Intelligent network connection automobile system mean square consensus method for asynchronous sampling control under privacy protection

Abstract

The invention relates to the field of intelligent connected automobile systems, in particular to an asynchronous sampling control intelligent connected automobile system mean square consensus method under privacy protection. Comprising the following steps: introducing a time conversion method and a shared sampling period to process asynchronous sampling interaction of heterogeneous intelligent networked automobile communication; acquiring a sampling distributed controller with time-varying noise and an algorithm for the intermittent interactive heterogeneous intelligent connected automobile system; a new hybrid closed-loop system is constructed, and a Lyapunov function is constructed for the closed-loop system to obtain conditions for realizing mean square output consensus of the heterogeneous intelligent connected automobile system; parameters in the algorithm are determined, and the convergence precision, the convergence speed and the differential privacy budget of the heterogeneous intelligent network connection automobile system are quantified. According to the method, the privacy protection mean square output consensus problem of the heterogeneous intelligent networked automobile system under the condition that asynchronous sampling interaction and transmission have bounded time-varying delay is solved.

Description

Technical Field

[0001] The present invention relates to the field of intelligent connected vehicle systems, and specifically to a mean square output consensus method for heterogeneous intelligent connected vehicle systems with asynchronous sampling control under privacy protection. Background Technique

[0002] With the rapid development of cloud computing and the Internet of Things, various intelligent control systems can be interconnected and collect a large amount of data, and then analyze these data to provide more intelligent and personalized services. In recent years, the distributed cooperative control of multi-agent systems has become a dynamic and promising research field, with extensive applications in the cooperative control of unmanned aerial vehicles, wireless sensor network communication, and the autonomous control of robotic vehicles. Among them, the intelligent transportation system has become an effective method to improve the performance of the transportation system and enhance driving safety. It is worth noting that the distributed consensus problem is a key issue. In this field, heterogeneous intelligent connected vehicle systems can represent the individual differences between vehicles, which makes them highly relevant in practical applications.

[0003] Through wireless network communication technology, vehicles can obtain richer information from adjacent vehicles and thus benefit from various control advantages, such as enhanced adaptability and flexibility. However, it is not easy to achieve continuous communication in a network environment because it implies infinite network bandwidth. In practical applications, sampled information is usually transmitted through the network for information exchange. The perfect periodic sampling theory provides a solid foundation for network control systems. However, in practical scenarios, unreliable wireless channels and limited bandwidth will inevitably lead to problems such as transmission delay, packet loss and misalignment, or denial of service attacks. The sampling interval between two adjacent sampling moments is usually time-varying. In addition, network limitations, the lack of a central node for synchronous control actions, and limited data sampling devices will exacerbate the asynchrony within multi-agent systems. However, introducing an asynchronous sampling scenario brings major challenges, which may complicate the situation.

[0004] However, there are a large number of potential risks in data transmission. In intelligent connected vehicle systems, the privacy of vehicles is damaged because the exchanged driving information may be eavesdropped, and even the communication channels of the vehicle fleet may be disrupted. Therefore, privacy protection between vehicles is essential. There are rich research results related to privacy protection, including methods such as cryptographic theory, state decomposition, output masking, and random noise perturbation. The privacy protection scheme based on adding random noise is simple in design, easy to implement, widely applied, and significantly reduces the computational complexity. Differential privacy is one of the most popular and promising methods at present. Differential privacy and sampling technology have the same attributes, which prompts us to combine them to improve the accuracy of the differential privacy mechanism. However, the transmission and update of information will not be completely regular and ideal, and the asynchrony of sampling also needs to be considered at the same time.

[0005] Therefore, how to solve the mean square consensus problem of intelligent connected vehicle systems with asynchronous sampling control under privacy protection is a technical problem that needs to be solved urgently in this field. Summary of the invention

[0006] The present invention discloses a mean square consensus method for an intelligent connected vehicle system with asynchronous sampling control under privacy protection, which solves the problem of privacy protection mean square output consensus of heterogeneous intelligent connected vehicle systems in an asynchronous sampling data environment, and can better protect privacy information while ensuring that the performance of the heterogeneous intelligent connected vehicle system is not damaged.

[0007] The present invention provides a mean square consensus method for an intelligent connected vehicle system with asynchronous sampling control under privacy protection, comprising the following steps:

[0008] Step 1: Introduce time conversion method and shared sampling cycle to handle asynchronous sampling interaction of heterogeneous intelligent connected vehicles;

[0009] Step 2: Obtain a sampling distributed controller with time-varying noise and a sampling data distributed differential privacy output consensus control algorithm for intermittently interacting heterogeneous intelligent connected vehicle systems;

[0010] Step 3: Build a new hybrid closed-loop system, and obtain the conditions for heterogeneous intelligent connected vehicle systems to achieve mean square output consensus by constructing a Lyapunov function for the closed-loop system.

[0011] Step 4: Determine the parameters in the algorithm and quantify the convergence accuracy, convergence speed and differential privacy budget of the heterogeneous intelligent connected vehicle system.

[0012] Furthermore, the specific process of step 1 is that the self-driving car drives on the horizontal road of the highway, and each vehicle can communicate and exchange information with its neighbors. The vehicle distance d between the i-th and i-1-th vehicles is i,i-1 , vehicle speed v i and vehicle acceleration Φ i Keep consistent; give a simplified nonlinear intelligent connected vehicle dynamics model as follows,

[0013]

[0014] Where t is the continuous time, m i is the mass of vehicle i, δ i is the position of vehicle i, Θ i is the combined aerodynamic drag coefficient, is the acceleration due to gravity, is the rolling resistance coefficient, Π i Indicates the actual driving / braking torque, Π i,desis the desired driving / braking torque, is the inertial delay of vehicle dynamics, Λ i represents the tire radius, is the mechanical efficiency of the powertrain;

[0015] The nonlinear intelligent connected vehicle dynamics model (1) is linearized using the exact feedback linearization technique,

[0016]

[0017] and then we get,

[0018]

[0019] The continuous-time heterogeneous intelligent connected vehicle system model is represented as follows,

[0020]

[0021] where, is the state of vehicle i, are the coefficient matrices of the heterogeneous intelligent connected vehicle system, respectively, u i is the output of vehicle i, y i is the control input of vehicle i. A sampling instant interaction scheme is introduced, where the vehicle only transmits information about its reference state ξ i (t) to its neighbors at the sampling instants, because asynchronous sampling data means that vehicle i transmits and samples data separately from other vehicles; the sampling instant sequence where is the sampling interval of vehicle i, k is obtained from natural numbers, using zero-order hold, the control signal is generated as piecewise constant and remains constant between neighborhood updates, and the sampled reference state is defined

[0022]

[0023] Assume that vehicle j receives ξ at time instant i (t), where represents the time-varying delay during the transmission from vehicle i to vehicle j. Here, it is assumed that the samples are sent in a sequential manner on all information links, i.e., The received reference state of vehicle j from other vehicle i is as follows:

[0024]

[0025] Assume that each vehicle samples its own reference state regularly and they all share a common sampling period T, i.e., for all k, Let For different vehicles, the initial sampling time of the reference state can start at different times, i.e., Take a vehicle i 0 , and virtually align the sampling times of other vehicles with it. By means of a time conversion method, a new reference state variable is introduced, i.e., Other variables change together, including the state Output Control input To avoid the situation of being received before , let the time delay satisfy Define, and give the time conversion reference state vector

[0026]

[0027] Furthermore, the sampling distributed controller with time-varying noise is designed as

[0028]

[0029] where K 1i and K 2i are gain matrices, α k is the step size, the l-th component of the noise vector η j follows a Laplace distribution at any time k, i.e., η j,l ~Lap(0,δ k ), δ k is the differential privacy noise parameter, N i ={j∈Υ:a ij ≠0} is the neighbor set of vehicle i, Υ={1,2,...,N} is a set of vehicles, a ij is an element in the weighted adjacency matrix, is the left limit at time i χ(t) is right continuous, i.e., And the initial value of the reference state Note that K 2i =Ω i -K 1i Ξ i i and Ξ i are two real matrices satisfying and I v×v is the identity matrix of dimension v;

[0030] The local controller of each vehicle models a continuous-time dynamic feedback controller and uses information about the states of neighboring vehicles to adjust the local controller each time information is obtained at the sampling moment. The following presents a sampled-data distributed differential privacy output consensus control algorithm:

[0031]

[0032] Furthermore, in step three, define Substituting the sampled distributed controller (8) into the heterogeneous intelligent connected vehicle system (4) gives

[0033]

[0034] where K 1 = diag{K 11 , K 12 ,..., K 1N} represents a diagonal matrix with diagonal elements K 11 K 12 ... K 1N ; Discretizing formula (9) gives

[0035]

[0036] The reference state in the controller is updated as

[0037]

[0038] Substituting formula (11) into gives

[0039]

[0040] where is the Laplacian matrix, A is the weighted adjacency matrix, is the Kronecker product, 1 is a column vector with all elements equal to 1; thus, the hybrid closed-loop system with respect to and is represented as follows

[0041]

[0042] where Ξ = diag{Ξ 1 , Ξ 2 ,..., Ξ N}; in the case of Hurwitz stability, define two Lyapunov functions and Taking the expectation on both sides gives E[V 1 (k + 1)+V 2 (k + 1)] = 0, which is equivalent to and obtaining the conditions for the heterogeneous intelligent connected vehicle system to achieve mean - square output consensus where E represents taking the expectation value.

[0043] Furthermore, in step four, a precision parameter (β * , θ * ) is given. Let the step - size in the algorithm be and the differential privacy noise parameter be where the parameter γ ∈ (0, 1], and the parameters are all real parameters greater than zero. First, according to the multi - dimensional Chebyshev inequality, we get

[0044]

[0045] where is a random variable that satisfies denotes the covariance matrix of the vector ; The inequality (14) can be rewritten as the inequality where only need to make to ensure that the output consensus of the heterogeneous intelligent connected vehicle system reaches the (β * , θ * ) precision. Substituting and simplifying, we get that as long as is satisfied, it can ensure that the output consensus of the heterogeneous intelligent connected vehicle system reaches the (β * , θ * ) precision; Substituting the step - size and the differential privacy noise parameter into and simplifying and scaling, we get

[0046]

[0047] The heterogeneous intelligent connected vehicle system will achieve mean - square output consensus with the (β * , θ * ) precision, that is

[0048] In the case of γ = 1, the mean - square convergence rate of the heterogeneous intelligent connected vehicle system is

[0049]

[0050] In the case of 0 < γ < 1, the mean - square convergence rate of the heterogeneous intelligent connected vehicle system is

[0051]

[0052] Among them, Ο represents infinitesimals of the same order. f(t) = Ο(g(t)) means that there exists a positive number z and t 0 , such that when t → t 0 , |f(t) / g(t)| ≤ z; is a constructed real symmetric matrix, and λ 2 (L 2 ) is the algebraic connectivity of L 2 .

[0053] The differential privacy budget ε is specifically expressed as

[0054]

[0055] Among them, T c = {1, 2,..., k c} is a finite set of sampling points, and k c is the last sampling point. is the sensitivity, and its expression is

[0056]

[0057] Among them, represents the degree of the directed graph G, and c min = min{c i , i ∈ 1, 2,..., N} is the minimum degree; Given the upper bound parameter ε * of the differential privacy budget, let the step size in the algorithm be The differential privacy noise parameter is Among them, the parameter γ ∈ (0, 1], and the parameters are all real parameters greater than zero. In the infinite time domain, the upper bound of the differential privacy budget is given in the following four cases. When γ = 1:

[0058] We get

[0059]

[0060] We get

[0061]

[0062] When 0 < γ < 1: We get

[0063]

[0064] We get

[0065]

[0066] Among them, is the upper incomplete gamma function.

[0067] The present invention provides a mean-square consensus method for an intelligent connected vehicle system with asynchronous sampling control under privacy protection. To solve the privacy protection average consensus problem of a continuous-time heterogeneous intelligent connected vehicle system with intermittent information transmission under asynchronous sampling data, the present invention models a sampled distributed controller with time-varying noise, enabling each vehicle to interact with sensitive information at the sampling moment, protecting privacy while maintaining trajectory availability.

[0068] The present invention proposes a differential privacy output consensus control algorithm for a sampled data distributed heterogeneous intelligent connected vehicle system. The algorithm is implemented based on the neighbor information of each vehicle at the sampling moment, overcoming difficulties such as channel congestion and intermittent information transmission. Differential privacy and sampling techniques have the same properties. The present invention introduces sampling techniques into a heterogeneous intelligent connected vehicle system to improve the accuracy of the differential privacy mechanism. To achieve optimal privacy protection, noise design is also crucial. The privacy noise changes over time to protect the initial state and the state after iterative updates. In summary, the present invention solves the mean-square consensus problem of an intelligent connected vehicle system with asynchronous sampling control under privacy protection. Brief Description of the Drawings

[0069] Figure 1 is a schematic diagram of the implementation process of the present invention;

[0070] Figure 2 is a vehicle communication topology diagram composed of 4 vehicles in the present invention;

[0071] Figure 3 is the reference state trajectory of 4 vehicles in the present invention at T max = 0.141;

[0072] Figure 4 is the output state trajectory of 4 vehicles in the present invention at T max = 0.141;

[0073] Figure 5 is the output state trajectory of 4 vehicles in the present invention at T max = 0.142;

[0074] Figure 6 is a more complex vehicle communication topology diagram composed of 12 vehicles in the present invention;

[0075] Figure 7 is the decaying noise trajectory in the existing literature;

[0076] Figure 8is a non-decaying noise trajectory with constant variance in the existing literature;

[0077] Figure 9 is a non-decaying noise trajectory with time-varying variance of the present invention;

[0078] Figure 10 is the output state trajectory of 12 vehicles under the noise of the present invention. Detailed implementation manners

[0079] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation manners. It should be understood that the following specific implementation manners are only used for the present invention and not for limiting the scope of the present invention.

[0080] As Figure 1 shown, a mean-square consensus method for an intelligent connected vehicle system with asynchronous sampling control under privacy protection provided by the present invention mainly includes the following steps in the specific implementation process.

[0081] Step 1: Introduce a time conversion method and a shared sampling period to process the asynchronous sampling interaction of heterogeneous intelligent connected vehicles;

[0082] Step 2: Obtain a sampling distributed controller with time-varying noise and a sampling data distributed differential privacy output consensus control algorithm for an intermittent interaction heterogeneous intelligent connected vehicle system;

[0083] Step 3: Construct a new hybrid closed-loop system, and obtain the conditions for the heterogeneous intelligent connected vehicle system to achieve mean-square output consensus by constructing a Lyapunov function for the closed-loop system;

[0084] Step 4: Determine the parameters in the algorithm, and quantify the convergence accuracy, convergence speed and differential privacy budget of the heterogeneous intelligent connected vehicle system.

[0085] In this embodiment, the specific process of Step 1 is that an autonomous vehicle travels on a horizontal road of a highway, and each vehicle can communicate and exchange information with its neighbors. The vehicle distance d i,i-1 between the i-th and the (i - 1)-th vehicles, the vehicle speed v i and the vehicle acceleration Φ i are kept consistent; a simplified non-linear dynamic model of an intelligent connected vehicle is given as follows.

[0086]

[0087] where t is continuous time, m i is the mass of vehicle i, δ i is the position of vehicle i, Θ i is the combined aerodynamic drag coefficient, is the acceleration caused by gravity, is the rolling resistance coefficient, Π i represents the actual driving / braking torque, Π i,des is the desired driving / braking torque, is the inertial delay of vehicle dynamics, Λ i represents the tire radius, is the mechanical efficiency of the powertrain;

[0088] The nonlinear intelligent connected vehicle dynamics model (1) is linearized using the exact feedback linearization technique,

[0089]

[0090] Then, we obtain,

[0091]

[0092] The continuous-time heterogeneous intelligent connected vehicle system model is represented as follows,

[0093]

[0094] where, is the state of vehicle i, are the coefficient matrices of the heterogeneous intelligent connected vehicle system, respectively, and u i is the output of vehicle i, and y i is the control input of vehicle i. A sampling instant interaction scheme is introduced, where the vehicle only transmits information about its reference state ξ i (t) to its neighbors at the sampling instant, because asynchronous sampling data means that vehicle i transmits and samples data separately from other vehicles; the sampling instant sequence where is the sampling interval of vehicle i, k is obtained from natural numbers, and using zero-order hold, the control signal is generated as piecewise constant, remaining constant between neighborhood updates. The sampling reference state is defined as

[0095]

[0096] Assume that vehicle j receives ξ at time i (t), where represents the time-varying delay during the transmission from vehicle i to vehicle j. Here, it is assumed that the samples are sent in a sequential manner on all information links, i.e., The received reference state of vehicle j from other vehicle i is as follows:

[0097]

[0098] Assume that each vehicle samples its own reference state regularly, and they all share a common sampling period T, i.e., for all k, Let For different vehicles, the initial sampling times of the reference states can start at different times, i.e., Take a vehicle i 0 , and virtually align the sampling times of other vehicles with it. By the time conversion method, introduce a new reference state variable, i.e., Other variables change together, including the state Output Control input To avoid the situation of being received before , let the time delay satisfy Define, given the time-converted reference state vector

[0099]

[0100] In this embodiment, the sampling distributed controller with time-varying noise in step two is designed as

[0101]

[0102] where K 1i and K 2i are gain matrices, α k is the step size, the l-th component of the noise vector η j follows a Laplace distribution at any time k, i.e., η j,l ~Lap(0,δ k ), δ k is the differential privacy noise parameter, N i ={j∈Υ:a ij ≠0} is the neighbor set of vehicle i, Υ={1,2,...,N} is a set of vehicles, a ij is an element in the weighted adjacency matrix, is the left limit at time i , χ while the initial value of the reference state Note that K 2i =Ω i -K 1i Ξ i , Ω i and Ξ i are two real matrices satisfying and I v×v is the identity matrix of dimension v;

[0103] The local controller of each vehicle models a continuous-time dynamic feedback controller. Each time information is obtained at the sampling moment, the information about the states of adjacent vehicles is used to adjust the local controller. The following gives a sampled-data distributed differential privacy output consensus control algorithm:

[0104]

[0105] In this embodiment, in step three, it is defined that After substituting the sampled distributed controller (8) into the heterogeneous intelligent connected vehicle system (4), it is obtained that

[0106]

[0107] where, K 1 = diag{K 11 , K 12 ,..., K 1N} represents a diagonal matrix with diagonal elements of K 11 K 12 ... K 1N ; Discretizing formula (9) gives

[0108]

[0109] The reference state in the controller is updated as

[0110]

[0111] Substituting formula (11) into gives

[0112]

[0113] where, is the Laplacian matrix, A is the weighted adjacency matrix, is the Kronecker product, 1 is a column vector with all elements being 1; thus, the hybrid closed-loop system with respect to and is represented as follows

[0114]

[0115] where, Ξ = diag{Ξ 1 , Ξ 2 ,..., Ξ N}; in the case of Hurwitz stable, two Lyapunov functions and Taking the expectation on both sides gives E[V 1 (k + 1)+V 2 (k + 1)] = 0, which is equivalent to and obtaining the conditions for the heterogeneous intelligent connected vehicle system to achieve mean - square output consensus where E represents taking the expectation value.

[0116] In this embodiment, in step four, a precision parameter (β * , θ * ) is given. Let the step - size in the algorithm be and the differential privacy noise parameter be where the parameter γ ∈ (0, 1], and the parameters are all real parameters greater than zero. First, according to the multi - dimensional Chebyshev inequality, we get

[0117]

[0118] where is a random variable satisfying denotes the covariance matrix of the vector ; Inequality (14) can be rewritten as inequality where only need to make to ensure that the output consensus of the heterogeneous intelligent connected vehicle system reaches (β * , θ * ) precision. Substituting and simplifying, we get that as long as is satisfied, it can ensure that the output consensus of the heterogeneous intelligent connected vehicle system reaches (β * , θ * ) precision; Substituting the step - size and the differential privacy noise parameter into and simplifying and scaling, we get

[0119]

[0120] The heterogeneous intelligent connected vehicle system will achieve mean - square output consensus with (β * , θ * ) precision, that is,

[0121] In the case of γ = 1, the mean - square convergence rate of the heterogeneous intelligent connected vehicle system is

[0122]

[0123] In the case of 0 < γ < 1, the mean - square convergence rate of the heterogeneous intelligent connected vehicle system is

[0124]

[0125] Among them, Ο represents infinitesimals of the same order. f(t) = Ο(g(t)) means that there exists a positive number z and t 0 , such that when t → t 0 , |f(t) / g(t)| ≤ z; is a constructed real symmetric matrix, and λ 2 (L 2 ) is the algebraic connectivity of L 2 .

[0126] The differential privacy budget ε is specifically expressed as

[0127]

[0128] where T c = {1, 2,..., k c} is a finite set of sampling points, and k c is the last sampling point. is the sensitivity, and its expression is

[0129]

[0130] where represents the degree of the directed graph G, and c min = min{c i , i ∈ 1, 2,..., N} is the minimum degree; the upper bound parameter ε of the differential privacy budget is given * , and let the step size in the algorithm be The differential privacy noise parameter is where the parameter γ ∈ (0, 1], and the parameters are all real parameters greater than zero. In the infinite time domain, the upper bound of the differential privacy budget is given in the following four cases. When γ = 1:

[0131] We get

[0132]

[0133] We get

[0134]

[0135] When 0 < γ < 1: We get

[0136]

[0137] We get

[0138]

[0139] Among them, is the upper incomplete gamma function.

[0140] To verify the effectiveness of the proposed theoretical results, the specific numerical values of the vehicle parameters used in the simulation are shown in Table 1. Table 1 Vehicle design parameters

[0141]

[0142] First, to illustrate the effectiveness of the proposed Algorithm 1 for asynchronous sampled data, four vehicles are coupled through the Figure 2 shown communication topology graph. Each vehicle satisfies the intelligent connected vehicle system (4) and the values of the vehicle design parameters shown in Table 1. To verify that while applying privacy noise, each vehicle still converges to a common random value, consider the average value of the output state as

[0143] In this example, our goal is to achieve output consensus up to (β * , θ * ) accuracy and the upper bound ε * of the differential privacy budget, where β * = 0.35, θ * = 3, ε * = 3. Set the differential privacy noise parameter δ k = (k + 1) 0.1 and the step size α k = 1 / (k + 1) 0.8 . Solve the maximum sampling interval for each vehicle's communication by using the spectral radius The total maximum sampling period is The results of the reference state χ(t) and the output state y(t) are shown in Figure 3 and Figure 4 respectively. However, if T max = 0.142, output consensus cannot be achieved, as shown in Figure 5 .

[0144] Next, a heterogeneous intelligent connected vehicle system with a more complex topology is considered to verify the effectiveness of the theory. Consider the Figure 6 random topology among 12 vehicles coupled in communication in . Each vehicle satisfies the intelligent connected vehicle system (4) and the values of the vehicle design parameters shown in Table 1. The goal of the simulation is to achieve output consensus up to (β * , θ * ) accuracy and the upper bound ε * of the differential privacy budget, where β * = 0.42, θ *= 4.5, ε * = 1.6, considering a set of random numbers in the interval [0, 70], the average value of the output state Set the step size α k = 1 / (k + 1) 0.8 , and the differential privacy noise parameter is further designed as δ k = (k + 1) 0.2 , the differential privacy noise parameter compared with the existing literature is designed as δ k = 5 * 0.9 k and δ ave = 2.66, and the total maximum sampling period is also T max = 0.138, and it is also executed within the stability threshold.

[0145] Figure 7 It is observed that the noise with parameter δ k = 5 * 0.9 k eventually decays to zero; Finally, it decays to zero; Figure 8 It is observed that the noise with parameter δ ave = 2.66 is non - decaying noise, but has a constant variance; while in this paper, as Figure 9 shown, the variance of the random noise is increasing. In contrast, the information protected by noise in this paper cannot be directly inferred over time, and the noise is easier to adjust. Figure 10 The output state trajectories of 12 cars are shown. It can be seen that under the sampling - based distributed controller with time - varying noise designed in the present invention, output consensus can still be achieved while ensuring that information is not leaked.

[0146] The above results show that the mean - square consensus method for an intelligent connected vehicle system with asynchronous sampling control under privacy protection proposed by the present invention effectively solves the privacy - protected average consensus problem of a continuous - time heterogeneous intelligent connected vehicle system with intermittent information transmission under asynchronous sampling data. The present invention models a sampling - based distributed controller with time - varying noise, enabling each vehicle to interact with sensitive information at the sampling moment, protecting privacy while maintaining the availability of the trajectory. The present invention proposes a sampling - data distributed differential privacy output consensus control algorithm, which is implemented based on the neighbor information of each vehicle at the sampling moment, overcoming difficulties such as channel congestion and intermittent information transmission. Differential privacy and sampling techniques have the same attributes. The present invention introduces sampling techniques into heterogeneous multi - agent systems to improve the accuracy of the differential privacy mechanism. To achieve optimal privacy protection, noise design is also crucial. The privacy noise changes over time to protect the initial state and the state after iterative updates.

[0147] In summary, the present invention introduces a time conversion method and a shared sampling period to handle asynchronous sampling interactions of heterogeneous intelligent connected vehicles; obtains a sampling distributed controller and algorithm with time-varying noise for an intermittent interaction heterogeneous intelligent connected vehicle system; constructs a new hybrid closed-loop system, and obtains the conditions for the heterogeneous intelligent connected vehicle system to achieve mean-square output consensus by constructing a Lyapunov function for the closed-loop system; determines the parameters in the algorithm, and quantifies the convergence accuracy, convergence speed and differential privacy budget of the heterogeneous intelligent connected vehicle system.

Claims

1. A mean square consensus method for intelligent connected vehicle system with asynchronous sampling control under privacy protection, characterized in that: The following steps are included: Step 1: Introduce time conversion method and shared sampling cycle to handle asynchronous sampling interaction of heterogeneous intelligent connected vehicles; Step 2: Obtain a sampling distributed controller with time-varying noise and a sampling data distributed differential privacy output consensus control algorithm for intermittently interacting heterogeneous intelligent connected vehicle systems; Step 3: Build a new hybrid closed-loop system, and obtain the conditions for heterogeneous intelligent connected vehicle systems to achieve mean square output consensus by constructing a Lyapunov function for the closed-loop system. Step 4: Determine the parameters in the algorithm and quantify the convergence accuracy, convergence speed and differential privacy budget of the heterogeneous intelligent connected vehicle system.

2. According to the privacy protection asynchronous sampling control intelligent connected vehicle system mean square consensus method of claim 1, it is characterized by: The specific process of step 1 is that the self-driving car drives on the horizontal road of the highway. Each vehicle can communicate and exchange information with its neighbors. The vehicle distance d between the i-th and i-1 vehicles is i,i-1 , vehicle speed v i and vehicle acceleration Φ i Keep consistent; give a simplified nonlinear intelligent connected vehicle dynamics model as follows, Where t is the continuous time, m i is the mass of vehicle i, δ i is the position of vehicle i, Θ i is the combined aerodynamic drag coefficient, is the acceleration due to gravity, is the rolling resistance coefficient, Π i Indicates the actual driving / braking torque, Π i,des is the desired driving / braking torque, is the inertial delay of vehicle dynamics, Λ i Indicates the tire radius, is the mechanical efficiency of the drive train; The nonlinear intelligent connected vehicle dynamics model (1) is linearized using the precise feedback linearization technique. Then get, The continuous-time heterogeneous intelligent connected vehicle system model is represented as follows: in, is the state of vehicle i, They are the coefficient matrices of the heterogeneous intelligent connected vehicle system, u i is the output of vehicle i, y i is the control input of vehicle i, and a sampling-time interaction scheme is introduced, where vehicles only communicate information about their reference states ξ to their neighbors at sampling times i (t), because asynchronous sampling data means that vehicle i performs data transmission and sampling separately from other vehicles; the sampling time sequence in is the sampling interval of vehicle i, k is obtained from natural numbers, and using zero-order hold, the control signal is generated to be piecewise constant and kept constant between neighborhood updates, defining the sampling reference state Assume that vehicle j is Receive at any time i (t), where represents the time-varying delay in the transmission process from vehicle i to vehicle j. Here, it is assumed that the samples are sent sequentially on all information links, that is, The accepted reference states of vehicle j and other vehicles i are as follows: Assume that each vehicle samples its own reference state periodically and they all share a common sampling period T, i.e., for all k, make For different vehicles, the initial sampling moment of the reference state can start at different times, i.e. Take a vehicle i0 and virtually align the sampling moments of other vehicles with it, and introduce a new reference state variable through the time conversion method, that is, Other variables change together, including state Output Control Input To avoid exist The situation that was received before, let the time delay satisfaction Definition, given the time transition reference state vector 3. The mean square consensus method for intelligent connected vehicle system with asynchronous sampling control under privacy protection according to claim 2 is characterized in that: The sampling distributed controller with time-varying noise in step 2 is designed as, Among them, K 1i and K 2i is the gain matrix, α k is the step size, the noise vector η j The lth component of at any time k follows the Laplace distribution, that is, η j,l ~Lap(0,δ k ), δ k is the differential privacy noise parameter, N i ={j∈Υ:a ij ≠0} is the set of neighbors of vehicle i, Υ={1,2,...,N} is a set of vehicles, a ij is an element in the weighted adjacency matrix, yes The left limit of the moment, χ i (t) is right continuous, that is, The initial value of the reference state Note K 2i =Ω i -K 1i Ξ i ,Ω i and i are two real matrices satisfying and I v×v is the identity matrix of dimension v; The local controller of each vehicle models a continuous-time dynamic feedback controller. Each time information is obtained at a sampling time, the local controller is adjusted using information about the state of neighboring vehicles. A distributed differential privacy output consensus control algorithm for sampled data is given below: S1, input: initial output state Step size α k and the differential privacy noise parameter δ k ; Among them, k∈0,1,2,...do S2, transmission phase: the vehicle transmits the original message Send to each neighbor; S3, receiving stage: add probability distribution as Lap(0,δ k ) noise, neighbors in Received information that has been interfered with by noise: S4, Update phase: Vehicle i receives the transmitted message from its neighbor j And update its reference status as follows: S5, output: reference state 4. The mean square consensus method for intelligent connected vehicle system with asynchronous sampling control under privacy protection according to claim 3 is characterized in that: In step three, define Substituting the sampled distributed controller (8) into the heterogeneous intelligent connected vehicle system (4), we get: Where K1 = diag{K 11 ,K 12 ,...,K 1N } represents K 11 K 12 ...K 1N is a diagonal matrix with diagonal elements, Discretize formula (9) to get: The reference state in the controller is updated as, Substituting formula (11) into get, in, is the Laplacian matrix, A is the weighted adjacency matrix, is the Kronecker product, 1 is a column vector whose elements are all 1; therefore, and The hybrid closed-loop system is expressed as follows: Among them, Ξ=diag{Ξ1,Ξ2,...,Ξ N },exist In the case of Hurwitz stability, define two Lyapunov functions and Taking the expectation on both sides, we get E[V1(k+1)+V2(k+1)]=0, which is equivalent to and The conditions for achieving mean square output consensus in heterogeneous intelligent connected vehicle systems are obtained Among them, E represents the expected value.

5. The mean square consensus method for intelligent connected vehicle system with asynchronous sampling control under privacy protection according to claim 4 is characterized in that: In step 4, a precision parameter (β * ,θ * ), assuming the step size in the algorithm is The differential privacy noise parameter is Among them, the parameter γ∈(0,1], the parameter are all real parameters greater than zero. First, we get them according to the multidimensional Chebyshev inequality. in is a random variable that satisfies Table vector The covariance matrix of ; Inequality (14) can be rewritten as inequality in Just let It can ensure that the output consensus of the heterogeneous intelligent connected vehicle system reaches (β * ,θ * ) accuracy, After substituting, we can simplify to get It can ensure that the output consensus of the heterogeneous intelligent connected vehicle system reaches (β * ,θ * ) accuracy; Substitute the step size and differential privacy noise parameters into After simplification and scaling, we get: Heterogeneous intelligent connected vehicle systems will be (β * ,θ * ) accuracy to achieve mean square output consensus, that is, 6. The mean square consensus method for intelligent connected vehicle system with asynchronous sampling control under privacy protection according to claim 5 is characterized in that: In step 4, let the step size in the algorithm be The differential privacy noise parameter is Among them, the parameter γ∈(0,1], the parameter are all real parameters greater than zero. When γ = 1, the mean square convergence rate of the heterogeneous intelligent connected vehicle system is, When 0<γ<1, the mean square convergence rate of the heterogeneous intelligent connected vehicle system is, Among them, Ο represents an infinitesimal of the same order, and f(t) = Ο(g(t)) means that there exists a positive number z and t0 such that |f(t) / g(t)|≤z when t→t0; is a real symmetric matrix constructed, and λ2(L2) is the algebraic connectivity of L2.

7. The mean square consensus method for intelligent connected vehicle system with asynchronous sampling control under privacy protection according to claim 6 is characterized in that: In step 4, the differential privacy budget ε is specifically expressed as, Among them, T c ={1,2,...,k c } is a finite set of sampling points, k c is the last sampling point, is the sensitivity, which is expressed as, in, represents the degree of the directed graph G, c min =min{c i ,i∈1,2,...,N} is the minimum degree; the upper bound parameter ε of the differential privacy budget is given * , assuming the step size in the algorithm is The differential privacy noise parameter is Among them, the parameter γ∈(0,1], the parameter are all real parameters greater than zero, In infinite time domain, the upper bound of differential privacy budget is given in the following four cases, when γ = 1: get get When 0<γ<1: get get in, is the upper incomplete gamma function.

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