the effectiveness of the proposed algorithm. This algorithm not only overcomes the ill-conditioned numerical problems caused by perturbation parameters during the design process by utilizing multi-scale control technology, achieving mean-square leader-follower consistency between the leader and followers in unmanned systems, but also simultaneously satisfies the requirement of initial state privacy protection for unmanned systems, demonstrating promising engineering application prospects and practical application value.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A collaborative privacy protection method for unmanned systems based on multi-scale control technology, characterized in that, Includes the following steps: S1: Establish a dynamic model based on the fast-slow coupling characteristics of unmanned systems; S2: Follower in unmanned systems Design a differential privacy leader-follower multi-scale collaborative controller with noise feedback; S3: Obtain the distributed singular perturbation standard form of the leader-follower dynamic error system model through matrix transformation; S4: Based on the dynamic error system model in step S3, solve the fast and slow state control gain in the multi-scale cooperative controller in step S2 using multi-scale control technology; S5: Based on probability theory and the properties of the correlation matrix spectrum, solve for the specific forms of noise control gain and differential privacy parameters in the multi-scale cooperative controller in step S2.

2. The method for collaborative privacy protection of unmanned systems based on multi-scale control technology as described in claim 1, characterized in that, In step S1, establishing a dynamic model based on the fast-slow coupling characteristics of the unmanned system specifically includes the following steps: S1.1: Establish a dynamic model of a leader with fast-slow coupling characteristics, specifically as follows: ， in, and These represent the superscripts for the slow and fast states, respectively. Indicates the time step. and Leaders at any time Slow and fast states; The dimension is unit array, , , and Given a known parameter matrix with compatible dimensions, These are perturbation parameters, which describe the variables. and The separation of dynamics on fast and slow time scales; S1.2: Establishing a follower with fast-slow coupling characteristics The dynamic model is as follows: ， in, The number representing the follower. and Followers At any moment The slow state and the fast state, For followers At any moment Control input; and A known parameter matrix with compatible dimensions; S1.3: Expand the number of leaders and followers respectively. The dynamic equations are as follows: ， in, and These represent the augmented forms of the leader's fast and slow states, and the followers, respectively. Augmented forms of fast and slow states, Represents the transpose of a vector or matrix. and Let represent the system state matrix and input matrix, respectively; based on the specific form of the augmented matrix, we obtain... The requirements must be controllable.

3. The method for collaborative privacy protection of unmanned systems based on multi-scale control technology as described in claim 1, characterized in that, The specific content of step S2 is as follows: S2.1: Design Differential Privacy Noise The specific form; defining the direction for each follower Injected Laplace noise in The value at time ,in, Represented as: ， in, Indicates follower Dimensions Represents the transpose of a vector or matrix; design probability density for: ， in, The mathematical expectation is expressed as The variance is expressed as , For time An exponentially decaying function, its specific form is: ,in, for initial value, Given the base of the exponentially decaying term, it is required that... ; S2.2: Design a differential privacy leader-follower consensus multi-scale collaborative controller with noise feedback as follows: ， It can be transformed into: ， in , and These represent the control gains for the slow and fast states in a multi-scale cooperative controller, respectively. , and These represent the control gains for noise injected into the slow and fast states in the multi-scale cooperative controller, respectively. Indicates follower Neighborhood set, Indicates follower With followers The adjacency coefficient, Indicates follower Adjacency coefficient with the leader; Followers At any moment Used to transmit the status data of other followers. Followers At any moment Receive neighbor follower The state in which, , and They are followers At any moment Used for slow and fast states in data transmission. , and They are followers At any moment Slow and fast states are used for data transmission.

4. The method for collaborative privacy protection of unmanned systems based on multi-scale control technology as described in claim 1, characterized in that, The specific content of step S3 is as follows: S3.1: Through leaders and followers The dynamic equations yield the following error system model for a single follower: ， in, For followers Error of the leader's state at time The value, The specific form of expression is ,in, , ; S3.2: Augment the error vector of each follower in S3.1 into a dynamic error system model with N followers: ， in, This represents the augmentation of the error vector for each follower. This represents the operation of the Crodic product. express An identity matrix of dimensions , For a multi-follower system, the Laplace matrix is ​​shown in the diagram. For leaders and every follower The adjacency diagonal matrix; This represents the combined term of all noise. The specific form of expression is: ； S3.3: Define the transformation matrix , This is an elementary matrix with two rows swapped. Based on the properties of the transformation matrix, the left and right sides of the dynamic error system model with N followers in step S3.2 are multiplied by the transformation matrix, thus grouping its odd-numbered rows and columns together, and even-numbered rows and columns together, resulting in a dynamic error system model with the standard form of distributed singular perturbations, specifically: ， The correlation matrix is ​​defined as follows: 。 5. The method for collaborative privacy protection of unmanned systems based on multi-scale control technology as described in claim 1, characterized in that, The specific content of step S4 is as follows: S4.1: Based on the dynamic error system model with distributed singular perturbation standard form established in step S3, construct a system containing multi-scale control techniques. Lyapunov function : ， in, The specific form is as follows: ； S4.2: By modifying the structure constructed in step S4.1, which contains... By performing finite difference operations on the Lyapunov equations and calculating their expected values, and utilizing the Schur complement principle and scaling properties, we derive the LMIs that ensure mean-square leader-follower consistency in unmanned systems. The LMIs are as follows: ， in, It is to satisfy Given parameters, , , and It is a symmetric matrix with compatible dimensions. , , and It is a matrix with compatible dimensions. , , , , , , and For a matrix with a certain dimension, its specific form is: ； S4.3: Obtained by solving the matrix inequality equations in S4.2 , , and Solve for the fast and slow state control gain. and Specifically: 。 6. The method for collaborative privacy protection of unmanned systems based on multi-scale control technology as described in claim 1, characterized in that, The specific content of step S5 is as follows: S5.1: Define a set - Initial state of adjacent followers and ,satisfy: ， ， Among them, there are followers. The initial state relationship satisfies , for One component is 0, and all other components are 0. There are two initial states. and The error vector between them; Define the initial state and The two corresponding times are 0 to 1. Noise sequence: ， in, Initial state At that time The value of the noise vector injected at time 1. Initial state Time from time 0 to time 1 The augmentation of the noise vector, Initial state At that time The value of the noise vector injected at time 1. Initial state Time from time 0 to time 1 Augmentation of the noise vector; S5.2: Assumptions - Initial state of adjacent followers and To ensure that the corresponding output sequence sets are identical, noise is designed according to the definition in S5.

1. and satisfy: ； S5.3: Based on probability theory and the random noise variable in step S5.2 and Based on the relationship, derive the initial state of the final unmanned system. Capable of achieving Differential privacy, where each follower Privacy level It can be represented as: ， in, , and A constant that satisfies certain conditions, namely: satisfy , satisfy , satisfy , Representation matrix The spectrum, This represents the decay rate of the added Laplace noise with attenuation characteristics. express The minimum value, express The minimum value, This represents the initial value of the added Laplace noise with attenuation characteristics; S5.4: Based on the properties of the spectrum and the requirements of the differential privacy parameter in step S5.3, the noise control gain in the multi-scale cooperative controller is obtained. ,satisfy: 。

Images