CN112099349B - Optimal cooperative control method for vehicle queue - Google Patents

Optimal cooperative control method for vehicle queue Download PDF

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CN112099349B
CN112099349B CN202010839990.3A CN202010839990A CN112099349B CN 112099349 B CN112099349 B CN 112099349B CN 202010839990 A CN202010839990 A CN 202010839990A CN 112099349 B CN112099349 B CN 112099349B
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陈建忠
李静
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Northwestern Polytechnical University
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Abstract

The invention discloses an optimal cooperative control method for a vehicle queue. Firstly, determining a dynamic model of a vehicle queue and a spacing strategy of the vehicle queue; then constructing a performance index function and a vehicle queue control input function of optimal cooperation of the vehicle queue; and then combining the performance index function with the control input function to construct an optimal cooperative control method, and solving the optimal control gain meeting the performance index function of the vehicle queue under the condition of ensuring the asymptotic stability of the vehicle queue so as to achieve driving safety, vehicle cooperativity and fuel economy. The method can effectively balance the problems of vehicle queue cooperativity and fuel economy, so that the vehicles can save energy and realize the cooperative driving of the vehicle queue.

Description

Optimal cooperative control method for vehicle queue
Technical Field
The invention belongs to the field of intelligent traffic, and particularly relates to a cooperative control method.
Background
The intelligent networked automobile has become a research hotspot in the fields of global automobiles, internet and the like. China intelligent networking development and positioning are shifted from an important component of the original concept of Internet of vehicles to intelligent integration industries such as intelligent manufacturing, intelligent networking and the like.
Under the intelligent networking environment, vehicles in communication with X (people, vehicles, roads, cloud ends and the like) are realized, the longitudinal motion state of the vehicles is automatically adjusted to form a queue, the consistent driving speed and the expected configuration are achieved, and a vehicle queue is formed. The vehicle queue can improve the road traffic capacity: by reducing the distance between vehicles, the traffic flow density of the road is improved and the traffic jam pressure is relieved on the premise of not expanding the road; the vehicle queue can promote road traffic safety: by sharing the state information among the vehicles in real time, the vehicles can make decisions more quickly and accurately, so that dangers are avoided, the safe distance and speed among the vehicles are kept, and accidents such as rear-end collision are avoided; the vehicle queue can effectively reduce the environmental pollution: the aerodynamic force of the vehicle queue running and the simulated analysis data thereof are researched, so that the air resistance borne by the vehicle can be effectively reduced by the vehicle queue running, and the oil consumption and the emission of the vehicle are effectively reduced; the vehicle queue running can exert the function and the advantage of the cooperative cooperation of the vehicles: in some special fields, a plurality of vehicles are required to form a vehicle queue or other formation in a specific form, and through mutual cooperation and cooperation, tasks such as exploration, rescue, patrol and the like are further completed.
In the vehicle queue control system, a control algorithm plays a key role in smooth and efficient operation of the vehicle queue. However, the cooperative control method for the vehicle queue in the prior art still has certain defects. Firstly, the cooperative driving of the vehicle queue mainly considers the characteristics of cooperativity, stability and the like, does not consider the fuel economy, and often needs to sacrifice other requirements when meeting the cooperativity requirement, so that the optimal overall performance of the vehicle queue is difficult to ensure. Secondly, there are some uncertain control parameters such as control gain in the vehicle queue cooperative control method, and the selection of the control parameters can have important influence on the stability and economy of the vehicle queue, so it is necessary to ensure the optimality of the control parameters.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an optimal cooperative control method for a vehicle queue. Firstly, determining a dynamic model of a vehicle queue and a spacing strategy of the vehicle queue; then constructing a performance index function and a vehicle queue control input function of optimal cooperation of the vehicle queue; and then combining the performance index function with the control input function to construct an optimal cooperative control method, and solving the optimal control gain meeting the performance index function of the vehicle queue under the condition of ensuring the asymptotic stability of the vehicle queue so as to achieve driving safety, vehicle cooperativity and fuel economy. The method can effectively balance the problems of vehicle queue cooperativity and fuel economy, so that the vehicles can save energy and realize the cooperative driving of the vehicle queue.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: constructing a vehicle queue, wherein the vehicle queue consists of N +1 vehicle groups, and according to the driving direction, a first vehicle arranged in the vehicle group is a head vehicle, and the rest vehicles are following vehicles; the head vehicle number is 0, the following vehicle number is represented by i, and i belongs to {1,2, …, N };
step 2: determining a dynamic model of the vehicle fleet;
defining the actual position of the following vehicle i as pi(t) actual velocity vi(t) control input is ui(t) following vehicleThe kinetic model for i is:
Figure GDA0003505972610000021
wherein A and B are different given parameters;
and step 3: determining a spacing strategy of the vehicle queue by adopting a variable time-distance spacing strategy;
obtaining speed v of the head vehicle through communication between vehicles in the vehicle queue0(t), setting a desired distance between the following vehicle i and the head vehicle 0:
Figure GDA0003505972610000022
wherein, ci0、hi0And di0Is a given coefficient;
setting the desired separation of the following vehicle j and the lead vehicle 0:
Figure GDA0003505972610000023
wherein, cj0、hj0And dj0Is a given coefficient, j ∈ {1,2, …, N };
setting a desired spacing between the following vehicles i and j:
Figure GDA0003505972610000024
wherein, cij、hijAnd dijA coefficient representing a desired separation of following vehicles i and j, satisfying the condition:
Figure GDA0003505972610000025
defining the position error of the following vehicle i relative to the head vehicle as
Figure GDA0003505972610000026
The speed error is
Figure GDA0003505972610000027
Specifically, as shown in formula (6):
Figure GDA0003505972610000031
the dynamic model (1) of the vehicle is converted into:
Figure GDA0003505972610000032
wherein,
Figure GDA0003505972610000033
a state vector representing vehicle i;
the state equation defining the global form of the vehicle fleet is:
Figure GDA0003505972610000034
wherein,
Figure GDA0003505972610000035
the expression of the kronecker product,
Figure GDA0003505972610000036
a global state vector representing the vehicle train, u (t) ═ u1(t) u2(t) … uN(t)]TIntegral control input function, I, representing vehicle fleetNRepresenting an N-order identity matrix;
and 4, step 4: constructing a vehicle queue performance index function;
constructing a performance index function of the vehicle i:
Ji(t)＝Ji1(t)+Ji2(t)+Ji3(t) (9)
wherein:
Figure GDA0003505972610000037
Ji1(t) a Performance indicator function representing the State error between vehicle i and vehicle j, aijRepresenting a communication connection of vehicle i with vehicle j, aij∈[0,1]，aij1 indicates that the vehicle i can acquire the information of the vehicle j, aij0 indicates that the vehicle i cannot acquire the information of the vehicle j; q. q.s1And q is2Weights respectively representing state errors between the vehicle i and the vehicle j;
Figure GDA0003505972610000038
Ji2(t) a Performance indicator function representing the State error between vehicle i and head vehicle 0, ai0Indicating a communication connection of vehicle i with head vehicle 0, ai0∈[0,1]ai01 indicates that the vehicle i can acquire the information of the head car 0, ai00 indicates that the vehicle i cannot acquire the information of the head vehicle 0; α and β represent the weight of the state error between the vehicle i and the head vehicle 0, respectively;
Figure GDA0003505972610000039
Ji3(t) a performance indicator function representing a control input of a vehicle i, r1To control the weight of the input, r2Weights for controlling the input derivatives;
the performance indicator function for a vehicle fleet is represented as:
Figure GDA0003505972610000041
wherein,
Figure GDA0003505972610000042
l represents the Laplace moment of a communication topological graph of the vehicle i and the vehicle jArray, L ═ Lij]∈RN×N，
Figure GDA0003505972610000043
lij＝-aij，i≠j，G＝diag{a10,a20,…,aN0Represents a communication topology matrix of the vehicle i and the head vehicle 0;
and 5: constructing a vehicle queue control input function;
the control input function for vehicle i is constructed as:
Figure GDA0003505972610000044
wherein k is1Representing the position error gain, k, of vehicles i and j2Representing the speed error gain, k, of vehicles i and j3Representing the position error gain, k, between vehicle i and head car 04Representing the speed error gain between vehicle i and head car 0, τ representing the communication time lag between vehicles, v0(t- τ) · τ represents compensation for position errors caused by communication skew;
the control input function for the vehicle fleet is:
Figure GDA0003505972610000045
wherein M is1＝[k1 k2]And M2＝[k3 k4]Gain matrix representing control input, D ═ diag { DiRepresents the incidence matrix of the communication topological graph of the vehicles i and j, wherein
Figure GDA0003505972610000046
Step 6: constructing an optimal cooperative control model of the vehicle queue:
Figure GDA0003505972610000047
and 7: solving the equation (16) to obtain an optimal control gain matrix M of the vehicle queue control input1＝[k1 k2]And M2＝[k3 k4]And the performance index function value of the vehicle queue is minimized, and the optimal cooperative control target of the vehicle queue is achieved.
Preferably, c isi0Has a value range of [ -0.1i,0.1i [)]，hi0Has a value range of [0,2i ]]，di0Has a value range of [5i,15i ]]。
The invention has the beneficial effects that:
in the optimal cooperative control method for the vehicle queue, disclosed by the invention, the factors such as the position error, the speed error, the control input, the derivative of the control input and the like of the vehicle are comprehensively considered, and the performance index function of the vehicle queue is constructed. In the control input function of the vehicle queue, factors such as vehicle queue control time lag, time lag compensation and the like are considered, a more reasonable spacing strategy is adopted, and the method is beneficial to improving the road utilization rate and the driving safety. And combining the performance index function with the control input function of the vehicle queue to construct the optimal vehicle queue cooperative control method meeting the optimal performance index function. The method can effectively balance the problems of vehicle queue cooperativity and fuel economy, so that the vehicles can save energy and realize the cooperative driving of the vehicle queue.
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FIG. 1 is a schematic diagram of the vehicle fleet optimal cooperative control method of the present invention.
FIG. 2 is a vehicle queue communication topology of the present invention.
FIG. 3 is a diagram of a variable time interval strategy used by the fleet of vehicles according to the present invention.
Fig. 4 is a vehicle state change diagram of the vehicle queue in the initial traffic scenario according to the embodiment of the invention.
Fig. 5 is a vehicle state change diagram of the vehicle queue in the trapezoidal disturbance traffic scene according to the embodiment of the invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
As shown in fig. 1 and 2, the present invention provides a vehicle queue optimal cooperative control method, including the steps of:
step 1: constructing a vehicle queue, wherein the vehicle queue consists of N +1 vehicle groups, and according to the driving direction, a first vehicle arranged in the vehicle group is a head vehicle, and the rest vehicles are following vehicles; the head vehicle number is 0, the following vehicle number is represented by i, and i belongs to {1,2, …, N };
step 2: determining a dynamic model of the vehicle fleet;
defining the actual position of the following vehicle i as pi(t) actual velocity vi(t) control input is ui(t), the dynamic model of the following vehicle i is:
Figure GDA0003505972610000051
wherein A and B are different given parameters;
and step 3: as shown in fig. 3, a Variable Time interval strategy (VTH) is used to determine the interval strategy of the vehicle fleet;
obtaining speed v of the head vehicle through communication between vehicles in the vehicle queue0(t), setting a desired distance between the following vehicle i and the head vehicle 0:
Figure GDA0003505972610000061
wherein, ci0、hi0And di0Is a given coefficient, ci0Has a value range of [ -0.1i,0.1i [)]，hi0Has a value range of [0,2i ]]，di0Has a value range of [5i,15i ]]；
Setting the desired separation of the following vehicle j and the lead vehicle 0:
Figure GDA0003505972610000062
wherein, cj0、hj0And dj0Is to giveA fixed coefficient, j ∈ {1,2, …, N };
setting a desired spacing between the following vehicles i and j:
Figure GDA0003505972610000063
wherein, cij、hijAnd dijA coefficient representing a desired separation of following vehicles i and j, satisfying the condition:
Figure GDA0003505972610000064
defining the position error of the following vehicle i relative to the head vehicle as
Figure GDA0003505972610000065
The speed error is
Figure GDA0003505972610000066
Specifically, as shown in formula (6):
Figure GDA0003505972610000067
the dynamic model (1) of the vehicle is converted into:
Figure GDA0003505972610000068
wherein,
Figure GDA0003505972610000069
a state vector representing vehicle i;
the state equation defining the global form of the vehicle fleet is:
Figure GDA00035059726100000610
wherein,
Figure GDA00035059726100000611
the expression of the kronecker product,
Figure GDA00035059726100000612
a global state vector representing the vehicle train, u (t) ═ u1(t) u2(t) … uN(t)]TIntegral control input function, I, representing vehicle fleetNRepresenting an N-order identity matrix;
and 4, step 4: constructing a vehicle queue performance index function;
constructing a performance index function of the vehicle i:
Ji(t)＝Ji1(t)+Ji2(t)+Ji3(t) (9)
wherein:
Figure GDA0003505972610000071
Ji1(t) a Performance indicator function representing the State error between vehicle i and vehicle j, aijRepresenting a communication connection of vehicle i with vehicle j, aij∈[0,1]，aij1 indicates that the vehicle i can acquire the information of the vehicle j, aij0 indicates that the vehicle i cannot acquire the information of the vehicle j; q. q.s1And q is2Weights respectively representing state errors between the vehicle i and the vehicle j;
Figure GDA0003505972610000072
Ji2(t) a Performance indicator function representing the State error between vehicle i and head vehicle 0, ai0Indicating a communication connection of vehicle i with head vehicle 0, ai0∈[0,1]ai01 indicates that the vehicle i can acquire the information of the head car 0, ai00 indicates that the vehicle i cannot acquire the information of the head vehicle 0; α and β represent the weight of the state error between the vehicle i and the head vehicle 0, respectively;
Figure GDA0003505972610000073
Ji3(t) a performance indicator function representing a control input of a vehicle i, r1To control the weight of the input, r2Weights for controlling the input derivatives;
the performance indicator function for a vehicle fleet is represented as:
Figure GDA0003505972610000074
wherein,
Figure GDA0003505972610000075
l represents a Laplace matrix of a communication topological graph of the vehicle i and the vehicle j, and L is [ < L >ij]∈RN×N，
Figure GDA0003505972610000076
lij＝-aij，i≠j，G＝diag{a10,a20,…,aN0Represents a communication topology matrix of the vehicle i and the head vehicle 0;
and 5: constructing a vehicle queue control input function;
the control input function for vehicle i is constructed as:
Figure GDA0003505972610000081
wherein k is1Representing the position error gain, k, of vehicles i and j2Representing the speed error gain, k, of vehicles i and j3Representing the position error gain, k, between vehicle i and head car 04Representing a speed error gain between the vehicle i and the head vehicle 0, and tau representing a communication time lag between the vehicles and taking a fixed value; v. of0(t- τ) · τ represents compensation for position errors caused by communication skew;
the control input function for the vehicle fleet is:
Figure GDA0003505972610000082
wherein M is1＝[k1 k2]And M2＝[k3 k4]Gain matrix representing control input, D ═ diag { DiRepresents the incidence matrix of the communication topological graph of the vehicles i and j, wherein
Figure GDA0003505972610000083
Step 6: the performance index function and the control input function are combined to construct an optimal cooperative control model of the vehicle queue, and the optimal control gain meeting the performance index function of the vehicle queue is solved under the condition of ensuring the asymptotic stability of the vehicle queue so as to achieve driving safety, vehicle cooperativity and fuel economy:
Figure GDA0003505972610000084
and 7: solving equation (16):
from the constraints of equation (16), the state equation of the vehicle fleet is obtained as follows:
Figure GDA0003505972610000085
constructing the Lyapunov function according to the Lyapunov-Krasovski theorem
Figure GDA0003505972610000086
Figure GDA0003505972610000087
Wherein P ∈ R2N×2N，S∈R2N×2NAnd Z ∈ R2N×2NAre all positive definite symmetric matrices;
to pair
Figure GDA0003505972610000088
And simultaneously performing derivation on two sides to obtain:
Figure GDA0003505972610000091
applying the Jensen inequality, equation (19) satisfies:
Figure GDA0003505972610000092
constructing a function from the performance indicator function of equation (16)
Figure GDA0003505972610000093
The following were used:
Figure GDA0003505972610000094
definition of
Figure GDA0003505972610000095
According to the formula (20):
Figure GDA0003505972610000096
wherein the matrix Ω satisfies:
Figure GDA0003505972610000097
wherein,
Figure GDA0003505972610000098
when omega is higher than<When the value of 0 is satisfied,
Figure GDA0003505972610000099
the establishment, according to Lyapunov-Krasovski theorem, of vehicle queues is growingNear-stable;
integrating over [0, T ] simultaneously on both sides of equation (22) yields:
Figure GDA00035059726100000910
since the system is asymptotically stable, when T → ∞,
Figure GDA00035059726100000911
the performance indicator function J satisfies:
Figure GDA00035059726100000912
when t → 0, according to Lyapunov-Krasovski's formula, we get:
Figure GDA00035059726100000913
according to equation (26), the performance indicator function J satisfies:
Figure GDA0003505972610000101
wherein λP、λSAnd λZP, S and Z, respectively;
according to equation (27), the performance indicator function is present in the upper bound, and the parameter λ is introduced such that λP≤λ、λS≤λ、λZNot more than lambda, the matrix P, S, Z satisfies lambda I, S not more than lambda I, Z not more than lambda I respectively; when the parameter lambda is minimum, the upper bound of the performance index function is minimum, and the determination of the minimum upper bound of the performance index function is converted into the following optimization problem:
Figure GDA0003505972610000102
solving Excellents by MATLAB LMI toolsetSolve the problem (28) to obtain an optimal control gain matrix M1＝[k1 k2]And M2＝[k3 k4]The control input of the optimal cooperative control method of the vehicle queue can be obtained by substituting the control input function (15) with the control input function; meanwhile, under the condition of meeting the asymptotic stability of the vehicle queue, the performance index function of the vehicle queue has the minimum upper bound:
Figure GDA0003505972610000103
and the vehicle queue performance index function value is minimized, so that the optimal cooperative control target of the vehicle queue is achieved.
Example (b):
as mentioned above, the parameters adopted in the embodiment of the present invention are shown in Table I.
TABLE I
Figure GDA0003505972610000104
Solving an optimization problem (28) by using a MATLAB LMI toolbox according to the parameters obtained in the table I, wherein the optimization problem can be solved by using an optimal control gain matrix M1＝[0.0014 0.0049]，M2＝[0.1485 0.7185]The optimum parameter λ 4.5003 × 106The minimum upper bound of the objective function can be obtained according to equation (29).
Solving the above example to obtain the optimal control gain matrix M1And M2And (5) carrying out the traffic scene simulation verification of the control input function through PLEXE simulation software after the control input function is brought into the formula (15), wherein the setting of specific traffic scene control parameters is shown in a table II.
TABLE II
Figure GDA0003505972610000111
According to the parameters in the table II, an initialization simulation scenario of the vehicle queue is set, assuming that the head vehicle runs at a constant speed of 25m/s, and the following vehicle runs at random initialization positions and initialization speeds, as shown in fig. 4, after a period of time adjustment, the position error and the speed error of the following vehicle and the head vehicle gradually become 0, the speeds of the following vehicle and the head vehicle gradually reach the same, and the desired distance between the vehicles gradually reaches the same. It is thus possible to verify that the control input function (15) enables the vehicle fleet to achieve optimal cooperative driving under the initialization simulation scenario.
According to the parameters in the table II, a trapezoidal disturbance simulation scene of the vehicle queue is set, the vehicle queue is supposed to be cooperatively driven at the constant speed of 25m/s at the initial speed, and the head vehicle is supposed to be driven at the constant speed of-2.5 m/s at 10s2Starting to decelerate to 10m/s constant speed for a period of time, and then driving at 2.5m/s2And accelerating to 25m/s and then driving at a constant speed. As shown in fig. 5, when the leading vehicle starts to decelerate or accelerate, the following vehicle can timely follow the change of the state of the leading vehicle, timely adjust the speed and the acceleration of the following vehicle, and gradually reach the agreement of the expected distance between the vehicles. It can thus be verified that the control input function (15) enables the following vehicle to follow the head vehicle state change at all times and maintain the cooperativity and stability of the vehicle queue at all times.

Claims (2)

1. The optimal cooperative control method for the vehicle queue is characterized by comprising the following steps of:
step 1: constructing a vehicle queue, wherein the vehicle queue consists of N +1 vehicle groups, and according to the driving direction, a first vehicle arranged in the vehicle group is a head vehicle, and the rest vehicles are following vehicles; the head vehicle number is 0, the following vehicle number is represented by i, and i belongs to {1,2, …, N };
step 2: determining a dynamic model of the vehicle fleet;
defining the actual position of the following vehicle i as pi(i) The actual speed is vi(t) control input is ui(t), the dynamic model of the following vehicle i is:
Figure FDA0003505972600000011
wherein A and B are different given parameters;
and step 3: determining a spacing strategy of the vehicle queue by adopting a variable time-distance spacing strategy;
obtaining speed v of the head vehicle through communication between vehicles in the vehicle queue0(t), setting a desired distance between the following vehicle i and the head vehicle 0:
Figure FDA0003505972600000012
wherein, ci0、hi0And di0Is a given coefficient;
setting the desired separation of the following vehicle j and the lead vehicle 0:
Figure FDA0003505972600000013
wherein, cj0、hj0And dj0Is a given coefficient, j ∈ {1,2, …, N };
setting a desired spacing between the following vehicles i and j:
Figure FDA0003505972600000014
wherein, cij、hijAnd dijA coefficient representing a desired separation of following vehicles i and j, satisfying the condition:
Figure FDA0003505972600000015
defining the position error of the following vehicle i relative to the head vehicle as
Figure FDA0003505972600000016
The speed error is
Figure FDA0003505972600000017
In particular as a formula(6) Shown in the figure:
Figure FDA0003505972600000018
the dynamic model (1) of the vehicle is converted into:
Figure FDA0003505972600000019
wherein,
Figure FDA0003505972600000021
a state vector representing vehicle i;
the state equation defining the global form of the vehicle fleet is:
Figure FDA0003505972600000022
wherein,
Figure FDA0003505972600000023
the expression of the kronecker product,
Figure FDA0003505972600000024
a global state vector representing the vehicle train, u (t) ═ u1(t) u2(t) … uN(t)]TIntegral control input function, I, representing vehicle fleetNRepresenting an N-order identity matrix;
and 4, step 4: constructing a vehicle queue performance index function;
constructing a performance index function of the vehicle i:
Ji(t)＝Ji1(t)+Ji2(t)+Ji3(t) (9)
wherein:
Figure FDA0003505972600000025
Ji1(t) a Performance indicator function representing the State error between vehicle i and vehicle j, aijRepresenting a communication connection of vehicle i with vehicle j, aij∈[0,1]，aij1 indicates that the vehicle i can acquire the information of the vehicle j, aij0 indicates that the vehicle i cannot acquire the information of the vehicle j; q. q.s1And q is2Weights respectively representing state errors between the vehicle i and the vehicle j;
Figure FDA0003505972600000026
Ji2(t) a Performance indicator function representing the State error between vehicle i and head vehicle 0, ai0Indicating a communication connection of vehicle i with head vehicle 0, ai0∈[0,1]ai01 indicates that the vehicle i can acquire the information of the head car 0, ai00 indicates that the vehicle i cannot acquire the information of the head vehicle 0; α and β represent the weight of the state error between the vehicle i and the head vehicle 0, respectively;
Figure FDA0003505972600000027
Ji3(t) a performance indicator function representing a control input of a vehicle i, r1To control the weight of the input, r2Weights for controlling the input derivatives;
the performance indicator function for a vehicle fleet is represented as:
Figure FDA0003505972600000028
wherein,
Figure FDA0003505972600000031
l represents a Laplace matrix of a communication topological graph of the vehicle i and the vehicle j, and L is [ < L >ij]∈RN×N，
Figure FDA0003505972600000032
lij＝-aij，i≠j，G＝diag{a10,a20,…,aN0Represents a communication topology matrix of the vehicle i and the head vehicle 0;
and 5: constructing a vehicle queue control input function;
the control input function for vehicle i is constructed as:
Figure FDA0003505972600000033
wherein k is1Representing the position error gain, k, of vehicles i and j2Representing the speed error gain, k, of vehicles i and j3Representing the position error gain, k, between vehicle i and head car 04Representing the speed error gain between vehicle i and head car 0, τ representing the communication time lag between vehicles, v0(t- τ) · τ represents compensation for position errors caused by communication skew;
the control input function for the vehicle fleet is:
Figure FDA0003505972600000034
wherein M is1＝[k1 k2]And M2＝[k3 k4]Gain matrix representing control input, D ═ diag { DiRepresents the incidence matrix of the communication topological graph of the vehicles i and j, wherein
Figure FDA0003505972600000035
Step 6: constructing an optimal cooperative control model of the vehicle queue:
Figure FDA0003505972600000036
and 7: solving the formula (1)6) Obtaining the optimal control gain matrix M of the vehicle queue control input1＝[k1 k2]And M2＝[k3k4]And the performance index function value of the vehicle queue is minimized, and the optimal cooperative control target of the vehicle queue is achieved.
2. The optimal cooperative vehicle queue control method according to claim 1, wherein c isi0Has a value range of [ -0.1i,0.1i [)]，hi0Has a value range of [0,2i ]]，di0Has a value range of [5i,15i ]]。
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