CN113485329B - Vehicle multi-queue cooperative control method - Google Patents
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Abstract
The invention discloses a vehicle multi-queue cooperative control method, which is based on a three-order vehicle longitudinal dynamics model, adopts a constant spacing strategy among fleet vehicles, adopts a constant headway spacing strategy in the fleet, and establishes a control model of queue leader vehicles and a cooperative control model of vehicles in the fleet; and (4) carrying out stability analysis on the vehicle multi-queue system by using a stability theory to obtain the stability condition of the multi-queue system. The invention can realize the cooperative control among the queues of the multi-queue system, simultaneously ensure the cooperative driving of the vehicles in the queues, has better adaptability to the complex queue system and improves the stability and the safety of the queue system.
Description
Technical Field
The invention belongs to the technical field of intelligent traffic, and particularly relates to a vehicle cooperative control method.
Background
An Intelligent Transportation System (ITS) mainly uses advanced scientific technologies, such as computer, data communication, information, sensors, automatic control, artificial intelligence and the like, so that resources of roads, automobiles and users are reasonably utilized, and a safe, efficient, clean and energy-saving comprehensive Transportation System is established. The continuous development of 5G communication technology also provides a certain technical foundation for ITS.
Vehicle queue control is one of research hotspots of an intelligent traffic system, and has important theoretical guiding significance for solving actual traffic problems. The stability control of the vehicle queue needs to consider the cohesion performance of the vehicle queue and the stability margin, wherein the cohesion performance is used for describing the robustness of the fleet under random disturbance, and the stability margin is used for describing the attenuation speed of the fleet under initial disturbance. The stability margin of the fleet is reduced along with the increase of the number of vehicles in the fleet and the reduction of the stability margin of the fleet is reduced along with the increase of the wireless communication distance between the vehicles, so that the number of the vehicles in the fleet is not easy to be excessive, and the fleet where a group of multiple vehicles travel cooperatively can be divided into multiple fleets. The cooperative control of the vehicles in the multiple queues can not only ensure the stability of the vehicle queues, but also ensure the communication quality among the vehicles. Meanwhile, the safe distance between vehicles can be effectively shortened by the multi-queue running of the vehicles, the traffic efficiency is improved, the traffic safety is ensured, and the vehicles can reduce the air resistance of the vehicles and reduce the oil consumption and the tail gas pollution by the streamline running of the vehicle queue. Therefore, the research on the vehicle multi-queue cooperative control is of great significance.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a vehicle multi-queue cooperative control method, which is based on a three-order vehicle longitudinal dynamics model, adopts a constant spacing strategy among fleets of vehicles, adopts a constant head-time spacing strategy in the fleets of vehicles, and establishes a control model of queue leader vehicles and a cooperative control model of vehicles in the fleets of vehicles; and (4) carrying out stability analysis on the vehicle multi-queue system by using a stability theory to obtain the stability condition of the multi-queue system. The invention can realize the cooperative control among the queues of the multi-queue system, simultaneously ensure the cooperative driving of the vehicles in the queues, has better adaptability to the complex queue system and improves the stability and the safety of the queue system.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: constructing a vehicle multi-queue, wherein the vehicle multi-queue is composed of N vehicles, wherein
The number of the fleet is m +1, and the serial numbers are 0,1, …, m and NkIndicates the number of vehicles in the k-th fleet, the number of vehicles in the fleet being 0,1, …, Nk-1；
Step 2: in the vehicle multi-queue system, each fleet has a leader vehicle which is positioned at the head of the fleet, and the leader vehicle of the first fleet is the leader vehicle of the whole vehicle multi-queue;
and step 3: the vehicle in the vehicle multi-queue system obtains the position, speed and acceleration information of other vehicles in a vehicle-to-vehicle communication mode, and adjacent vehicle fleets can communicate with each other;
and 4, step 4: determining a longitudinal dynamics model of a vehicle in a vehicle multi-fleet system, represented as:
wherein x isi,k、vi,k、ai,kAnd ui,k(t) respectively representing the position, velocity, acceleration and control input of the ith vehicle within the kth fleet; t isi,kRepresenting the transmission coefficient of a longitudinal power system of an ith vehicle in the kth vehicle fleet; t represents time;
and 5: in the multi-fleet system, a constant spacing strategy is adopted among fleets, and the expected spacing between the fleets is SminRepresents; the vehicles in the fleet adopt a spacing strategy of constant head-time distance, and the minimum safety spacing between two adjacent vehicles in the fleet is sminRepresents;
obtaining the state information of the leading vehicle according to the step 1, the step 2 and the step 3, and calculating the expected distance d between the ith following vehicle and the leading vehicle of the own fleet in the kth fleeti0,k：
di0,k＝i(Lk+smin+hkv0) (2)
Wherein L iskIndicates the length of the vehicle in the k-th fleet, hkRepresenting constant time intervals, v, between vehicles in the kth fleet0Representing the speed of the multi-fleet leader vehicle;
step 6: the leader vehicle control targets of the vehicle multi-queue system are as follows:
wherein x is0,k、v0,kAnd a0,kRespectively representing the position, speed and acceleration, x, of the leading vehicle of the k-th fleet0And a0Respectively representing the position and acceleration of the lead vehicle in the multi-train, LjIndicates the length of the vehicle in the jth fleet, hjRepresenting a constant time interval between vehicles in a jth fleet;
and 7: the control targets of the vehicles in the vehicle queue in the vehicle multi-queue system are as follows:
and 8: the cooperative control method of the vehicles in the vehicle queue in the vehicle multi-queue system comprises the following steps:
wherein, aijRepresenting the vehicle adjacency matrix A in the k-th fleetkAn element of (1); alpha is alpha>0、β>0、γ>0、α1>0、α2>0 and alpha3>0 is the control gain; vi,kIndicating the desired speed of the ith vehicle in the kth fleet,
represents the average distance between two adjacent vehicles between the vehicle i and the vehicle j in the kth vehicle group, tau (t) represents the communication time delay of the vehicles in the queue, and xj,kAnd vj,kRespectively representing the position and speed of the jth vehicle in the kth vehicle fleet, dij,kRepresenting the desired separation between vehicle i and vehicle j within the kth fleet, dij,k＝di0,k-dj0,k；
Desired speed V of ith vehicle in the kth vehicle fleeti,k(△xij(t)) is expressed as:
wherein d isminAnd dmaxAre given two distances; v. ofmaxRepresenting a maximum speed of the vehicle fleet; when Δ xij(t) is less than dminWhen the desired speed of the vehicle is zero; when Δ xij(t) is greater than dmaxThen, the fleet vehicles travel at the maximum allowable speed;
and step 9: the cooperative control method for the kth leading vehicle for constructing the vehicle multi-queue system comprises the following steps:
wherein u is0,k(t) control input, x, for the kth fleet leader vehiclej,k-1Indicating the position of the jth vehicle of the kth-1 fleet, gamma1、γ2、γ3、γ4All represent control gains; tau isjRepresenting the communication delay of the jth vehicle and the kth leading vehicle in the kth-1 fleet in the multi-queue; v. of0(t-τj)τjRepresentation of time delay taujCompensation for the resulting position error;
pj,k-1an adjacency matrix D representing the jth vehicle and the kth leading vehicle in the kth-1 fleet in the multi-queuekThe element (b); v0,k(△x0k) Representing the desired speed function of the kth fleet leader vehicle,
step 10: and (4) carrying out stability derivation verification on the cooperative control method provided in the step (9) to obtain a system gradual stability constraint condition and a time delay upper bound.
Further, hkHas a value range of (0, 2)]，sminThe value range of (a) is (0,20]，hjhas a value range of (0, 2)]，dminIs in the range of [10,20 ]]，dmaxIs in the range of [40,100 ]]；
Further, the specific method for obtaining the system gradual stability constraint condition and the time delay upper bound includes:
step 10-1: defining a position error for a kth lead vehicle
Error in velocity
Error in acceleration
The following were used:
according to the formula (1), the formula (3) and the formula (7), the closed-loop dynamic model of the ith vehicle leading vehicle state error is expressed as:
wherein the content of the first and second substances,
representing the distance error of the jth vehicle of the kth-1 fleet from the fleet leader vehicle; delta x*＝hkv0+smin，
Defining the communication time delay of the ith fleet and the kth fleet as tauik(t) and define τq(t),q＝1,2,...,M(M＝m(m-1))，τq(t)∈{τik(t), i ═ 1, …, m; k 1, …, m, time delay tauq(t) is bounded, i.e.
0≤τq(t)≤τ*，τ*Is an upper bound of the time delay, and
and d isqLess than or equal to 1; the communication time delay of the vehicle is not considered;
definition of
And
the system formula (9) is expressed as:
wherein:
wherein:
Q＝diag(q1,q2,...,qk,...,qm)，
step 10-2: the derivation of equation (10) according to newton-lebeniz equation translates to:
wherein:
wherein:
step 10-3: according to the Lyapunov-Krasovski theorem, a Lyapunov function is constructed as follows:
wherein, P and SqIs a positive definite real symmetric matrix, i.e. P ═ PT>0 and
q＝1,…,M；
derivation is performed on both sides of the Lyapunov function in equation (17):
when formula (14) is substituted into formula (18):
Step 10-4: the utilization conclusion is as follows: for any vector a, b ∈ RnAnd an arbitrary positive definite matrix F ∈ Rn×nHaving a matrix inequality 2aTb≤aTFa+bTF-1b is established; definition of
F＝P-1Equation (19) can be expressed as:
defining augmented state error vectors
Formula (20) is represented as:
wherein Λ ═ diag (Λ)1,Λ2,…,ΛM+1) Specifically, the following are shown:
step 10-5: when the diagonal matrix Λ is negative, i.e.:
each inequality in inequalities (23) is less than 0, then
When in use
According to the Lyapunov-Krasovski stability theorem, the time-lag closed-loop system (10) is consistent and asymptotically stable, namely
While obtaining an upper delay bound.
The invention has the following beneficial effects:
the invention establishes a control model of the vehicle multi-queue leader vehicle, designs a cooperative control method of the vehicles in the fleet, realizes the cooperative control of the vehicles in the fleet and between the fleets of the vehicle multi-queue system, ensures that the vehicles stably run according to the expected distance and speed, and ensures the quick and timely response of the vehicles in the queue when the motion state of the leader vehicle in the vehicle queue changes, thereby ensuring the stability of the vehicle multi-queue. The method has better adaptability to a complex queue system, and meanwhile, the vehicle multi-queue cooperative control method can realize formation execution of tasks by multiple vehicle teams and has important guiding significance for cooperative execution of the tasks by the multiple vehicle teams.
Drawings
FIG. 1 is a schematic diagram of a multi-queue spacing strategy for vehicles according to the method of the present invention.
FIG. 2 is a schematic diagram of the communication topology of vehicles in a vehicle multi-queue in accordance with the method of the present invention.
Fig. 3 is a diagram of the motion state of the lead vehicle in the multi-queue under the initialization scenario of the embodiment of the present invention, where (a) the acceleration of the lead vehicle, (b) the speed of the lead vehicle, and (c) the distance between the lead vehicles.
FIG. 4 is a diagram of the motion states of vehicles in a third fleet of vehicles under an initialization scenario, where (a) vehicle acceleration, (b) vehicle speed, and (c) vehicle separation distance are shown.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
A vehicle multi-queue cooperative control method comprises the following steps:
step 1: constructing a vehicle multi-queue, wherein the vehicle multi-queue is composed of N vehicles, wherein
The number of the fleet is m +1, and the serial numbers are 0,1, …, m and NkIndicates the number of vehicles in the k-th fleet, the number of vehicles in the fleet being 0,1, …, Nk-1；
Step 2: in the vehicle multi-queue system, each fleet has a leader vehicle which is positioned at the head of the fleet, and the leader vehicle of the first fleet is the leader vehicle of the whole vehicle multi-queue;
and step 3: as shown in fig. 2, in the vehicle multi-queue system, the vehicle obtains the state information of the position, speed, etc. of other vehicles through vehicle-to-vehicle communication (V2V), and the communication between adjacent vehicle fleets is good;
and 4, step 4: determining a longitudinal dynamics model of a vehicle in a vehicle multi-fleet system, represented as:
in the formula: x is the number ofi,k、vi,k、ai,kAnd ui,k(t) respectively representing the position, velocity, acceleration and control input of the ith vehicle within the kth fleet; t isi,kRepresenting the transmission coefficient of a longitudinal power system of the ith vehicle in the kth vehicle fleet;
and 5: as shown in figure 1, a constant spacing strategy is adopted among fleets in a multi-fleet system, and S is usedminRepresenting; the vehicles in the fleet adopt a spacing strategy of constant head-time distance, and the minimum safety spacing between two adjacent vehicles in the fleet is sminRepresents; obtaining the state information of the leading vehicle according to the steps 1, 2 and 3, and calculating the expected distance d between the ith following vehicle and the leading vehicle of the own fleet in the kth fleeti0,k：
di0,k＝i(Lk+smin+hkv0) (2)
In the formula: l iskIndicates the length of the vehicle in the k-th fleet, hkRepresenting constant time intervals, v, between vehicles in the kth fleet0Representing the speed of the multi-fleet leader vehicle; h is a total ofkHas a value range of (0, 2)]；
Step 6: the leader vehicle control targets of the vehicle multi-queue system are as follows:
in the formula: x is the number of0,k、v0,kAnd a0,kRespectively representing the position, speed and acceleration, x, of the leading vehicle of the k-th fleet0And a0Respectively, the position and acceleration of the lead vehicle of the multiple trains, LjIndicates the length of the vehicle in the jth fleet, hjRepresenting a constant time interval between vehicles in a jth fleet; h is a total ofjHas a value range of (0, 2)]；
And 7: the in-vehicle control targets in the vehicle multi-queue system are as follows:
and 8: the cooperative control method of the vehicles in the vehicle queue in the vehicle multi-queue system comprises the following steps:
in the formula: a isijRepresenting the vehicle adjacency matrix A in the k-th fleetkThe element (b); alpha is alpha>0、β>0、γ>0、α1>0、α2>0 and alpha3>0 is the control gain; vi,kIndicating the desired speed of the ith vehicle in the kth fleet,
represents the average distance between two adjacent vehicles between the vehicle i and the vehicle j in the kth vehicle group, tau (t) represents the communication time delay of the vehicles in the queue, and xj,kAnd vj,kRespectively representing the position and speed of the jth vehicle in the kth vehicle fleet, dij,kRepresenting the desired separation between vehicle i and vehicle j within the kth fleet, dij,k＝di0,k-dj0,k；
Desired speed V of ith vehicle in kth vehicle fleeti,k(△xij(t)) may be taken as (Jin I G, Orosz G. optimal control of connected vehicle Systems with communication delay and driver response time. IEEE Transactions on Intelligent transfer Systems,2016,18(8): 2056-:
wherein, dminAnd dmaxIs given two distances, dminIs in the range of [10,20 ]]，dmaxIs in the range of [40,100 ]]；vmaxRepresenting a maximum speed of the vehicle fleet; when Δ xij(t) is less than dminIn time, in order to ensure the safety of the fleet of vehicles, the expected speed of the vehicles is zero; when Δ xij(t) is greater than dmaxIn time, in order to increase traffic volume, fleet vehicles may travel at the maximum allowable speed; v. ofmaxRepresenting a maximum speed of the vehicle fleet; get dmin＝15m，dmax＝42.32m，vmax30m/s is the maximum speed of the vehicle queue;
and step 9: according to the steps, the kth leader vehicle cooperative control method of the vehicle multi-queue system is constructed, and the method comprises the following steps:
in the formula: u. of0,k(t) control input, x, for the kth fleet leader vehiclej,k-1Representing the k-1 th fleetPosition of jth vehicle, gamma1，γ2，γ3，γ4Represents a control gain; tau isjRepresenting the communication delay of the jth vehicle in the kth-1 th fleet in the multi-queue; v. of0(t-τj)τjRepresenting time delay taujCompensation for the resulting position error;
pj,k-1an adjacency matrix D representing the jth vehicle and the kth leading vehicle in the kth-1 fleet in the multi-queuekAn element of (1); v0,k(△x0k) Representing the desired speed function of the kth fleet leader vehicle,
further, according to equations (1), (3) and (7), the closed-loop dynamical model of the ith vehicle lead vehicle state error can be expressed as:
in the formula:
representing the distance error of the jth vehicle of the kth-1 fleet from the fleet leader vehicle;
△x*＝hkv0+smin，
in order to more compactly describe queue dynamics under the condition of relevant time delay in different communication links, the communication time delay of the ith fleet and the kth fleet is defined as tauik(t) and define τq(t),q＝1,2,...,M(M＝m(m-1))，τq(t)∈{τik(t), i ═ 1, …, m; k is 1, …, m }. Definition of
And
system equation (9) may be expressed as:
in the formula:
in the formula:
Q＝diag(q1,q2,...,qk,...,qm)，
i＝1,…,m；k＝1,…,m，Bq∈Rm×m，q＝1,...,M；
further, the derivation of equation (10) from the newton-lebeniz equation can be converted to:
in the formula:
in the formula:
further, according to the Lyapunov-Krasovskii theorem, the Lyapunov function is constructed as follows:
in the formula: p and SqIs a positive definite real symmetric matrix, i.e. P ═ PT>0 and
q＝1,…,M。
derivation is performed on both sides of the Lyapunov function in equation (17):
when formula (14) is substituted into formula (18):
Further, according to the matrix inequality 2aTb≤aTFa+bTF-1b, where F ∈ Rn×nIs a positive definite matrix, defines
F＝P-1Equation (19) can be expressed as:
defining augmented state error vectors
Equation (20) can be expressed as:
in the formula: Λ ═ diag (Λ)1,Λ2,…,ΛM+1) Specifically, the following are shown:
further, when the diagonal matrix Λ is negative, i.e.:
each inequality in inequalities (23) is less than 0, then
When in use
According to the Lyapunov-Krasovski stability theorem, the time-lag closed-loop system (10) is consistent and asymptotically stable, namely
While obtaining an upper delay bound.
The specific embodiment is as follows:
according to the deduction, the vehicle multi-queue system meets the consistent progressive stability. And carrying out traffic scene simulation by utilizing PLEXE simulation software. And (3) experimental simulation setting: the vehicle multi-queue consists of 12 vehicles in total, and the number of the vehicles is 0-11. The number 0-3 is a first fleet, the first vehicle is a leader vehicle (number 0), and the first vehicle is also a leader vehicle of the whole vehicle multi-queue; no. 4-7 are second motorcades, and the fifth vehicle is a leader vehicle (number 4); no. 8-11 are third motorcades, and the ninth vehicle is a leader vehicle (No. 8). The vehicle multi-queue control parameters and traffic related parameters are set as shown in table 1.
TABLE 1 vehicle Multi-queue control parameters and traffic related parameter Table
Fig. 3(a) and 3(b) are graphs of the acceleration and speed, respectively, of the lead vehicle in an initialization scenario, from which it can be seen that the lead vehicle speed increases and then decreases, and then gradually reaches the desired speed of 25 m/s. Wherein the first leading vehicle is the leading vehicle of the whole multi-queue system, the speed of 25m/s is always kept to be driven in the fleet, and the acceleration of other leading vehicles is not more than 2.5m/s2And the speed change curve is smooth, so that the riding comfort of passengers is ensured. Fig. 3(c) is a vehicle spacing diagram of a leading vehicle in an initialization scenario, with no vehicles in front of the first leading vehicle, and therefore no vehicle spacing. Over time, the second and third leading cars gradually reached the desired separation within 30 s. In the whole process, a safe distance is kept between vehicles, rear-end collision of the vehicles is avoided, and safe driving of a motorcade is guaranteed.
To evaluate the stability of vehicles in the fleet in the multi-fleet, the stability in the fleet of the multi-fleet was analyzed, taking the vehicle in the third fleet in the multi-fleet as an example, vehicle number 8 was the leader vehicle of the third fleet. FIG. 4(a) is a graph of acceleration of all vehicles in a third fleet, where it can be seen that the acceleration of the entire fleet of vehicles does not vary by more than 3m/s2The vehicle No. 8 and the vehicle No. 9 reach a balanced state firstly, the fluctuation of the acceleration change curve of the vehicle No. 11 is large, and the vehicle No. 8 and the vehicle No. 9 reach the balanced state at the latest. This means that the further the following vehicle is from the lead vehicle, the slower the speed at which the equilibrium state is reached. Fig. 4(b) is a graph of all vehicle speeds for a third fleet. In the initialization scenario, the fleet vehicles start moving at a random speed, and the speed of the vehicles changes in the same trend, and gradually increases and then gradually decreases to the desired speed of 25 m/s. The vehicle number 11 reaches the expected speed at the latest, which shows that the communication between the vehicles has time delay, and the farther the vehicle is from the leader, the longer the time is for reaching the expected speed. Fig. 4(c) is a plot of the distance between all vehicles in the third fleet. As can be seen from the figure, the variation curve of the vehicle spacing in the fleet fluctuates greatly and gradually reaches the expected spacing within 40 s. In the whole process, the distance between the vehicles is always larger than the safety distance. This indicates that the vehicle fleet is stable, verifying the effectiveness of the control algorithm.
Claims (3)
1. A vehicle multi-queue cooperative control method is characterized by comprising the following steps:
step 1: constructing a vehicle multi-queue, wherein the vehicle multi-queue is composed of N vehicles, wherein
The number of the fleet is m +1, and the serial numbers are 0,1, …, m and NkIndicates the number of vehicles in the k-th fleet, the number of vehicles in the fleet being 0,1, …, Nk-1；
Step 2: in the vehicle multi-queue system, each fleet has a leader vehicle which is positioned at the head of the fleet, and the leader vehicle of the first fleet is the leader vehicle of the whole vehicle multi-queue;
and step 3: the vehicle in the vehicle multi-queue system obtains the position, speed and acceleration information of other vehicles in a vehicle-to-vehicle communication mode, and adjacent vehicle fleets can communicate with each other;
and 4, step 4: determining a longitudinal dynamics model of a vehicle in a vehicle multi-fleet system, represented as:
wherein x isi,k、vi,k、ai,kAnd ui,k(t) respectively representing the position, velocity, acceleration and control input of the ith vehicle within the kth fleet; t isi,kRepresenting the transmission coefficient of a longitudinal power system of an ith vehicle in the kth vehicle fleet; t represents time;
and 5: in the multi-fleet system, a constant spacing strategy is adopted among fleets, and the expected spacing between the fleets is SminRepresents; the vehicles in the fleet adopt a spacing strategy of constant head-time distance, and the minimum safety spacing between two adjacent vehicles in the fleet is sminRepresents;
obtaining the state information of the leading vehicle according to the step 1, the step 2 and the step 3, and calculating the expected distance d between the ith following vehicle and the leading vehicle of the own fleet in the kth fleeti0,k：
di0,k＝i(Lk+smin+hkv0) (2)
Wherein L iskIndicates the length of the vehicle in the k-th fleet, hkRepresenting constant time intervals, v, between vehicles in the kth fleet0Representing the speed of the multi-fleet leader vehicle;
and 6: the leader vehicle control targets of the vehicle multi-queue system are as follows:
wherein x is0,k、v0,kAnd a0,kRespectively representing the position, speed and acceleration of the leader vehicle of the k-th fleet,x0and a0Respectively representing the position and acceleration of the lead vehicle in the multi-train, LjIndicates the length of the vehicle in the jth fleet, hjRepresenting a constant time interval between vehicles in a jth fleet;
and 7: the control targets of the vehicles in the vehicle queue in the vehicle multi-queue system are as follows:
and step 8: the cooperative control method of the vehicles in the vehicle queue in the vehicle multi-queue system comprises the following steps:
wherein, aijRepresenting the vehicle adjacency matrix A in the k-th fleetkAn element of (1); alpha is alpha>0、β>0、γ>0、α1>0、α2>0 and alpha3>0 is the control gain; vi,kIndicating the desired speed of the ith vehicle in the kth fleet,
represents the average distance between two adjacent vehicles between the vehicle i and the vehicle j in the kth vehicle group, tau (t) represents the communication time delay of the vehicles in the queue, and xj,kAnd vj,kRespectively representing the position and speed of the jth vehicle in the kth vehicle fleet, dij,kRepresenting the desired separation between vehicle i and vehicle j within the kth fleet, dij,k＝di0,k-dj0,k；
The expected speed V of the ith vehicle in the kth vehicle fleeti,k(△xij(t)) is represented as:
wherein d isminAnd dmaxAre given two distances; v. ofmaxRepresenting a maximum speed of the vehicle train; when Δ xij(t) is less than dminWhen the desired speed of the vehicle is zero; when Δ xij(t) is greater than dmaxThen, the fleet vehicles travel at the maximum allowable speed;
and step 9: the cooperative control method for the kth leading vehicle for constructing the vehicle multi-queue system comprises the following steps:
wherein u is0,k(t) control input, x, for the kth fleet leader vehiclej,k-1Indicating the position of the jth vehicle of the kth-1 fleet, gamma1、γ2、γ3、γ4All represent control gains; tau isjRepresenting the communication delay of the jth vehicle and the kth leading vehicle in the kth-1 fleet in the multi-queue; v. of0(t-τj)τjRepresenting time delay taujCompensation for the resulting position error;
pj,k-1an adjacency matrix D representing the jth vehicle and the kth leading vehicle in the kth-1 fleet in the multi-queuekAn element of (1); v0,k(△x0k) Representing the desired speed function of the kth fleet leader vehicle,
step 10: and (4) carrying out stability derivation verification on the cooperative control method provided in the step (9) to obtain a system gradual stability constraint condition and a time delay upper bound.
2. The vehicle multi-queue cooperative control method according to claim 1, wherein h iskHas a value range of (0, 2)]，sminHas a value range of (0, 20)]，hjHas a value range of (0, 2)]，dminIs in the range of [10,20 ]]，dmaxIs in the range of [40,100 ]]。
3. The vehicle multi-queue cooperative control method according to claim 1, wherein the specific method for obtaining the system gradual stability constraint condition and the time delay upper bound is as follows:
step 10-1: defining a position error for a kth lead vehicle
Error in velocity
Error in acceleration
The following were used:
according to the formula (1), the formula (3) and the formula (7), the closed-loop dynamic model of the ith vehicle leading vehicle state error is expressed as:
wherein the content of the first and second substances,
representing the distance error of the jth vehicle of the kth-1 fleet from the fleet leader vehicle; delta x*＝hkv0+smin，
Defining the communication time delay of the ith fleet and the kth fleet as tauik(t) and define τq(t),q＝1,2,...,M(M＝m(m-1))，τq(t)∈{τik(t), i ═ 1, …, m; k 1, …, m, time delay tauq(t) is bounded, i.e.
0≤τq(t)≤τ*，τ*Is an upper bound of the time delay, and
and d isqLess than or equal to 1; the communication time delay of the vehicle is not considered;
definition of
And
the system formula (9) is expressed as:
wherein:
wherein:
Q＝diag(q1,q2,...,qk,...,qm)，
step 10-2: the derivation of equation (10) according to newton-lebeniz equation translates to:
wherein:
wherein:
step 10-3: according to the Lyapunov-Krasovski theorem, a Lyapunov function is constructed as follows:
wherein, P and SqIs a positive definite real symmetric matrix, i.e. P ═ PT>0 and
derivation is performed on both sides of the Lyapunov function in equation (17):
when formula (14) is substituted into formula (18):
leader vehicle node 0 is globally reachable across the entire multi-queue system, matrix in equation (14)
Is Hurwitz stable; according to Lyapunov's stability theory, define
Y is positive definite real symmetric matrix, Y ═ YT>0；
Step 10-4: the utilization conclusion is as follows: for an arbitrary vector a, b ∈ RnAnd an arbitrary positive definite matrix F ∈ Rn×nWith a matrix inequality 2aTb≤aTFa+bTF-1b is established; definition of
F＝P-1Equation (19) can be expressed as:
defining augmented state error vectors
Formula (20) is represented as:
wherein Λ ═ diag (Λ)1,Λ2,…,ΛM+1) Specifically, the following are shown:
step 10-5: when the diagonal matrix Λ is negative, i.e.:
each inequality in inequalities (23) is less than 0, then
When in use
According to the Lyapunov-Krasovski stability theorem, the time-lag closed-loop system (10) is consistent and asymptotically stable, namely
While obtaining an upper delay bound.
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