Intelligent networked vehicle group formation control and intermittent control method in zero-trust environment

Abstract

The invention discloses an intelligent networked vehicle group formation control and intermittent control method in a zero-trust environment, and particularly relates to the technical field of information security, and the method comprises the steps: building a state-space equation of an intelligent networked vehicle according to a dynamic model and a communication topological structure of a leader-following vehicle formation system containing a zero-trust framework and measurable noise; the consistency control problem of a single follower vehicle and a leader vehicle in the system is converted into the stability problem of an error system; designing an augmented system by using the system state and measurable noise, and designing an observer to realize estimation when part of the system state is unmeasurable and interference exists; defining an event triggering strategy during the control interval, designing a triggering function and obtaining a triggering threshold value; an intermittent control protocol is designed according to system state information, and the designed observer and controller complete state monitoring estimation and coordination control.

Description

Technical Field

[0001] The present invention relates to the field of information security technology, and particularly to an intelligent connected vehicle group formation control and intermittent control method in a zero-trust environment. Background Art

[0002] The core concept under the zero-trust framework is "never trust, always verify", which requires maintaining a dynamic and continuous check on trust relationships and ensuring system security through continuous verification. Decision-making and actions mainly rely on verified identities. Vehicle state information, such as position, speed, acceleration, and corresponding estimated states, in addition, there are also control inputs. Only after passing the trust verification process can the system transmit the corresponding verified information. The above description also applies to other vehicles. In an intelligent connected vehicle formation system, vehicle-to-vehicle (V2V) communication relies on mutual authentication between both parties. Under the zero-trust architecture, the entire time interval of the intelligent connected vehicle formation control system is divided into the following two key time intervals: the zero-trust check time interval and the zero-trust information update time interval. However, when the system is in the trust verification stage, the entire system will be in a state of overly frequent data transmission and redundant calculations, making the continuous control strategy inefficient, the communication burden too heavy, and unable to effectively adapt to the dynamic changes of the system. In addition, in the intelligent connected vehicle formation system under the zero-trust framework, the information required for continuous trust verification needs to be updated continuously for a period of time, which also occupies communication bandwidth and computing resources, thus affecting the timeliness of information interaction and the overall response speed of the formation. Summary of the Invention

[0003] To this end, the present invention provides an intelligent connected vehicle group formation control and intermittent control method in a zero-trust environment, introducing an event-triggered intermittent control strategy to solve the problems proposed in the background art.

[0004] To achieve the above object, the present invention provides the following technical solutions: An intelligent connected vehicle group formation control and intermittent control method in a zero-trust environment, comprising the following steps:

[0005] Step 1, establish the state space equation of the intelligent connected vehicle according to the dynamic model and communication topology of the leader-follower vehicle formation system containing the zero-trust framework and measurable noise, and transform the consensus control problem of a single follower and the leader vehicle in the system into the stability problem of the error system;

[0006] Step 2, design an augmented system using the system state and measurable noise, and design an observer to achieve the estimation when part of the system states are unmeasurable and there are interferences;

[0007] Step 3, define the event-triggered strategy during the control interval, design the trigger function and obtain the trigger threshold;

[0008] Step 4: Design an intermittent control protocol based on the system status information. The proof steps show that the designed observer and controller complete state monitoring estimation and coordinated control to achieve consensus control.

[0009] Preferably, the specific operation of Step 1 is as follows: The construction of a continuous-time leader-follower multi-agent system composed of an intelligent connected vehicle formation system with 1 leader and N followers is as follows:

[0010] The dynamic model of vehicle i is represented by the following non-linear third-order model:

[0011]

[0012] where z i (t), v i (t) and a i (t) represent the position, speed, and acceleration of the vehicle respectively, c i (t) is the engine or brake input, is the engine time constant, Q is the specific mass of air, m i , A i , C di , and d mi represent the mass, cross-sectional area, drag coefficient, and mechanical resistance of vehicle i respectively, represents the air resistance, ω i (t) is an unknown external disturbance caused by gusts or rough road conditions;

[0013] Let

[0014]

[0015] Thus, the longitudinal dynamic equation of the vehicle is written as:

[0016]

[0017] In practice, since the mechanical resistance d mi and the air resistance cannot be accurately obtained, therefore, the non-linear function f i (v i , a i , t) is unknown. Then, let the acceleration a i (t) range from [-a imax , a imax , v i (t) range from [0, v imax , the time constant range from (0, 1), and is an increasing coefficient. Then, the non-linear function f i (vi , a i , the range of t is assumed to be:

[0018]

[0019] Define x i (t) = [z i (t) v i (t) a i (t)], combined with Equation (3), the state - space expression of the system is obtained as follows:

[0020]

[0021] Among them, the discrete - system equation of the follower vehicle is described as:

[0022]

[0023] The discrete equation of the leader is described as:

[0024]

[0025] Among them, Define the sampling interval h > 0, and the time gap is h g , n = 3 represents the state vector of the i - th agent, represents the input vector of the i - th agent, represents the non - linear - term interference existing in the i - th agent, represents the unknown perturbation existing in the i - th agent, is the measurable output vector of the i - th agent, and A, B, C, D, E are known parameter matrices with appropriate dimensions;

[0026] According to Equation (6) and Equation (5), define the system - error variable as:

[0027] δ i,k = x 0,k - x i,k i = 1, 2, …, N (7)

[0028] Among them, δ i,k represents the system - error variable, x 0,k represents the leader - state variable, x i,k represents the state variable of the i - th follower;

[0029] Then, from Equation (6), (7), (5), the global - state following - error change is:

[0030]

[0031] Among them, Define the global output following error:

[0032] Υ i,k = y 0,k - y i,k (9)

[0033] where Υ i,k represents the global output error, y 0,k represents the leader output, and y i,k represents the output of the i-th follower;

[0034] Then, from equations (9), (5), and (6), we have:

[0035]

[0036] Thus, the global following error system is obtained:

[0037]

[0038] Through the transformation of equations (1)-(11), the consensus control problem between a single follower and the leader in the system is transformed into the stability problem described by equation (12);

[0039] Preferably, define the generalized vector Design an augmented system using the system state and measurable noise:

[0040]

[0041] where M = [I n 0 n×q ,

[0042] The following assumption conditions are given:

[0043] Assumption 1 The unknown disturbance satisfies the following conditions:

[0044]

[0045] where θ is a non-negative scalar;

[0046] Assumption 2 The nonlinear term satisfies the Lipschitz condition with a constant γ > 0, i.e.:

[0047]

[0048] Since

[0049]

[0050] There must exist a column full-rank matrix T and a general matrix N such that:

[0051]

[0052] Therefore, Equation (12) can be further written as:

[0053]

[0054] where Verify M C = rank[B AB A 2 B] = n, [A B] is controllable; [CA] is observable, so the augmented system obtained by linear transformation is also controllable and observable.

[0055] When part of the system states are unmeasurable and there are disturbances in the system, design the following observer:

[0056]

[0057] where, is the estimated value of the system state vector x i,k and the disturbance ω i,k , is the estimated value of the nonlinear function contained in the system, and L is the observer gain matrix;

[0058] Define the observer estimation error Then there is:

[0059]

[0060] When there is a suitable L such that it indicates that the observer can accurately estimate the system state.

[0061] Preferably, consider the event triggering condition of the i-th vehicle as follows:

[0062] Set a fixed period η, which is used to regularly sample the state estimation to determine the triggering moment of the event where

[0063] Under this setting, it is deduced that Furthermore, there is Therefore, through this strategic method, the time-varying formation control problem is effectively solved, and at the same time, the occurrence of Zeno behavior is fundamentally prevented;

[0064] Whenever the i-th following vehicle performs state feedback control at the sampling point, define:

[0065]

[0066] Thus, there is

[0067] Based on the estimated output of the observer, to construct an event-triggered driving strategy, define p i,k as a combined measurement variable as follows:

[0068]

[0069] Adopt the fixed vehicle interval method, and take d ij as a constant value, which represents the expected vehicle spacing under static conditions. This spacing includes the required distance between vehicle i and vehicle j and the length of the vehicle itself;

[0070] Set the state estimates of vehicles i and j to be and i = 1, 2,..., N, denote the in-degree of node i; thus, define the measurement error as: and set the triggering function to be Meanwhile, define the synchronization error of the agent state and the synchronization error of the external disturbance as follows:

[0071]

[0072] When any triggering function reaches the triggering condition, the corresponding event will be triggered; in the case of using the event-triggering mechanism, the next sampling moment is expressed as:

[0073]

[0074] When in the designed event-triggered control strategy, an event is triggered at the moment of satisfying the triggering condition, the agent can obtain information according to the topological structure and update the controller. Among them, the threshold is:

[0075]

[0076] The threshold processes the vehicle state and sensor information from the external environment to ensure the authenticity and integrity of the input data. Within this interval, the controller perceives the vehicle queue state in real time and dynamically evaluates key variables such as vehicle spacing and speed error through the event-triggered strategy;

[0077] Preferably, according to the estimation result of the descriptor system observer, design the following control protocol:

[0078]

[0079] where ρ 1 , ρ 2 > 0, denote the in-degree of node i;

[0080] In an undirected graph, a ij = a ji , then there is:

[0081]

[0082] Define e k = (e 1,k ,…, e N,k ), ε k = (ε 1,k ,…, ε N,k ), then from the Laplacian matrix and the Kronecker product, there is:

[0083]

[0084] Consider a vehicle platoon control system composed of 4 connected and automated vehicles. When the original system is controllable and observable, the external disturbance satisfies Assumption 1, and the nonlinear term satisfies Assumption 2, the eigenvalues λ a of L i are obtained according to the system parameters. For a given H ∞ performance index ψ, the augmented Laplacian eigenvalues λ i (i = 0, 1,…, N) and non - negative scalar constants γ and θ. The following Theorem 1 is given.

[0085] Theorem 1 If there exist appropriate - dimension symmetric positive - definite matrices P 1 , P 2 and appropriate - dimension matrices U 1 , U 2 , U 3 such that the linear matrix inequality

[0086]

[0087] holds, where:

[0088] Ω 11 = - P 1 + κγ 2 I + I,

[0089]

[0090] Ω 33 = (TE) T P 1 (TE)- κI - ι 2 I,

[0091] Ω 44 = (TE) T P2 (TE)-κI,

[0092] Ω 45 =λ i (TE) T U 2 ,

[0093] Ω 46 =λ i (TE) T U 3 ,

[0094] Ω 55 =0,

[0095] Ω 58 =λ i U 2 ,

[0096] Ω 56 =λ i 2 U 2 T ,

[0097] Ω 66 =0,

[0098] Ω 69 =λ i U 3 ,

[0099] Ω 77 =-P 1 ,

[0100] Ω 88 =-P 2 ,

[0101] Ω 99 =-P 2 ,

[0102] L = P 1 -1 U 1 is the observer gain matrix, U 2 = TBP 1 , U 3 = TBP 2 , then the designed observer and controller can enable the intelligent connected vehicle formation control system to complete state monitoring estimation and coordinated control, that is

[0103] Proof: According to the constructed generalized error system and the synchronous error system, construct the Lyapunov functional, then there is:

[0104]

[0105] The difference equation is ΔV k = V k+1 - V k . Further, according to Hypothesis 2, we can obtain That is Similarly, we have

[0106] From the properties of the undirected graph, we know that there exists an orthogonal matrix Π such that L a = ΠΛΠ where Λ = diag{λ 1 , λ 2 , …, λ N}, and {λ 1 , λ 2 , …, λ N} are the eigenvalues of the Laplacian matrix L a , and λ 1 = 0. Define

[0107]

[0108] Then the difference equation has:

[0109]

[0110] It is easy to obtain

[0111]

[0112] Define the following performance index:

[0113]

[0114] When Equation (23) holds, it can be shown that the theorem given in the text holds, and we can obtain

[0115]

[0116] From Equations (23) and (25), it is easy to obtain

[0117]

[0118] Define

[0119] where

[0120]

[0121]

[0122] Using the Schur complement lemma to deal with Φ, when Φ < 0 is equivalent to (21), solve the unknown matrices therein through the LMI toolbox, and obtain the optimal observer gain L and control gain K. Therefore, when (21) holds, it can be shown that the given theorem holds. That is, the error system (11) satisfies H ∞ performance index.

[0123] At this time, it shows that the designed observer and controller complete the system state monitoring and estimation as well as coordinated control, that is

[0124] The present invention has the following advantages:

[0125] The present invention establishes the state space equation of the intelligent connected vehicle according to the dynamic model and communication topology of the leader-follower vehicle formation system containing the zero-trust framework and measurable noise, and transforms the consensus control problem of a single follower in the system with the leader vehicle into the stability problem of the error system; designs an augmented system using the system state and measurable noise, and designs an observer to achieve the estimation when part of the system states are unmeasurable and there are disturbances; defines an event-triggering strategy during the control interval, designs a triggering function and obtains the triggering threshold; designs an intermittent control protocol according to the system state information, and through the proof steps, it shows that the designed observer and controller complete the state monitoring and estimation as well as coordinated control, realizing consensus control. Compared with the prior art, when the system is in the trust verification stage, the present invention avoids the system from being in a state of overly frequent data transmission and redundant calculation, improves the efficiency of the continuous control strategy, reduces the communication burden, effectively adapts to the dynamic changes of the system, and in the intelligent connected vehicle formation system under the zero-trust framework, avoids occupying too much communication bandwidth and computing resources, and improves the timeliness of information interaction and the overall response speed of the formation. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1 It is a flowchart of the event-triggered intermittent control effect provided by the present invention;

[0127] Figure 2 It is a periodic intermittent control process diagram provided by the present invention;

[0128] Figure 3 It is a flowchart of the event-triggered periodic intermittent control provided by the present invention;

[0129] Figure 4 It is a communication topology diagram of the connected vehicle formation system provided by the present invention;

[0130] Figures 5-6 It is the system state and estimated value in the simulation experiment provided by the present invention;

[0131] Figures 7-9The changes in the position, speed, and acceleration of the system under the control protocol provided by the present invention;

[0132] Figure 10 The actual value and estimated value of the non - linear function provided by the present invention;

[0133] Figure 11 The actual value and estimated value of the system disturbance quantity provided by the present invention;

[0134] Figure 12 The control input and event - trigger time interval (combination) provided by the present invention; Detailed implementation mode

[0135] The following specific embodiments illustrate the implementation mode of the present invention. Those skilled in the art can easily understand the other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0136] The present invention provides an intelligent connected vehicle group formation control and intermittent control method in a zero - trust environment, including the following steps:

[0137] Step 1: Establish the state - space equation of the intelligent connected vehicle according to the dynamic model and communication topology structure of the leader - follower vehicle formation system containing the zero - trust framework and measurable noise, and transform the consensus control problem of a single follower and the leader vehicle in the system into the stability problem of the error system;

[0138] The specific operation of Step 1 is as follows: The construction of a continuous - time leader - follower multi - agent system composed of an intelligent connected vehicle formation system with 1 leader and N followers is as follows:

[0139] The dynamic model of vehicle i is represented by the following non - linear third - order model:

[0140]

[0141] where z i (t), v i (t) and a i (t) respectively represent the position, speed, and acceleration of the vehicle, c i (t) is the engine or brake input, is the engine time constant, Q is the specific mass of air, m i , A i , C di , and d mirespectively represent the mass, cross-sectional area, drag coefficient and mechanical resistance of vehicle i, represents the aerodynamic drag, ω i (t) is an unknown external disturbance caused by gusts or rough road conditions;

[0142] Let

[0143]

[0144] Thus, the longitudinal dynamics equation of the vehicle is written as:

[0145]

[0146] where, here u i (t) is used instead of c i (t), so the input does not depend on the vehicle mass. In practice, since the mechanical resistance d mi and the aerodynamic drag Therefore, the non-linear function f i (v i ,a i ,t) is unknown. In a vehicle platoon, the specific numerical ranges of the mechanical resistance and the aerodynamic drag vary due to various factors such as vehicle type, speed, road conditions, distance between vehicles, etc. Generally, the mechanical resistance of an intelligent connected vehicle is set to 0 - 25 N, and the aerodynamic drag is proportional to the square of the speed, so its influence will increase significantly with the speed. Let the acceleration a i (t) have a value range of [-a imax ,a imax , v i (t) have a value range of [0, v imax , the time constant have a value range of (0, 1), and is the amplification factor, then the range of the non-linear function f i (v i ,a i ,t) is assumed to be:

[0147]

[0148] Define x i (t) = [z i (t) v i (t) a i (t)], combining with Equation (3), the state-space expression of the system is obtained as follows:

[0149]

[0150] Considering that most current actual calculations and decisions are completed by computers, the discrete system case is considered to include unknown external disturbances and nonlinear terms caused by gusts or rough road conditions. Among them, the discrete system equation of the follower vehicle is described as:

[0151]

[0152] The discrete equation of the leader is described as:

[0153]

[0154] Among them, Define the sampling interval h > 0, and the time interval is h g , n = 3 represents the state vector of the i-th agent, represents the input vector of the i-th agent, represents the nonlinear term interference existing in the i-th agent, represents the unknown disturbance existing in the i-th agent, is the measurable output vector representing the i-th agent, and A, B, C, D, E are known parameter matrices with appropriate dimensions;

[0155] According to Equation (6) and Equation (5), define the system error variable as:

[0156] δ i,k = x 0,k - x i,k i = 1, 2,..., N (7)

[0157] Among them, δ i,k represents the system error variable, x 0,k represents the leader state variable, x i,k represents the state variable of the i-th follower;

[0158] Then, from Equation (6), (7), (5), the global state following error changes as:

[0159]

[0160] Among them, Define the global output following error:

[0161] Υ i,k = y 0,k - y i,k (9)

[0162] Among them, Υ i,k represents the global output error, y 0,k represents the leader output, y i,k represents the output of the i-th follower;

[0163] Then, from Equation (9), Equation (5), and Equation (6), we have:

[0164]

[0165] Thus, the global following error system is obtained:

[0166]

[0167] Through the transformation of Equation (1) - Equation (11), the consensus control problem of a single follower and a leader in the system is transformed into the stability problem described by Equation (12);

[0168] The core concept under the zero - trust framework is "never trust, always verify". This requires maintaining a dynamic and continuous check of trust relationships and ensuring system security through continuous verification. Decisions and actions mainly rely on verified identities. According to Figure 1 As shown, the state information of vehicle i, such as position z i,K , speed v i,k , acceleration a i,k and the corresponding estimated state In addition, there is also the control input u i,k . Only after passing the trust verification procedure can the system transmit the verified corresponding information The above description also applies to vehicle j. In the intelligent connected vehicle formation system, vehicle - to - vehicle (V2V) communication depends on mutual authentication between both parties. Under the zero - trust architecture, the entire time interval of the intelligent connected vehicle formation control system is divided into the following two key time intervals: zero - trust check time interval and zero - trust information update time interval. However, when the system is in the trust verification stage, the entire system will be in a state of overly frequent data transmission and redundant calculations, making the continuous control strategy inefficient, the communication burden too heavy, and unable to effectively adapt to the dynamic changes of the system. In addition, in the intelligent connected vehicle formation system under the zero - trust framework, the information required for continuous trust verification needs to be continuously updated for a period of time, which also occupies communication bandwidth and computing resources, thus affecting the timeliness of information interaction and the overall response speed of the formation. To solve this problem, it is particularly necessary to introduce an event - triggered intermittent control strategy.

[0169] For the intermittent control (IC) strategy, the present invention considers the general case of a periodic intermittent control topology, that is, the communication period is divided into a control interval and a rest interval. As Figure 2 shown, the yellow part represents the control interval, k ∈ [μT c +1, μT c +τ), k = 0, 1, 2…. During this period, τ represents the width of the control time, and the white part represents the rest time interval, During the control time interval, the intelligent connected vehicle exchanges information through an undirected communication topology, and the distributed controller executes the control algorithm on each ICV. During the rest time, the information exchange is interrupted. As Figure 1 shown, in the zero-trust framework, the transmission of control signals must ensure security and credibility. Intermittent control is regulated through discontinuous cycles. When combined with an event-triggered strategy, once the conditions are met during the control interval, the control action will be triggered. This process is divided into a zero-trust check time period (i.e., the event-triggered control time period) and a zero-trust information update time period (i.e., the intermittent control rest time period).

[0170] Step 2: Design an augmented system using the system state and measurable noise, and design an observer to achieve the estimation when part of the system state is unmeasurable and there are disturbances.

[0171] Define the generalized vector Design an augmented system using the system state and measurable noise:

[0172]

[0173] where, M = [I n 0 n×q ,

[0174] Give the following assumption conditions:

[0175] Assumption 1 The unknown disturbance satisfies the following conditions:

[0176]

[0177] where, θ is a non-negative scalar;

[0178] Assumption 2 The non-linear term satisfies the Lipschitz condition, with a constant γ > 0, i.e.:

[0179]

[0180] To ensure the controllability and stability of the system, the main purpose of these assumptions is to simplify the analysis process and provide theoretical support for the system stability. The necessary assumptions given in this paper are general and have been widely used in the literature on consensus control.

[0181] Assumption 1 imposes an upper bound on the unknown disturbance magnitude, which ensures that the disturbance energy is bounded. This is beneficial for the stability and operability analysis of the system, and this assumption is commonly used in the literature on adaptive and robust control. For example, the commonly used linear matrix inequality (LMI) method in the literature usually requires the disturbance energy to be finite to ensure that the designed controller can effectively handle unknown disturbances.

[0182] Suppose that 2 represents that the change rate of the nonlinear dynamics is bounded. This condition is often used in nonlinear and robust control research to simplify the analysis by restricting the growth of the nonlinearity, thereby preventing instability.

[0183] Since

[0184]

[0185] There must exist a column full-rank matrix T and a general matrix N such that:

[0186]

[0187] Therefore, Equation (12) is further written as:

[0188]

[0189] where Verify that M C = rank[B AB A 2 B] = n, [A B] is controllable; [CA] is observable. Therefore, the augmented system obtained by the linear transformation is also controllable and observable.

[0190] When part of the system states are unmeasurable and there are disturbances in the system, design the following observer:

[0191]

[0192] where, is the estimate of the system state vector x i,k and the disturbance ω i,k , is the estimate of the nonlinear function contained in the system, and L is the observer gain matrix;

[0193] Define the observer estimation error Then there is:

[0194]

[0195] When there is an appropriate L such that Then it indicates that the observer can accurately estimate the system state.

[0196] As Figure 3 shown in the flowchart, the entire stage of the formation control of intelligent connected vehicles under the zero-trust framework is divided into the following two key cycles: the zero-trust information update interval period and the zero-trust check period.

[0197] The zero-trust information update interval, i.e., the intermittent control rest period, refers to the stage when the vehicle system is operating stably and the system is in the low-frequency information update mode, while accumulating necessary environmental and status information for subsequent inspection cycles. During this period, the vehicle control system does not perform real-time triggering or continuous communication, but only maintains basic stability control using the existing status information.

[0198] The zero-trust inspection cycle is the control cycle and the event trigger action cycle. Within this cycle, based on the preset event trigger conditions, the communication and control signal updates between vehicles are triggered. According to the trust verification results, the motion state of the vehicle formation is understood in real time, and accurate speed following and information interaction are achieved to ensure the safety and stability of the system. The successful authentication criterion is a predefined threshold, and only when this threshold is reached can vehicle communication be triggered. Based on the intermittent control strategy under the zero-trust framework (as shown in Figure 1 and Figure 2 ), and combined with the event trigger method, the event trigger strategy during the control interval can be defined. As shown in Figure 3 , an event trigger strategy is introduced to update the controller signal, reducing the signal update frequency when the system does not meet the trigger conditions, thereby saving communication and computing resources.

[0199] Step 3: Define the event trigger strategy during the control interval, design the trigger function and obtain the trigger threshold;

[0200] Consider the event trigger condition for the i-th vehicle as follows:

[0201] Set a fixed period η, for regular sampling of the state estimation to determine the event trigger moment where

[0202] Under this setting, it is deduced that Furthermore, there is Therefore, through this strategy method, the time-varying formation control problem is effectively solved, and at the same time, the occurrence of Zeno behavior is fundamentally prevented;

[0203] Whenever the i-th following vehicle performs state feedback control at the sampling point, define:

[0204]

[0205] Thus, there is

[0206] Based on the estimated output of the observer, in order to construct an event-triggered drive strategy, define p i,k as a combined measurement variable, as follows:

[0207]

[0208] Using the fixed vehicle interval method, let d ij be a constant value, which represents the desired vehicle spacing under static conditions. This spacing includes the distance required between vehicle i and vehicle j and the length of the vehicle itself;

[0209] Set the state estimates of vehicles i and j to be and represent the in-degree of node i; thus, define the measurement error as: and set the triggering function to At the same time, define the synchronization error of the agent state and the external disturbance synchronization error as follows:

[0210]

[0211] When any triggering function reaches the triggering condition, the corresponding event will be triggered; in the case of using the event-triggered mechanism, the next sampling time is expressed as:

[0212]

[0213] When in the designed event-triggered control strategy, the event is triggered at the moment when the triggering condition is satisfied, the agent can obtain information according to the topology structure and update the controller. Among them, the threshold is:

[0214]

[0215] The threshold processes the vehicle state and sensor information from the external environment to ensure the authenticity and integrity of the input data. Within this interval, the controller continuously perceives the vehicle queue state and dynamically evaluates key variables such as vehicle spacing and speed error through the event-triggered strategy;

[0216] Step 4: Design an intermittent control protocol based on the system state information. The proven steps show that the designed observer and controller complete state monitoring estimation and coordinated control to achieve consensus control.

[0217] According to the estimation results of the descriptor system observer, design the following control protocol:

[0218]

[0219] where ρ 1 ,ρ 2 >0, represents the in-degree of node i;

[0220] In an undirected graph, a ij =a ji , then there is:

[0221]

[0222] Define \(e\) k =(e 1,k ,…,e N,k ), \(\varepsilon\) k =( \(\varepsilon\) 1,k ,…,\(\varepsilon\) N,k ), Then, from the Laplacian matrix and the Kronecker product, we have:

[0223]

[0224] Consider a vehicle platoon control system consisting of 4 connected and automated vehicles. When the original system is controllable and observable, the external disturbance satisfies Assumption 1, and the non - linear term satisfies Assumption 2, the eigenvalues \(\lambda\) a of \(L\) i are obtained according to the system parameters. For a given performance index \(\psi\) of \(H\) ∞ , the augmented Laplacian eigenvalues \(\lambda\) i (\(i = 0,1,\cdots,N\)) and non - negative scalar constants \(\gamma\) and \(\theta\). The following Theorem 1 is given.

[0225] Theorem 1 If there exist a proper - dimension symmetric positive - definite matrix \(P\) 1 , \(P\) 2 and proper - dimension matrices \(U\) 1 , \(U\) 2 , \(U\) 3 such that the linear matrix inequality

[0226]

[0227] holds, where:

[0228] \(\Omega\) 11 =-P 1 +\(\kappa\gamma\) 2 I + I,

[0229]

[0230] \(\Omega\) 33 =(TE) T P 1 (TE)-\(\kappa\)I-\(\iota\) 2 I,

[0231] \(\Omega\) 44 =(TE) T P 2 (TE)-\(\kappa\)I,

[0232] \(\Omega\) 45 =\(\lambda\) i(TE) T U 2 ,

[0233] Ω 46 = λ i (TE) T U 3 ,

[0234] Ω 55 = 0,

[0235] Ω 58 = λ i U 2 ,

[0236] Ω 56 = λ i 2 U 2 T ,

[0237] Ω 66 = 0,

[0238] Ω 69 = λ i U 3 ,

[0239] Ω 77 = -P 1 ,

[0240] Ω 88 = -P 2 ,

[0241] Ω 99 = -P 2 ,

[0242] L = P 1 -1 U 1 is the observer gain matrix, U 2 = TBP 1 , U 3 = TBP 2 , then the designed observer and controller can enable the intelligent connected vehicle formation control system to complete state monitoring estimation and coordinated control, that is

[0243] Proof: According to the constructed generalized error system and the synchronous error system, construct the Lyapunov functional, then there is:

[0244]

[0245] The difference equation is ΔV k = V k+1 - V kAccording to Hypothesis 2, it can be further obtained that That is Similarly, there is

[0246] From the properties of the undirected graph, it can be known that there exists an orthogonal matrix Π such that L a = ΠΛΠ where Λ = diag{λ 1 , λ 2 , …, λ N}, {λ 1 , λ 2 , …, λ N} are the eigenvalues of the Laplacian matrix L a , and λ 1 = 0. Define

[0247]

[0248] Then the difference equation has:

[0249]

[0250] It is easy to obtain:

[0251]

[0252] Define the following performance index:

[0253]

[0254] When Equation (23) holds, it can be shown that the theorem given in the text holds, and

[0255]

[0256] It is easy to obtain from Equation (23) and Equation (25) that

[0257]

[0258] Define

[0259] where

[0260]

[0261]

[0262] Using the Schur complement lemma to process Φ, when Φ < 0 is equivalent to Equation (21), solve for the unknown matrices in it through the LMI toolbox, and obtain the optimal observer gain L and control gain K. Therefore, when Equation (21) holds, it can be shown that the given theorem holds. That is, the error system Equation (11) satisfies the H ∞ performance index.

[0263] At this time, it indicates that the designed observer and controller can enable the intelligent connected vehicle formation control system to complete state monitoring estimation and coordinated control, that is

[0264] Embodiment: In the leader-follower networked vehicle multi-agent system, since the leader is not affected by the followers and can have an impact on the followers, in the simulation verification, the system state control can be completed by controlling the movement of the leader, which greatly simplifies the control process and reduces the control cost. Therefore, in order to verify the effectiveness of the design method of this embodiment, a leader-follower multi-agent system composed of 1 leader with the system model of Equation (6) and 3 followers with the system model of Equation (5) will be considered. The communication topology structure of this agent is as Figure 4 shown, where Vehicle 1 represents the leader, and agents 2, 3, and 4 represent the followers.

[0265] This embodiment demonstrates the effectiveness of the developed scheme through computer simulation and runs in a virtual environment using MATLAB. In the simulation, the desired vehicle spacing is d i = 10m, the safety factor is σ = 0.2, the vehicle mass parameter m i = 1527kg, and other parameters are given in Table 1.

[0266] Table 1 Vehicle system dynamics parameters

[0267]

[0268] Take γ d = 0.11, the measurable disturbance is assumed to be: ω i,k = g 1 × sin(g 2 × k), the continuous non-linear function is assumed to be f i,k = g 2 × i × e -k - g 1 × sin(x i (g 2 , k)), and (i = 1, 2,..., N), g 1 ∈ [0, 1], g 2 ∈ [1, N]. From this, the coefficient matrix of the system is calculated as:

[0269] From a set of T and N can be obtained as:

[0270]

[0271] Substituting the above data into LMI(22), the required parameters L, K, and κ can be obtained as

[0272]

[0273] κ = 12.4858

[0274] κ = 2.3271e -8 。

[0275] To verify the effectiveness of the designed observer for the system and the convergence of the control protocol, a series of simulation experiments were conducted. Figures 5-12 The following is a detailed description of the experimental results.

[0276] The simulation results are as Figures 5 to 12 shown. Figures 5-6 It shows the system state of each agent and its estimated value, and it can be seen that the state estimation effect of the proposed observer is good. Figures 7-9 It shows the changes in the position, speed, and acceleration of the intelligent connected vehicle formation under the control protocol, and it can be seen that the control effect of consensus is also satisfactory. Figure 10 It shows the actual value and the estimated value of the nonlinear function. Figure 11 It shows the actual value and the estimated value of the disturbance. Figure 12 It shows the comprehensive control input u of each agent i,k and the time interval of event triggering. From Figure 12 it can be seen that the intermittent control method based on event triggering improves the efficiency of system response because this method enables the system to respond faster. Because it avoids unnecessary continuous communication and ensures that data transmission occurs only when key events occur. In addition, it helps to reduce the computational burden of the controller. Through Figures 5 to 12 the shown effect, it can be seen that the proposed method is correct and effective. The results show that the control is effective, the estimation effect of system disturbance is accurate, and the event-triggered control is also effective. The intermittent control strategy based on event triggering greatly saves the system communication and computational resources.

[0277] Although the present invention has been described in detail with general descriptions and specific embodiments above, based on the present invention, some modifications or improvements can be made, which are obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of protection required by the present invention.

Claims

1. A method for controlling the formation and intermittent control of a group of intelligent connected vehicles in a zero-trust environment, characterized by: The following steps are involved: Step 1: Based on the dynamic model and communication topology of the leader-follower vehicle formation system with a zero-trust framework and measurable noise, the state space equation of the intelligent connected vehicle is established, and the consistency control problem of a single follower and leader vehicle in the system is transformed into a stability problem of the error system; Step 2: Design an augmented system using the system state and measurable noise, and design an observer to estimate when some system states are unmeasurable and there are interferences; Step 3: Define the event triggering strategy during the control interval, design the triggering function and obtain the triggering threshold; Step 4: Design an intermittent control protocol based on the system state information, and implement the designed observer and controller to complete state monitoring estimation and coordinated control.

2. The method for platoon control and intermittent control of intelligent connected vehicles in a zero-trust environment according to claim 1, characterized in that: The specific operation of step 1 is as follows: The construction of a continuous-time leader-follower multi-agent system consisting of a leader and N followers of an intelligent connected vehicle platoon system is as follows: The dynamic model of vehicle i is represented by the following nonlinear third-order model: In the formula, z i (t), v i (t) and a i (t) represent the position, velocity and acceleration of the vehicle, respectively, c i (t) is the engine or brake input, is the engine time constant, Q is the specific mass of air, m i , A i , C di , and d mi denote the mass, cross-sectional area, drag coefficient and mechanical resistance of vehicle i, respectively. is the air resistance, ω i (t) Unknown external disturbances caused by gusty winds or rough road conditions; set up Thus, the longitudinal dynamics equation of the vehicle is written as: In practice, since it is impossible to accurately obtain the mechanical resistance d mi and air resistance Therefore, the nonlinear function f i (v i ,a i ,t) is unknown, then let the acceleration a i The value range of (t) is [-a imax ,a imax ],v i The value range of (t) is [0,v imax ], time constant The value range of is (0,1), and To increase the coefficient, the nonlinear function f i (v i ,a i ,t) is assumed to be: Define x i (t) = [z i (t) v i (t) a i (t)], combined with formula (3), the state space expression of the system is obtained as follows: Among them, the discrete system equation of the following vehicle is described as: The discrete equation for the leader is described as: in, Define the sampling interval h>0, the time interval is h g , represents the state vector of the ith agent, represents the input vector of the ith agent, represents the nonlinear interference in the ith agent, represents the unknown disturbance in the ith agent, is the measurable output vector of the ith agent, A, B, C, D, E are known parameter matrices with appropriate dimensions; According to equation (6) and equation (5), the system error variable is defined as: δ i,k =x 0,k -x i,k i=1,2,…,N (7) Among them, δ i,k represents the system error variable, x 0,k represents the leader state variable, x i,k Represents the state variable of the i-th follower; Then, according to equations (6), (7), and (5), the global state following error changes to: in, Define the global output following error: γ i,k =and 0,k -and i,k (9) Among them, γ i,k Represents the global output error, y 0,k represents the leader output, y i,k represents the output of the i-th follower; Then, from equation (9), equation (5) and equation (6), we can get: This results in the global following error system: By transforming equation (1) to equation (11), the consistency control problem between a single follower and a leader in the system is transformed into the stability problem described in equation (12).

3. The method for controlling the formation and intermittent control of a group of intelligent connected vehicles in a zero-trust environment according to claim 1, characterized in that: Define generalized vector Design an augmented system using system states and measurable noise: Where M = [I n 0 n×q ], The following necessary assumptions are given: Assumption 1 The unknown disturbance satisfies the following conditions: Among them, θ is a non-negative scalar; Assumption 2 Nonlinear term Satisfies the Lipschitz condition, constant γ >0, that is: because There must exist a column-full rank matrix T and a normal matrix N such that: Therefore, formula (12) can be further written as: in Verify M C =rank[B AB A 2 B]=n, [AB] is controllable; [CA] is observable, so the augmented system obtained by linear transformation is also controllable and observable; When some states of the system are unmeasurable and there are disturbances in the system, the following observer is designed: in, is the system state vector x i,k And interference ω i,k The estimate, is a nonlinear function contained in the system Estimate of, L is the observer gain matrix; Define the observer estimation error Then we have: When there is a suitable L so that This indicates that the observer can accurately estimate the system state.

4. The method for controlling the formation and intermittent control of a group of intelligent connected vehicles in a zero-trust environment according to claim 1, characterized in that: Consider the event triggering conditions of the i-th vehicle as follows: Set a fixed period η, Used to periodically sample state estimates to determine the triggering moment of an event in Under this setting, it is deduced that Further Whenever the i-th following vehicle performs state feedback control at a sampling point, define: Thus there is Based on the estimated output of the observer, in order to construct an event-triggered driving strategy, we define p i,k is a combined measurement variable, as follows: Using the fixed vehicle spacing method, dij As a constant value, it represents the desired vehicle spacing under static conditions, which includes the required distance between vehicle i and vehicle j and the length of the vehicle itself; Assume that the state estimates of vehicles i and j are and represents the in-degree of node i; Therefore, the measurement error is defined as: And set the trigger function to At the same time, the synchronization error of the agent state and the external interference synchronization error are defined as follows: When any trigger function reaches the trigger condition, the corresponding event will be triggered; when the event trigger mechanism is used, the next sampling time It is expressed as: When the designed event-triggered control strategy triggers an event when the trigger condition is met, the agent can obtain information according to the topological structure and update the controller; the threshold is: The threshold processes the vehicle status and sensor information from the external environment to ensure the authenticity and integrity of the input data; within this range, the controller perceives the vehicle queue status in real time and dynamically evaluates key variables such as vehicle spacing and speed error through event-triggered strategies.

5. The method for formation control and intermittent control of intelligent connected vehicle groups in a zero-trust environment according to claim 1, characterized in that: According to the estimation results of the generalized system observer, the following control protocol is designed: in ρ1 , ρ2＞0 , represents the in-degree of node i; In an undirected graph a ij =a ji , Then we have: Definition k =(e 1,k ,…,e N,k ), ε k =(ε 1,k ,…,ε N,k ), Then the Laplacian matrix and Kronecker product are: Consider a vehicle formation control system consisting of four intelligent connected vehicles. The original system is controllable and observable, the external interference satisfies assumption 1, and the nonlinear term satisfies assumption 2. According to the system parameters, L is obtained. a The eigenvalue λ i ; For a given H ∞ Performance index ψ, augmented Laplace feature λ i (i=0,1,…,N) and non-negative scalar constants γ and θ; the following Theorem 1 is given; Theorem 1 If there exist appropriately dimensioned symmetric positive definite matrices P1, P2 and appropriately dimensioned matrices U1, U2, U3 such that the linear matrix inequality Established, of which: Oh 11 =-P1+κγ 2 I+I, Oh 33 =(TE) T P1(TE)-κI-ί 2 I, Oh 44 =(TE) T P2(TE)-κI, Oh 45 =λ i (TE) T u2, Oh 46 =λ i (TE) T U3, Oh 55 =0, Oh 58 =λ i U2, Oh 56 =λ i 2U2 T , Oh 66 =0, Oh 69 =λ i U3, Oh 77 =-P1, Oh 88 =-P2, Ω 99 =-P2,L=P1 -1 U1 is the observer gain matrix, U2=TBP1, U3=TBP2, then the designed observer and controller can enable the intelligent connected vehicle platoon control system to complete state monitoring estimation and coordinated control, that is,

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