An Adaptive Event-Triggered Control Method for a Vehicle Platoon

Abstract

The present invention discloses an adaptive event-triggered control method for a vehicle platoon, belonging to the technical fields of automation and vehicle engineering. The method first establishes a nonlinear dynamic model of a single vehicle. Secondly, graph theory is used to describe the communication topology among vehicles. Then, an adaptive event-triggered mechanism is introduced, and a distributed controller is designed in combination with the adaptive event-triggered mechanism. According to the communication topology, a closed-loop error model of the vehicle platoon is established. Finally, the Lyapunov stability theory and linear matrix inequalities are introduced. According to the closed-loop error model, an H ∞ performance index is introduced to obtain a sufficient condition for ensuring the stability of the vehicle platoon. The present invention ensures the stability of the vehicle platoon, can reduce the communication resource expenditure, improve the performance, and greatly improve the flexibility of data transmission among vehicles.

Description

Technical Field

[0001] The present invention belongs to the technical fields of automation technology and vehicle engineering technology, and particularly relates to an adaptive event-triggered control method for a vehicle queue. Background Art

[0002] With the rapid development of communication technology, vehicles can communicate with each other through vehicle ad hoc networks and can efficiently share vehicle data information with other vehicles and infrastructure within a specific communication range. In most current research on vehicle queues, the data transmission mechanism usually realizes in a continuous-time or periodic manner, which means that vehicle data packets will be transmitted at any continuous time or any sampling moment. Undoubtedly, regardless of the real-time network conditions, this transmission mechanism will continuously transmit vehicle data packets, inevitably resulting in excessive consumption of communication resources in the vehicle queue.

[0003] To solve this problem, researchers have proposed an event-triggered transmission mechanism to prevent some unnecessary data packet transmissions. So far, some scholars have studied queue control based on the event-triggered mechanism and obtained many meaningful results.

[0004] In Document 1 (Yue W, Wang L, Guo G. Event-triggered platoon control of vehicles with time-varying delay and probabilistic faults. Mechanical Systems & Signal Processing, 2017, 87(Pt.B): 96 - 117.), an event-triggered mechanism is designed to achieve the desired platoon performance in the case of sensor and actuator faults.

[0005] In Document 2 (Linsenmayer S, Dimarogonas D V, Allgower F. Event-based vehicle coordination using nonlinear unidirectional controllers. IEEE Transactions on Control of Netword Systems, 2018, 5(4): 1575 - 1584.), the event-triggered vehicle coordination problem is solved by some nonlinear unidirectional controllers.

[0006] The above-mentioned event-triggering mechanisms all have a common feature, that is, the threshold parameter of the triggering condition is fixed, which is also called the static event-triggering mechanism. This static event-triggering mechanism cannot reflect the actual situation of time-varying transmission rates and dynamic network loads, because the event-triggering mechanism therein has nothing to do with the network bandwidth state. Summary of the Invention

[0007] The present invention adopts a new adaptive event-triggering mechanism to improve the communication efficiency between vehicles, relieve the communication pressure between vehicles, and designs a new constraint condition to ensure that the vehicle platoon can travel at a desired speed and maintain a fixed desired inter-vehicle distance when receiving disturbances.

[0008] The present invention includes the following steps:

[0009] Step 1: Establish a non-linear dynamic model of a single vehicle.

[0010] Step 2: Use graph theory to describe the communication topology between vehicles.

[0011] Step 3: Introduce an adaptive event-triggering mechanism to control the information transmission between vehicles, save the communication resources between vehicles, and jointly design a distributed controller with the adaptive event-triggering. According to the non-linear dynamic model of a single vehicle and the communication topology described by graph theory, establish a closed-loop error model of the vehicle platoon.

[0012] Step 4: Introduce Lyapunov stability theory and linear matrix inequality method. According to the closed-loop error model, introduce H ∞ performance index to obtain a sufficient condition for ensuring the stability of the vehicle platoon.

[0013] Further, Step 1 is specifically as follows:

[0014] There are non-linear links such as engines, transmissions, and quadratic wind resistance in the longitudinal dynamics of vehicles. Considering a vehicle platoon consisting of N + 1 vehicles driving on a straight road, ignoring lateral and vertical movements, the vehicle is regarded as a rigid body and is completely symmetric left and right, ignoring the slip of the tires. Establish a non-linear longitudinal dynamic model of a single vehicle as follows:

[0015]

[0016] In the formula, i ∈ {0, 1, 2..., N} represents the i-th vehicle, p i (t), v i (t) represent the position and speed of the i-th vehicle, m i is the mass of the vehicle, C A,i is the air resistance coefficient, g is the gravitational acceleration constant, f i is the rolling resistance coefficient, T i (t) is the actual driving force of the vehicle, Tdes,i (t) is the desired driving force, τ i is the inertia time constant of the vehicle longitudinal power system, r w,i is the wheel radius, η T,i is the mechanical efficiency of the transmission system.

[0017] From equation (1), we can obtain:

[0018]

[0019] a i (t) represents the acceleration of the vehicle, and the following linear feedback control strategy is adopted:

[0020]

[0021] where u i is the control input of the vehicle after feedback linearization. Furthermore, equation (2) is transformed into:

[0022]

[0023] Assuming the sampling period h > 0 and adding the zero-order hold mechanism, the discrete-time single-vehicle third-order state-space model is obtained as follows:

[0024] x i (k + 1) = Ax i (k) + B(u i (k) + w i (k)) (5)

[0025] where u i (k) is the control input of the vehicle after feedback linearization, and x i (k) = [p i (k) v i (k) a i (k)] T , w i (k) represents the unknown disturbance input on vehicle i, and a i (k) represents the acceleration of vehicle i.

[0026] Furthermore, step 2 is specifically as follows:

[0027] Based on graph theory, the information flow topology structure of information transfer between vehicles is intuitively abstracted into the structure of a graph, and then characterized by the corresponding matrices and their properties.

[0028] Considering a vehicle queue consisting of a leading vehicle with index 0 and N following vehicles with indices from 1 to N, regarding each vehicle as a node in the network, the information transfer between following vehicles can be represented by a directed graph for representation. is a set of nodes, representing N following vehicles, represents a set of edges, represents a directed edge from node j to node i, indicating that vehicle i can receive information from vehicle j. Define the adjacency matrix of the directed graph a ij = 1 means that following vehicle i can receive communication data from following vehicle j, otherwise a ij = 0. Assume that there are no self-loops in the graph , that is, a ii = 0.

[0029] Define the neighborhood set of node i Define the in-degree matrix where Define the Laplacian matrix

[0030] Define the traction matrix If vehicle i can receive information from the leading vehicle, then p i = 1, otherwise p i = 0. At the same time, define the following traction set:

[0031]

[0032] Define the set matrix And assume that each following vehicle can directly or indirectly receive information from the leading vehicle.

[0033] Furthermore, step 3 is specifically as follows:

[0034] Assume that the sampling period of all vehicles is h > 0. The event generator on each vehicle decides whether to transmit the sampling data packet of each vehicle. For Use to represent the s-th trigger time of vehicle i, and the subsequent trigger times are determined by the following adaptive trigger mechanism:

[0035]

[0036] where represents the state at the most recent trigger time of the i-th following vehicle; is the difference between the data at the current time and the most recent trigger; And d i,j (k) = d i,0 (k) - d j,0 (k) represents the desired spacing between vehicle i and vehicle j, d i,0(k) represents the desired gap between vehicle i and the leading vehicle; Φ is a positive weighting matrix to be determined; σ i (k) is a dynamic threshold parameter, and it is adjusted according to the following function:

[0037]

[0038] where and σ i respectively represent the lower and upper bounds of the dynamic threshold parameter. The threshold parameter is adjusted between the threshold lower bound and the threshold upper bound according to the magnitude of the triggering error. When the triggering error increases, the threshold parameter tends to the lower bound, increasing the triggering frequency to improve the control performance. When the triggering error decreases, the threshold tends to the upper bound, reducing the triggering frequency to save more communication resources. Compared with the traditional static event-triggering mechanism with a fixed threshold, the data transmission is more flexible. π is the pi; ε > 0 is used to adjust the sensitivity.

[0039] Based on the adaptive event-triggering mechanism, for each vehicle the following distributed controller is adopted:

[0040]

[0041] where, K = [k p k v k a is the control gain matrix to be solved.

[0042] The tracking error between the ith following vehicle and the leading vehicle is established as follows:

[0043]

[0044] Define δ i (k) = [δ i p (k) δ i v (k) δ i a (k)] T , δ i p (k), δ i v (k) and δ i a (k) respectively represent the position, speed, and acceleration errors between the ith following vehicle and the leading vehicle. Combining the single-vehicle third-order state-space model in Equation (5) and the distributed controller in Equation (9), when the leading vehicle is traveling at a constant speed and a fixed desired spacing is taken, the error model between a single following vehicle and the leading vehicle is obtained as:

[0045]

[0046] Among them Define the vectors: δ(k) = [δ1 T (k), δ2 T (k),..., δ N T (k)] T , e(k) = [e1 T (k), e2 T (k),..., e N T (k)] T , combining the error model of a single vehicle and the leading vehicle in Equation (11), the following closed-loop error model can be obtained:

[0047]

[0048] Among them, y(k) = [y1(k), y2(k),..., y N (k)] T , y i (k) = Cδ i (k) represents the position error output, and C = [1, 0, 0].

[0049] Furthermore, the specific process of Step 4 is as follows:

[0050] Step 4.1: For the closed-loop error model of the vehicle platoon in Equation (12), the control objective of the present invention is:

[0051]

[0052] That is

[0053] Construct the Lyapunov function According to Equation (13), the sufficient condition for the stability of Equation (12) is:

[0054] Given a scalar γ > 0, 1 > α > 0, if there exist positive definite matrices P > 0 and Φ > 0 and a matrix K such that:

[0055]

[0056] Among them:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] Diagonal matrix If I is an arbitrary identity matrix, then Equation (12) is exponentially stable and satisfies H ∞ The performance index is γ.

[0064] Step 4.2: Linearize Equation (14), decouple the coupled terms to be solved therein, and derive the distributed control gain matrix.

[0065] By using the Schur complement lemma for Equation (14), we can obtain:

[0066]

[0067] Where:

[0068]

[0069]

[0070] Multiply both the left and right sides of Equation (15) by the diagonal matrix And define the matrix P -1 = X, K = YX -1 , P -1 ΦP -1 = F, we can obtain:

[0071]

[0072] Where:

[0073]

[0074]

[0075] Solve the matrices X, Y, and F through the linear matrix inequality, then the control gain matrix.

[0076] Advantages of the present invention: The present invention introduces a novel adaptive event-triggering mechanism, whose threshold is no longer a constant but is dynamically adjusted in combination with the state information of the system to ensure the stability of the vehicle queue. Compared with the traditional static event-triggering mechanism, the adaptive event-triggering mechanism can further reduce the communication resource expenditure by extending the event interval time or improve the performance by allowing more data transmissions, greatly enhancing the flexibility of data transmission between vehicles. Description of the drawings

[0077] Figure 1 Schematic diagram of the queue control method for the specific embodiment of the present invention;

[0078] Figure 2 Communication topology relationship diagram for the specific embodiment of the present invention;

[0079] Figure 3(a) is the vehicle position simulation diagram for the specific embodiment of the present invention;

[0080] Figure 3(b) is the vehicle spatial error simulation diagram for the specific embodiment of the present invention;

[0081] Figure 3(c) is the vehicle speed error simulation diagram for the specific embodiment of the present invention;

[0082] Figure 3(d) is the vehicle acceleration error simulation diagram for the specific embodiment of the present invention;

[0083] Figure 4 Event trigger time diagram of five following vehicles for the specific embodiment of the present invention. Specific embodiment

[0084] The present invention proposes a new adaptive event-triggering mechanism to improve the communication efficiency between vehicles. The process is as Figure 1 shown and includes the following steps:

[0085] Step 1: Establish a non-linear dynamic model of a single vehicle.

[0086] Step 2: Use graph theory to describe the communication topology structure between vehicles.

[0087] Step 3: Introduce an adaptive event-triggering mechanism to control the information transmission between vehicles, save the communication resources between vehicles, and jointly design a distributed controller with the adaptive event trigger. According to the communication topology structure, establish a closed-loop error model of the vehicle queue.

[0088] Step 4: Introduce the Lyapunov stability theory and linear matrix inequality method. According to the closed-loop error model, introduce H ∞ performance index to obtain a sufficient condition for ensuring the stability of the vehicle queue.

[0089] Further, Step 1 is specifically as follows:

[0090] There are non-linear links such as engines, transmissions, and quadratic wind resistance in the longitudinal dynamics of vehicles. Considering a fleet of N + 1 vehicles driving on a straight road, ignoring lateral and vertical movements, the vehicle is regarded as a rigid body, and it is completely symmetric left and right, ignoring the slip of the tires. The non-linear longitudinal dynamic model of a single vehicle is established as follows:

[0091]

[0092] In the formula, \(i\in\{0,1,2,\cdots,N\}\) represents the \(i\)-th vehicle, \(p\) i (t), \(v\) i (t) represent the position and speed of the \(i\)-th vehicle, \(m\) i is the mass of the vehicle, \(C\) A,i is the air resistance coefficient, \(g\) is the gravitational acceleration constant, \(f\) i is the rolling resistance coefficient, \(T\) i (t) is the actual driving force of the vehicle, \(T\) des,i (t) is the desired driving force, \(\tau\) i is the time-delay constant of the vehicle longitudinal dynamic system, \(r\) w,i is the wheel radius, \(\eta\) T,i is the mechanical efficiency of the transmission system.

[0093] From equation (1), we can obtain:

[0094]

[0095] \(a\) i (t) represents the acceleration of the vehicle, and the following linear feedback control strategy is adopted:

[0096]

[0097] In the formula, \(u\) i is the control input of the vehicle after feedback linearization. Furthermore, equation (2) is transformed into:

[0098]

[0099] Assume that the sampling period \(h > 0\). With the zero-order hold mechanism added, the discrete-time single-vehicle third-order state-space model is obtained as follows:

[0100] \(x\) i (k + 1)=Ax i (k)+B(u i (k)+w i (k)) (5)

[0101] where \(u\) i (k) is the control input of the vehicle after feedback linearization, and \(x\) i (k)=[p i (k) \(v\) i (k) \(a\) i (k)] T , \(w\) i (k) represents the unknown disturbance input on vehicle \(i\), and \(a\) i (k) represents the acceleration of vehicle \(i\).

[0102] Furthermore, Step 2 is specifically as follows:

[0103] Based on graph theory, the information flow topology structure of information transmission between vehicles is intuitively abstracted into the structure of a graph, and then characterized by corresponding matrices and their properties.

[0104] Consider a vehicle queue consisting of a leading vehicle with index 0 and N following vehicles with indices from 1 to N. Regarding each vehicle as a node in the network, the information transmission between the following vehicles can be represented by a directed graph for representation, is the set of nodes, representing N following vehicles, represents the set of edges, represents a directed edge from node j to node i, indicating that vehicle i can receive the information of vehicle j. Define for the directed graph the adjacency matrix a ij = 1 means that following vehicle i can receive the communication data of following vehicle j, otherwise a ij = 0. Assume that there are no self-loops in the graph i.e., a ii = 0.

[0105] Define the neighborhood set of node i Define the in-degree matrix where Define the Laplacian matrix

[0106] Define the traction matrix If vehicle i can receive the information of the leading vehicle, then p i = 1, otherwise p i = 0. At the same time, define the following traction set:

[0107]

[0108] Define the set matrix And assume that each following vehicle can directly or indirectly receive the information of the leading vehicle.

[0109] Furthermore, Step 3 is specifically as follows:

[0110] Assume that the sampling period of all vehicles is h > 0. The event generator on each vehicle decides whether to transmit the sampling data packet of each vehicle. For Use to represent the s-th triggering moment of vehicle i, and furthermore, the subsequent triggering moments are determined by the following adaptive triggering mechanism:

[0111]

[0112] where Denote the state of the i-th following vehicle at the most recent triggering moment; is the difference between the data at the current moment and the most recent triggering; And d i,j (k) = d i,0 (k) - d j,0 (k) represents the desired spacing between vehicle i and vehicle j, and d i,0 (k) represents the desired interval between vehicle i and the leading vehicle; Φ is a positive weighting matrix to be determined; σ i (k) is a dynamic threshold parameter, and it is adjusted according to the following function:

[0113]

[0114] where and σ i respectively represent the lower and upper bounds of the dynamic threshold parameter. The threshold parameter is adjusted between the threshold lower bound and the threshold upper bound according to the magnitude of the triggering error. When the triggering error increases, the threshold parameter tends to the lower bound, increasing the triggering frequency to improve the control performance. When the triggering error decreases, the threshold tends to the upper bound, reducing the triggering frequency to save more communication resources. Compared with the traditional static event-triggering mechanism with a fixed threshold, the data transmission is more flexible. π is the pi; ε > 0 is used to adjust the sensitivity.

[0115] The present invention is based on an adaptive event-triggering mechanism, and for each vehicle adopts the following distributed controller:

[0116]

[0117] where, K = [k p k v k a is the control gain matrix to be solved.

[0118] Establish the tracking error of the i-th following vehicle and the leading vehicle as follows:

[0119]

[0120] Define δ i (k) = [δ i p (k) δ i v (k) δ i a (k)] T , δ i p (k), δ iv (k) and δ i a (k) represent the position, speed, and acceleration errors between the i-th following vehicle and the leading vehicle, respectively. Combining the state model of a single vehicle in Equation (5) and the distributed controller in Equation (9), when the leading vehicle is traveling at a constant speed and a fixed desired spacing is taken, the error model between a single following vehicle and the leading vehicle is obtained as follows:

[0121]

[0122] where Define the vectors: δ(k) = [δ1 T (k), δ2 T (k),..., δ N T (k)] T , e(k) = [e1 T (k), e2 T (k),..., e N T (k)] T . Combining the error model in Equation (11) between a single vehicle and the leading vehicle, the following closed-loop error model can be obtained:

[0123]

[0124] where y(k) = [y1(k), y2(k),..., y N (k)] T , y i (k) = Cδ i (k) represents the position error output, and C = [1, 0, 0].

[0125] Furthermore, the specific process of Step 4 is as follows:

[0126] Step 4.1: For the closed-loop error system of the vehicle platoon in Equation (12), the control objective of the present invention is:

[0127]

[0128] That is

[0129] Construct a Lyapunov function According to Equation (13), the sufficient condition for the stability of Equation (12) is:

[0130] Given a scalar γ > 0, scalars α, 1 > α > 0, if there exist positive definite matrices P > 0 and Φ > 0 and a matrix K such that:

[0131]

[0132] Among them:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] Diagonal matrix If I is an arbitrary identity matrix, then equation (12) is exponentially stable and satisfies H ∞ The performance index is γ. The proof of the above sufficient condition for stability is as follows:

[0140] Define the vector When there is no perturbation, i.e., At this time, we can get:

[0141]

[0142] Among them,

[0143]

[0144] The matrix elements are:

[0145]

[0146]

[0147]

[0148] From the adaptive triggering condition equation (7), the following inequality always holds:

[0149]

[0150] Define the vector:

[0151]

[0152] And the diagonal matrix Combined with equation (17), we can get:

[0153]

[0154] Among them, Inequality (15) makes the following hold:

[0155]

[0156] From this, it can be obtained that:

[0157]

[0158] From this, it can be deduced that:

[0159]

[0160] Let a = λ min (P), b = λ max (P), and it can be obtained that:

[0161] a||δ(k)|| 2 ≤V(k)≤α k V(0)≤bα k ||δ(0)|| 2 (21)

[0162] Combining equations (19) and (20) can obtain:

[0163]

[0164] where is a constant, and lnα is negative, then the closed-loop dynamic system of the vehicle platoon in equation (12) is exponentially stable without disturbances.

[0165] When there are disturbances, that is at this time, define the vector and it can be obtained that:

[0166]

[0167] Combining equation (14) can obtain:

[0168]

[0169] Accumulating both sides of the above equation and considering the zero initial conditions can obtain:

[0170]

[0171] Then the closed-loop dynamic system of the vehicle platoon in equation (12) satisfies the H ∞ performance, and the performance index is γ.

[0172] Step 4.2: Linearize equation (14), decouple the coupled terms to be solved, and deduce the distributed control gain matrix.

[0173] Applying the Schur complement lemma to (13) gives:

[0174]

[0175] where:

[0176]

[0177]

[0178] Multiplying both sides of equation (26) by the diagonal matrix and defining the matrix P -1 = X, K = YX -1 , P -1 ΦP -1 = F gives:

[0179]

[0180] where:

[0181]

[0182]

[0183] Solving the matrix X, Y, and F through the linear matrix inequality, the control gain matrix K = YX -1 , the matrix Φ = X -1 FX -1 .

[0184] The present invention will now be further described in conjunction with specific embodiments and the accompanying drawings;

[0185] The specific embodiments of the present invention include the following steps:

[0186] (1) Establishment of the state equation

[0187] Consider a vehicle platoon consisting of a leader vehicle indexed 0 and five follower vehicles indexed 1 to 5. The leader vehicle travels at a constant speed on a straight road. The discrete state space model of a single vehicle is shown in equation (5), and the closed-loop queue error model of the vehicle queue is shown in equation (12). The selected sampling period h = 0.002 s, and the time delay constant τ i = 0.5 s. The desired fixed inter-vehicle distance is d i,0 = -5 m, and the desired speed is v0 = 4 (m / s).

[0188] (2) Design of relevant parameters

[0189] The vehicle can share its state information with the surrounding vehicles through a communication network, and the information transmission of the follower vehicles is controlled by an adaptive event-triggering strategy, where the event-triggering strategy is shown in Equation (7), and the adaptive threshold parameter adjustment strategy in the event-triggering strategy is shown in Equation (8). Set the upper bound of the threshold parameter The lower bound of the threshold σ i = 0.05, the sensitivity parameter is taken as ε = 100. The constant α = 0.998, γ = 15, and the simulation runs for 1500 time steps. The disturbance suffered by the vehicle is assumed to be w(k) = sin(10k). The communication topology among the vehicles is as Figure 2 shown.

[0190] (3) Verification of vehicle queue stability and adaptive event-triggering performance

[0191] Select the initial states of the vehicles as x0 = [5; 4; 0], x1 = [3; 1; 0], x2 = [2; 2; 0], x4 = [0; 3; 0], x5 = [-1; 2; 0].

[0192] At the initial moment k = 0, all vehicles transmit their own state information to the on-vehicle ad hoc network, and then obtain the control input u i (0). At subsequent moments, all follower vehicles will judge whether to transmit their own information through the adaptive event-triggering strategy and update the control input based on the latest trigger information of the surrounding vehicles. Record the moments when each vehicle meets the event-triggering condition and transmits its own state information through simulation.

[0193] The queue stability results of the vehicle queue are shown in Figures 3(a), 3(b), 3(c), and 3(d), which respectively represent the position trajectory, spatial error trajectory, velocity error trajectory, and acceleration error trajectory of the vehicle queue. It can be seen from the figures that the method ensures the queue stability of the vehicle queue. Figure 4 This is the event-triggering moment diagram for all follower vehicles. By calculation, the total triggering rate of the vehicle fleet is 56.83%, saving 43.17% of the communication resources.

Claims

1. An adaptive event-triggered control method for a vehicle queue, characterized in that, It includes the following steps: Step 1: Establish a non-linear dynamic model of a single vehicle; Step 2: Use graph theory to describe the communication topology among vehicles; Step 3: Introduce an adaptive event-triggering mechanism and jointly design a distributed controller with the adaptive event-triggering. According to the non-linear dynamic model of a single vehicle and the communication topology described by graph theory, establish a closed-loop error model of the vehicle platoon. The specific process is as follows: Assume that the sampling period for all vehicles is h > 0. The event generator on each vehicle decides whether to transmit the sampled data packet of each vehicle. For use to represent the s-th triggering moment of vehicle i. And the subsequent triggering moments are determined by the following adaptive triggering mechanism: where represents the state of the i-th following vehicle at the most recent triggering moment; is the difference between the data at the current moment and the most recent trigger; and d i,j (k) = d i,0 (k) - d j,0 (k) represents the desired spacing between vehicle i and vehicle j, and d i,0 (k) represents the desired interval between vehicle i and the leading vehicle; Φ is a positive weighting matrix to be determined; σ i (k) is a dynamic threshold parameter, and it is adjusted according to the following function: wherein and σ i respectively represent the upper and lower bounds of the dynamic threshold parameter, π is the pi; ε > 0 is used to adjust the sensitivity; Based on the adaptive event-triggered mechanism, for each vehicle Adopt the following distributed controller: where K = [k p k v k a is the control gain matrix; Establish the tracking error between the i-th following vehicle and the leading vehicle as follows: Definition δ i p (k), δ i v (k) and δ i a (k) respectively represent the position, speed, and acceleration errors between the i-th following vehicle and the leading vehicle; combining the third-order state-space model of a single vehicle and a distributed controller, when the leading vehicle is traveling at a constant speed and a fixed desired spacing is taken, the error model of a single following vehicle and the leading vehicle is obtained as: Among them Define the vector δ(k) = [δ1 T (k), δ2 T (k),..., δ N T (k)] T , e(k) = [e1 T (k), e2 T (k),..., e N T (k)] T , combining the error model between a single vehicle and the leading vehicle, the following closed-loop error model is obtained: where y(k) = [y1(k), y2(k),..., y N (k)] T , y i (k) = Cδ i (k) represents the position error output, I N is an N×N identity matrix, and C = [1, 0, 0]; Step 4: Introduce the Lyapunov stability theory and linear matrix inequalities. According to the closed-loop error model, introduce the H ∞ performance index to obtain a sufficient condition for ensuring the stability of the vehicle platoon.

2. The adaptive event-triggered control method for a vehicle platoon according to claim 1, wherein, The process of establishing the non-linear dynamic model described in Step 1 is as follows: There are non-linear links in the longitudinal dynamics of the vehicle. Considering a platoon of N + 1 vehicles driving on a straight road, ignoring lateral and vertical motions, the vehicle is regarded as a rigid body and is completely symmetric left and right. Ignoring tire slip, establish the non-linear longitudinal dynamic model of a single vehicle as follows: Where \(i\in\{0,1,2,\cdots,N\}\) represents the \(i\)-th vehicle, \(p\) i (t), \(v\) i (t) represent the position and speed of the \(i\)-th vehicle, \(m\) i is the mass of the vehicle, \(C\) A,i is the air resistance coefficient, \(g\) is the gravitational acceleration constant, \(f\) i is the rolling resistance coefficient, \(T\) i (t) is the actual driving force of the vehicle, \(T\) des,i (t) is the desired driving force, \(\tau\) i is the inertia time constant of the vehicle longitudinal power system, \(r\) w,i is the wheel radius, \(\eta\) T,i is the mechanical efficiency of the transmission system; Assume that the sampling period h > 0. With the zero-order hold mechanism added, the discrete-time third-order state-space model of a single vehicle is obtained from the non-linear longitudinal dynamic model as follows: x i (k + 1) = Ax i (k) + B(u i (k) + w i (k)) where u i (k) is the control input of the vehicle after feedback linearization, and x i (k) = [p i (k) v i (k) a i (k)] T , w i (k) represents the unknown disturbance input on vehicle i, and a i (k) represents the acceleration of vehicle i.

3. An adaptive event-triggered control method for a vehicle platoon according to claim 2, characterized in that, The specific process of Step 2 is as follows: Consider a vehicle queue consisting of a lead vehicle indexed 0 and N following vehicles indexed 1 to N. Regarding each vehicle as a node in the network, the information transfer between the following vehicles is represented by a directed graph for presentation, where is the node set, represents the edge set, and (j, i) ∈ ε N represents a directed edge from node j to node i, indicating that vehicle i can receive information from vehicle j; define the adjacency matrix for the directed graph a ij = 1 means that following vehicle i can receive communication data from following vehicle j, otherwise a ij = 0. Assume that there are no self-loops in the graph , that is, a ii = 0; Define the neighborhood set of node i Define the in-degree matrix where Define the Laplacian matrix Define the traction matrix If vehicle i can receive the information of the leading vehicle, then p i = 1, otherwise p i = 0; At the same time, define the following traction set: Define a set Matrix And assume that each following vehicle can directly or indirectly receive information from the leading vehicle.

4. An adaptive event-triggered control method for a vehicle queue according to claim 3, characterized in that The dynamic threshold parameter is adjusted between the lower bound and the upper bound of the threshold according to the magnitude of the triggering error. When the triggering error increases, the threshold parameter tends to the lower bound, increasing the triggering frequency to improve the control performance. When the triggering error decreases, the threshold tends to the upper bound, and the triggering frequency decreases to save more communication resources.

5. The adaptive event-triggered control method for a vehicle platoon according to claim 4, characterized in that The specific process of Step 4 is as follows: Step 4.1: For the platoon closed-loop error model, the platoon control objective is: That is Construct the Lyapunov function According to the platoon control objective, a sufficient condition for the stability of the closed-loop error model is as follows: Given a scalar γ > 0, 1 > α > 0, if there exist positive definite matrices P > 0 and Φ > 0 and a matrix K such that: Where: Diagonal matrix If I is an arbitrary identity matrix, then the closed-loop error model is exponentially stable and satisfies H ∞ The performance index is γ; Step 4.2: Using the Schur complement lemma for the Π equation, we get: Where: Multiply both sides of the formula obtained from the Schur complement lemma by a diagonal matrix And define the matrix P -1 = X, K = YX -1 , P -1 ΦP -1 = F to obtain: Where: Solve the matrices X, Y, and F by the sub - linear matrix inequality, then the control gain matrix K = YX -1 .

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