CN109656255A - Consider the vehicle platoon under communication topology time-varying with stability control method of speeding - Google Patents
Consider the vehicle platoon under communication topology time-varying with stability control method of speeding Download PDFInfo
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Abstract
The invention discloses the vehicle platoons under a kind of consideration communication topology time-varying with stability control method of speeding, this method comprises: step 1, establishes vehicle platoon with the mathematical model speeded；Step 2, the node power unit is described as node linear model；Step 3, the higher-dimension closed loop states equation for considering the vehicle platoon of communication topology time-varying with control system of speeding is established；Step 4, according to higher-dimension closed loop states equation, provide and consider the vehicle platoon of communication topology time-varying there are the adequate condition of stability controller to be: when average residence time is longer than lower bound, there are feasible solutions for the stability controller of vehicle platoon system；Step 5, using vehicle platoon, there are the adequate condition of stability controller, propose low-dimensional Riccati inequality, acquire controller gain.The present invention can guarantee that vehicle platoon is with the stability and robustness of the system of speeding under communication topology time-varying.
Description
Technical field
The present invention relates to intelligent driving technical fields, more particularly to the vehicle platoon under a kind of consideration communication topology time-varying
With stability control method of speeding.
Background technique
In recent years, being continuously increased with car ownership, automobile have also caused friendship while bringing convenience to the mankind
The problems such as logical safety, traffic congestion, energy crisis and environmental degradation.International research shows: in the driving process of expressway, if
It allows vehicle to be queued up traveling, then can change integrated air dynamical resistance with speeding spacing by shortening, be expected to improve and hand over
Through-current capacity reduces fuel consumption.
Everyday driver due to gender, age, physical condition and driving environment etc. difference, between speeding with speeding on
Away from usually it is different, cause path resource that cannot be fully utilized.Moreover, because the response delay of different drivers and being applied
The brake force added is different, when more vehicles continuously with speeding to form vehicle platoon when, the slight braking action of head vehicle is be easy to cause
The brake force of rear car is saturated, to threaten to traffic safety.Automatic Pilot is the effective way to solve the above problems, but existing
There is longitudinal direction to be based only upon front truck information such as ACC (self-adaption cruise system) with the system of speeding automatically and controlled, be cannot be considered in terms of whole
The safety of a vehicle platoon, it will usually cause the control intensity of queue tail vehicle excessive, influence safety and comfort.
The development of the emerging communication technology in recent years, such as DSRC (dedicated short-range communication technology), 5G, in order to solve the above problem
Provide new approaches.Bus or train route cooperative system is contacted member's vehicle of vehicle platoon using high bandwidth, the wireless communication of low delay
Form entirety, it can be with shared information, from vehicle controller on the basis of more member's vehicle information before and after synthesis between member's vehicle
Optimal control gain, thus realize with error of speeding fast convergence, further shorten on the basis of guaranteeing safety queue with
It speeds spacing, improves traffic efficiency, reduce fuel consumption.
But with the system of speeding, still there are many problem and defects based on the vehicle platoon of truck traffic.Vehicle platoon is travelling
It is needed in the process in face of complicated road conditions, wherein there are many disturbing factors, it is easy to cause signal of communication unstable, and vehicle
The phenomenon that queue constantly switches in and out during actual travel there may be member's vehicle, these all will lead to communication topology
Structure change.The performance of different communication topology is different, and the controller of vehicle platoon needs to guarantee system under different communication topology
Stability.
Summary of the invention
The purpose of the present invention is to provide the vehicle platoons under a kind of consideration communication topology time-varying with stability control side of speeding
Method overcomes or at least mitigates at least one of the drawbacks described above of the prior art.
To achieve the above object, the present invention provide it is a kind of consideration communication topology time-varying under vehicle platoon with stability control of speeding
Method processed, method includes the following steps:
Step 1, vehicle platoon includes N+1 member's vehicle, and N is the natural number greater than 1, establishes vehicle platoon with the mathematics speeded
Model: the mathematical model includes node power unit, geometry topological structure, Communication topology and distributed director, and one
Member's vehicle corresponds to a node, wherein the node power unit is according to the expectation acceleration a of inputdes, obtain
It is expected that accelerator open degree αdesOr desired braking pressure Pdes, control the quantity of state from vehicle；The geometry topological structure is each for determining
Longitudinal physics spacing between member's vehicle；The Communication topology is for the information exchange between each member's vehicle；
The distributed director is based on the Communication topology and uses static feedback control using the information of other member's vehicles
System, is obtained from the expectation acceleration a of vehicledes；
Step 2, in step 1 in the node power unit, by feedback linearization constructing tactics, non-linear lower layer is controlled
The node power unit is described as node linear model by gain processed；
Step 3, according to the specific Communication topology being likely to occur, the vehicle platoon for considering communication topology time-varying is established
With the higher-dimension closed loop states equation for control system of speeding；
Step 4, the higher-dimension closed loop states equation provided according to step 3, to there are vehicle platoon under communication topology time-varying into
Row mathematical modeling provides consider communication topology time-varying accordingly to calculate the average residence time lower bound during communication topology
There are the adequate condition of stability controller to be for vehicle platoon: when average residence time is longer than lower bound, the town of vehicle platoon system
Determining controller, there are feasible solutions；
Wherein, the value of ε can refer to following formula (21):
In formula (21), PHσ(t)Meet following formula (24), Hσ(t)For time-varying communication topology battle array, λ (PHσ(t)) it is matrix PHσ(t)'s
Characteristic value, max [λ (PHσ(t))] it is matrix PHσ(t)Characteristic value maximum value, min [λ (PHσ(t))] it is matrix PHσ(t)Characteristic value
Minimum value；
Wherein, the value of η can refer to following formula (22):
AP+PAT-μBBT+ η P < 0 (22)
In formula (22), P is the positive definite solution of formula (22), P > 0；μ meets following linear matrix inequality (23) and formula
(25):
In formula (23), λ1(Hσ(t)) be Communication topology characteristic value,For λ1(Hσ(t)) conjugate complex number；
In formula (25), λg(H) g-th of characteristic value for being communication topology battle array H,For λg(H) conjugate；
Step 5, using the vehicle platoon provided in step 4, there are the adequate condition of stability controller, propose low-dimensional
Riccati inequality constructs stability controller, controller gain is acquired, to control using the solution of the Riccati inequality
The static feedback control for stating distributed director guarantees vehicle platoon receiving with error of speeding with the system of speeding under communication topology time-varying
It holds back.
Further, in step 3, " higher-dimension closed loop states equation " is described as formula (7):
In formula (7),, absolutely with error of speeding as the total quantity of state of the vehicle platoon of element, to be defined as following using member's vehicle
Formula (9)；For the first derivative to the time；INFor N-dimensional unit matrix；A is the state square of the node linear model of i-th vehicle
Battle array；B is the input matrix of the node linear model of i-th vehicle；For Kronecker product；Hσ(t)For time-varying communication topology battle array,
It is expressed as formula (8):
Hσ(t)=Lσ(t)+Rσ(t) (8)
In formula (8), Lσ(t)For Laplce's battle array of time-varying, Rσ(t)For the traction matrix of time-varying；
In formula (9),ForTransposition,For the absolute with error of speeding of i-th vehicle, quantity of state is expressed as formula (10):
In formula (10), xiFor the node linear model state amount of i-th vehicle, x0For the node linear model state amount of head vehicle,
Di,0For i-th vehicle vehicle to the end expectation with spacing of speeding.
Further, " the low-dimensional Riccati inequality " in step 5 is expressed as following formula (26), is solved by formula (26)
Object is positive definite matrix P:
AP+PAT-μBBT< 0 (26)
In formula (26), A is vehicle platoon node linear model state matrix；ATFor the transposition of A；B is vehicle platoon node
Linear model input matrix；BTFor the transposition of B；P is the solution of Riccati inequality, P > 0；
According to the P that formula (26) acquires, (27) seek stability controller gain K as the following formula:
Further, " to there are vehicle platoons under communication topology time-varying to carry out mathematical modeling " in step 4 includes:
Firstly, time shaft is divided into continuous time series such as following formula (11) to formula (13):
0 < tk-tk-1≤Tup (12)
t0=0 (13)
Formula (11) is into formula (13), tkFor the k moment；tk-1For the k-1 moment；t0For initial time；K is oneself more than or equal to 1
So number；N is nature manifold；TupFor the upper limit of a time interval length, TupFor the constant greater than 0；
Then, by time interval [tk-1, tk) it is divided into finite continuous, nonoverlapping timeslice, so that each timeslice
In communication topology there is no variation, be expressed as following formula (14) to formula (18):
mk> 0 (18)
Formula (14) into formula (18),For time interval [tk-1, tk) in the l-1 moment；For time interval
[tk-1, tk) in first of moment；For time interval [tk-1, tk) initial time, with tk-1It is of equal value；For time zone
Between [tk-1, tk) end of time, with tkIt is of equal value；L is time interval [tk-1, tk) in first of moment；mkFor time interval
[tk-1, tk) in mkAt a moment, also correspond to time interval；N is to be divided into mkPart, that is, it is divided into mkA timeslice；
TlowIndicate the lower limit of a time leaf length, TlowIt, can be random according to preset time interval length for the constant greater than 0
Value；
Finally, enabling time interval [ti, tj), communication topology number of transitions is N in 0≤i≤jσ(ti, tj), then average residence
Time π is defined as formula (19):
Further, in step 5, the expectation acceleration u of i-th vehicleiIt is represented by formula (6):
In formula (6), lijFor the i-th row, the jth column element in Laplce's battle array L；riFor adjacency matrix；Di,jFor i-th vehicle
The desired state difference between jth vehicle；K is controller gain, K=[k1 k2 k3]；Di,0For the interphase of i-th Che Yutou vehicle
The state difference of prestige；xjFor the quantity of state of jth vehicle；xiFor the quantity of state of i-th vehicle；x0For the quantity of state of head vehicle.
Further, in the step 1 " distributed director is based on the Communication topology, and utilization is other
The information of member's vehicle, is controlled using static feedback, is obtained from the expectation acceleration a of vehicledes" include the following steps:
In the step 1 " distributed director be based on the Communication topology, utilize other member's vehicles
Information, controlled using static feedback, be obtained from the expectation acceleration a of vehicledes" include the following steps:
Step 11, the quantity of state sought in i-th vehicle and received vehicle platoon between other member's vehicles is poor, the shape
State amount difference includes that the poor lengthwise position between i-th vehicle and other member's vehicles, longitudinal velocity difference and longitudinal acceleration are poor；
Step 12, i-th vehicle of step 11 acquisition and the sum of the quantity of state difference of other member's vehicles are sought, the quantity of state difference
And including the sum of the sum of lengthwise position difference between i-th vehicle and other member's vehicles, longitudinal velocity difference, longitudinal acceleration difference
With；
Step 13, the sum of the sum of the sum of lengthwise position difference step 12 obtained, longitudinal velocity difference, longitudinal acceleration difference point
Not multiplied by the position feedback coefficient k of corresponding i-th vehicle1, velocity feedback coefficient k2, accelerator feedback coefficient k3, step 5
In controller gain correspond to static feedback COEFFICIENT K={ k1, k2, k3}；
Step 14, the quantity of state obtained to step 13 is summed, the phase as distributed director output
Hope acceleration ades；
Wherein, i indicate member's vehicle number, i=0,1,2 ... N.
Further, " non-linear lower layer controls gain by feedback linearization constructing tactics " in the step 2 is specific
Include:
As the expectation acceleration adesWhen >=0, output:
As the expectation acceleration adesWhen < 0, output:
In formula (1) and formula (2), TedesTo guarantee that vehicle reaches desired acceleration adesRequired engine it is expected torque,
TbdesTo guarantee that vehicle reaches desired acceleration adesRequired wheel side desired braking torque, rwFor vehicle wheel roll radius, m is vehicle
Quality, CAFor vehicle air resistance coefficient, v is car speed, τeFor engine response time lag,It is car speed to the derivative of time,
G is acceleration of gravity, and f is wheel rolling frictional resistance, ηTFor vehicle drive system mechanical efficiency, i0For vehicle main retarder speed ratio, ig
For transmission gear ratio, M1P-1() indicates that engine is schemed against M1P, τbTime lag, K are responded for electric controlled brake systembFor vehicle wheel
Side brake gain coefficient.
Further, " the node power unit is described as node linear model " in the step 2 specifically includes:
Firstly, according to formula (1) and formula (2) and τe≈τb, by the actual acceleration a of i-th vehicleiWith desired acceleration ades
Between relationship description be formula (3):
Wherein, τ=τeFor system time lags, s is Laplace operator；
Then, the quantity of state for taking i-th vehicle includes practical lengthwise position pi, practical longitudinal velocity vi, practical longitudinal acceleration
ai, it is expected acceleration adesFor input quantity, then obtaining " node linear model " is formula (4):
In formula (4), xiFor the quantity of state of the node linear model of i-th vehicle, A is the node linear model of i-th vehicle
State matrix, B are the input matrix of the node linear model of i-th vehicle, and κ indicates the time constant of inertial delay, and the τ of κ=1/；
ui=ades。
The present invention has the advantage that the 1, present invention uses " bus or train route collaboration " thought, leads to due to taking above technical scheme
Cross automatically control vehicle platoon with speeding on to alleviate the operating burden of driver, avoiding may be caused by driving fatigue
Security risk.2, present invention introduces the communication information, status information interaction is carried out by Communication topology between queue member vehicle,
The integral power characteristic for improving vehicle platoon makes with error more rapid convergence of speeding, so as to smaller using driving than the mankind
With spacing of speeding, queue entirety windage is reduced, reduces energy consumption, improves traffic efficiency.3, the present invention caused by communication shakiness to because leading to
Believe that topological time-varying carries out mathematical modeling, gives adequate condition existing for stability controller, facilitate in engineering practice and communication is disturbed
The stability of dynamic lower vehicle queue system is analyzed.Promote the robustness that vehicle platoon disturbs communication in engineering practice.4,
The present invention furthermore present communication disturbance it is lower can line control unit method for solving, solve calculation amount and advised independently of vehicle platoon
Mould, feasible zone is larger, facilitates and seeks stability controller in engineering practice according to the actual situation.
Detailed description of the invention
Fig. 1 is the provided vehicle platoon considered under communication topology time-varying of the embodiment of the present invention with stability control system of speeding
The structural schematic diagram of system；
Fig. 2 is the structural schematic diagram of the node power unit in vehicle platoon stabilitrak shown in FIG. 1；
Fig. 3 is the flow chart for the method for analyzing stability that the present invention considers under communication topology time-varying；
Fig. 4 is the flow chart of controller design method of the present invention.
Specific embodiment
In the accompanying drawings, same or similar element is indicated using same or similar label or there is same or like function
Element.The embodiment of the present invention is described in detail with reference to the accompanying drawing.
As shown in Figure 1, the vehicle platoon under consideration communication topology time-varying provided by the present embodiment is with stability control of speeding
Method the following steps are included:
Step 1, vehicle platoon includes N+1 member's vehicle, and N is the natural number greater than 1, establishes vehicle platoon with the mathematics speeded
Model: the mathematical model includes node power unit 1, geometry topological structure 2, Communication topology 3 and distributed director
4, in vehicle platoon, member's vehicle corresponds to a node.Wherein, the node power unit 1 is according to phase of input
Hope acceleration ades, obtain expectation accelerator open degree αdesOr desired braking pressure Pdes, control the quantity of state from vehicle.The geometry is opened up
Structure 2 is flutterred for determining longitudinal physics spacing between each member's vehicle.Communication topology 3 for each member's vehicle it
Between information exchange.Distributed director 4 is based on Communication topology 3 and uses static state using the information of other member's vehicles
Feedback control is obtained from the expectation acceleration a of vehicledes." time-varying ", which refers to, to be changed over time, i.e., in the allowed band of setting, uses
Number of vehicles to indicate in vehicle platoon may change over time this case.
Step 2, in step 1 in node power unit 1, increased by the non-linear lower layer's control of feedback linearization constructing tactics
Node power unit 1 is described as node linear model by benefit.
Step 3, according to the specific Communication topology 3 being likely to occur, the vehicle team for considering communication topology time-varying is established
Arrange the higher-dimension closed loop states equation with control system of speeding.
Step 4, the higher-dimension closed loop states equation provided according to step 3, calculate communication topology during average residence when
Between lower bound, provide accordingly and consider the vehicle platoon of communication topology time-varying there are the adequate condition of stability controller to be: when averagely staying
When the time being stayed to be longer than lower bound, there are feasible solutions for the stability controller of vehicle platoon system.
Step 5, using the vehicle platoon provided in step 4, there are the adequate condition of stability controller, propose low-dimensional
Riccati inequality constructs stability controller, controller gain is acquired, to control using the solution of the Riccati inequality
The static feedback control for stating distributed director guarantees vehicle platoon receiving with error of speeding with the system of speeding under communication topology time-varying
It holds back.
In the step 5, Riccati inequality is provided in the form of linear matrix inequality, and has low dimensional characteristic,
That is, the dimension of MATRIX INEQUALITIES is equal with the dimension of father of node linear kinetic model, and with member's vehicle in vehicle platoon
Quantity is unrelated.And influence of the Communication topology 3 to vehicle platoon stability of control system passes through topological coefficient (scalar) and controls
In Riccati inequality.
The present embodiment be for have the probabilistic vehicle platoon of kinetic parameter, its stability that gives one's hand it is abundant
Condition, and provide corresponding stability controller method for solving, with guarantee vehicle platoon with error fast convergence at any time of speeding, thus
Reduce vehicle platoon with spacing of speeding, increase the magnitude of traffic flow, reduce energy consumption.
As shown in Figure 1, application scenarios of the invention are longitudinal " vehicle platoon " with speeding, in the present embodiment of vehicle platoon
Refer to that more vehicles composed by the automatic catch passenger car to be differed greatly as kinetic characteristics are longitudinal with the system of speeding, specifically includes 1 head
Vehicle and the N vehicle with speeding at head vehicle rear amount to N+1 member's vehicle.Each member's vehicle all has automatic Pilot ability, vehicle
Queue only carries out automatically controlling the longitudinal dynamics behavior of each member's vehicle in vehicle platoon with the control system speeded, not at
The horizontal dynamic behavior of member's vehicle is controlled, and driver no longer carries out braking and the operation of throttle, it is only necessary to operation side
To disk.For convenience, the number of head vehicle is set as 0, the N number with speeding in the vehicle at head vehicle rear by the present embodiment
Successively be set as 1,2 ... N, N are the natural number greater than 1.I in text indicates that number is member's vehicle of i, referred to as " i-th
Vehicle ".I, j, k in text indicate the number of member's vehicle, i=0,1,2 ... N, j=0,1,2 ... N, k=0,1,2 ...
N, such as: " i-th vehicle ", " jth vehicle ", " kth vehicle ".The quantity of state of i-th vehicle (node i) includes: lengthwise position pi, it is vertical
To speed viWith longitudinal acceleration ai.Similarly, (quantity of state of node j) includes: lengthwise position p to jth vehiclej, longitudinal velocity vj
With longitudinal acceleration aj.(quantity of state of node k) includes: lengthwise position p to kth vehiclek, longitudinal velocity vkWith longitudinal acceleration ak。
All member's vehicles in vehicle platoon are constituted vehicle platoon longitudinal direction with control system of speeding by the present embodiment.Pass through addition
Feedback control, vehicle platoon longitudinal direction provided in this embodiment include node power unit 1, geometry topological structure with control system of speeding
2, Communication topology 3 and distributed director 4, in which: node power unit 1 and distributed director 4 have collectively constituted vehicle
Longitudinal system, longitudinal direction of car dynamical system determine state change behavior of vehicle during with speeding.
Node power unit 1 reacts longitudinal lower layer's dynamic behavior of vehicle, determines that vehicle underlying system receives upper layer
Generated response characteristic after expectation acceleration given by system.The node power unit 1 includes 11 He of lower layer's controller
Lower layer's power plant module 12, in which: lower layer's controller 11 receives the expectation acceleration provided from the distributed director 4
ades, seek specifically it is expected accelerator open degree α by nonlinear algorithmdesOr desired braking pressure Pdes(synchronization, αdesWith
PdesIn only one non-zero).Lower layer's power plant module 12 controls the bottom kinetic characteristics of vehicle itself, lower layer's controller
11 for providing desired accelerator open degree α to lower layer's power plant module 12desOr desired braking pressure Pdes, actually refer to holding for vehicle
Row device (E-Gas and electric controlled brake system) responds desired amount αdesAnd Pdes.The output quantity of lower layer's power plant module 12 is
It include practical lengthwise position p, longitudinal velocity v and longitudinal acceleration a, such as i-th vehicle from the quantity of state of vehicle from the quantity of state of vehicle
Quantity of state include practical lengthwise position pi, longitudinal velocity viWith longitudinal acceleration ai。
Geometry topological structure 2 is the space geometry configuration of vehicle platoon, for determining between longitudinal physics between member's vehicle
Away from.The present embodiment is using constant distance with strategy of speeding, that is, the expectation spacing d between i-th vehicle and jth vehicleijFor constant.
Node refers to the member of composition vehicle platoon, and from the perspective of communication topology, member's vehicle is geometry topological structure 2
In a node.
Communication topology 3 is the information flow network structure of vehicle platoon, is used between member's vehicle in vehicle platoon
Information exchange.In the present embodiment, Communication topology 3 is limited to symmetrical structure, that is to say, that the communication between member's vehicle is adopted
With two-way communication, when i-th vehicle is received from the communication information of jth vehicle, jth vehicle is also received from i-th simultaneously
The communication information of vehicle.It should be understood that head vehicle only sends information, information is not received.Communication information packet between member's vehicle
The quantity of state of vehicle is included, such as: the communication information from i-th vehicle to jth vehicle only includes the quantity of state of i-th vehicle, from jth
The communication information of vehicle to i-th vehicle only includes the quantity of state of jth vehicle.
Distributed director 4 is the top level control algorithm of vehicle, is based on the Communication topology 3, utilizes vehicle team
The information of other member's vehicles, is controlled using static feedback in column, calculates the expectation acceleration a from vehicledes.It is with i-th vehicle below
Example illustrates that " distributed director is based on the Communication topology, and using the information of other member's vehicles, use is quiet
State feedback control is obtained from the expectation acceleration a of vehicledes" specific method, following step 11 to step 14.
Step 11, its in vehicle platoon that Communication topology 3 receives is passed through with it to the quantity of state of i-th vehicle
Quantity of state between its member's vehicle is poor, the quantity of state difference include the lengthwise position between i-th vehicle and other member's vehicles it is poor, i-th
Longitudinal velocity difference between vehicle and other member's vehicles and the longitudinal acceleration between i-th vehicle and other member's vehicles are poor.Such as:
The quantity of state of i-th vehicle amount corresponding with the quantity of state of jth vehicle carries out seeking respectively the shape of difference, i-th vehicle obtained
State amount and the quantity of state difference of jth vehicle can indicate are as follows: lengthwise position difference pi-pj, longitudinal velocity difference vi-vj, longitudinal acceleration is poor
ai-aj。
Step 12, the quantity of state of i-th vehicle of step 11 acquisition and the sum of the quantity of state difference of other member's vehicles, the shape are sought
The sum of state amount difference includes between the sum of lengthwise position difference between i-th vehicle and other member's vehicles, i-th vehicle and other member's vehicles
The sum of longitudinal velocity difference, the sum of the longitudinal acceleration difference between i-th vehicle and other member's vehicles.
Step 13, by the sum of lengthwise position difference between i-th vehicle and other member's vehicles, i-th vehicle and other member's vehicles
Between the sum of longitudinal velocity difference, the sum of longitudinal acceleration difference between i-th vehicle and other member's vehicles is respectively multiplied by respectively right
The position feedback coefficient k for i-th vehicle answered1, velocity feedback coefficient k2, accelerator feedback coefficient k3, the controller in step 5 increases
Benefit corresponds to static feedback COEFFICIENT K={ k1, k2, k3}.Such as: the data that step 13 obtains include: i-th that step 12 obtains
The sum of lengthwise position difference between vehicle and other member's vehicles and position feedback coefficient k1Product, step 12 obtain i-th vehicle
The sum of longitudinal velocity difference between other member's vehicles and velocity feedback coefficient k2Product, step 12 obtain i-th vehicle with
The sum of longitudinal acceleration difference between other member's vehicles and accelerator feedback coefficient k3Product.
Step 14, the quantity of state obtained to step 13 is summed, the expectation acceleration exported as distributed director 4
ades, the as expectation acceleration a that is given to node power unit 1 of distributed director 4des。
In one embodiment, " being increased by the non-linear lower layer's control of feedback linearization constructing tactics in the step 2
Benefit " specifically includes:
As the expectation acceleration adesWhen >=0, output:
As the expectation acceleration adesWhen < 0, output:
In formula (1) and formula (2), TedesTo guarantee that vehicle reaches desired acceleration adesRequired engine it is expected torque,
TbdesTo guarantee that vehicle reaches desired acceleration adesRequired wheel side desired braking torque, rwFor vehicle wheel roll radius, m is vehicle
Quality, CAFor vehicle air resistance coefficient, v is car speed, τeFor engine response time lag,It is car speed to the derivative of time,
G is acceleration of gravity, and f is wheel rolling frictional resistance, ηTFor vehicle drive system mechanical efficiency, i0For vehicle main retarder speed ratio, ig
For transmission gear ratio, M1P-1() indicates that engine is schemed against M1P, τbTime lag, K are responded for electric controlled brake systembFor vehicle wheel
Side brake gain coefficient.
As shown in Fig. 2, node power unit 1 is according to desired acceleration ades, node power unit 1 seeks required for vehicle
Accelerator open degree αdesOr brake pressure Pdes, and control the driving status of vehicle.Specifically, node power unit 1 includes lower layer
Controller 11 and lower layer's power plant module 12, wherein lower layer's controller 11 receives the expectation acceleration that distributed director 4 exports
ades, and according to desired acceleration ades, seek accelerator open degree α required for vehicledesOr brake pressure Pdes.Lower layer's power plant module
The driving status of 12 control vehicles.In conjunction with the block schematic illustration that Fig. 2 is provided, pass through following step 21 to step 27, Ke Yishi
" by feedback linearization constructing tactics, non-linear lower layer controls gain " in the existing step 2.
Step 21, it sets lower layer's controller 11 to include switch logic module, engine expectation torque calculation mould
Block, wheel side desired braking Calculating Torque during Rotary module, engine inversion model and braking inversion model.
Step 22, the switch logic module receives the expectation acceleration a that the distributed director 4 exportsdes, and will
It is expected that acceleration adesIt is compared with 0.In desired acceleration adesIn the case of 0, it would be desirable to acceleration adesInput
Torque calculation module it is expected to engine.In desired acceleration adesIn the case of 0, it would be desirable to acceleration adesIt is input to wheel
Side desired braking Calculating Torque during Rotary module.
Step 23, the engine expectation torque calculation module receives the expectation acceleration a of inputdes, and added according to expectation
Speed ades, it is calculated as guaranteeing that vehicle reaches desired acceleration a using pre-set formula (1)desRequired engine expectation turns
Square Tedes, formula (1) expression are as follows:
Step 24, the wheel side desired braking Calculating Torque during Rotary module receives the expectation acceleration a of inputdes, and according to expectation
Acceleration ades, it is calculated as guaranteeing that vehicle reaches desired acceleration a using pre-set formula (2)desIt is expected system in required wheel side
Kinetic moment Tbdes, formula (2) expression are as follows:
In formula (1) and formula (2), TedesTo guarantee that vehicle reaches desired acceleration adesRequired engine it is expected torque,
TbdesTo guarantee that vehicle reaches desired acceleration adesRequired wheel side desired braking torque, rwFor vehicle wheel roll radius, m is vehicle
Quality, CAFor vehicle air resistance coefficient, v is car speed, τeFor engine response time lag,It is car speed to the derivative of time,
G is acceleration of gravity, and f is wheel rolling frictional resistance, ηTFor vehicle drive system mechanical efficiency, i0For vehicle main retarder speed ratio, ig
For transmission gear ratio, M1P-1() indicates that engine is schemed against M1P, τbTime lag, K are responded for electric controlled brake systembFor vehicle wheel
Side brake gain coefficient.
Step 25, the guarantee vehicle that the engine inversion model receives the engine expectation torque calculation module input reaches
To desired acceleration adesRequired engine it is expected torque Tedes, and according to Tedes, using formula (1), obtain to guarantee engine
It is expected that the expectation accelerator open degree α needed for torquedes。
Step 26, the guarantee vehicle that the braking inversion model receives the wheel side desired braking Calculating Torque during Rotary module input reaches
To desired acceleration adesRequired wheel side desired braking torque Tbdes, and according to Tbdes, using formula (2), obtain to guarantee to take turns side
The desired braking pressure P needed for desired braking torquedes。
Step 27, lower layer's power plant module includes engine, automatic transmission, electric controlled brake system and vehicle body, is started
Machine output torque is expressed as Te, gearbox output torque is expressed as Td, transmission output speed is expressed as ωw, engine output
Shaft counter is shown as ωe, wheel braking moment is expressed as Tb.Lower layer's power plant module is defeated for receiving lower layer's controller
Accelerator open degree α outdesOr brake pressure Pdes.Accelerator open degree α is received in lower layer's power plant moduledesIn the case of, throttle
Aperture αdesFor the input quantity of automatic transmission.Brake pressure P is received in lower layer's power plant moduledesIn the case of, braking
Pressure PdesFor the input quantity of electric controlled brake system.Automatic transmission and electric controlled brake system when receiving corresponding input quantity,
The corresponding quantity of state for changing vehicle body.It is identical that this directly steps on the gas or step on the effect of braking with driver, only adopts in the present embodiment
With automatic control, gone to execute throttle and brake operating automatically by actuator.
In one embodiment, " non-linear lower layer controls gain by feedback linearization constructing tactics " tool in step 2
Body further include:
Step 28, lower layer's controller 11 further includes PI controller, and PI controller is arranged in the switch logic module
Between the distributed director 4 and receive vehicle body quantity of state.By PI controller, the actual acceleration of vehicle is detected
A is responded, and actual acceleration is responded into a and desired acceleration adesIt is compared, to compensate unmodeled uncertainty, so that vehicle
The longitudinal static error with control system of speeding of queue is zero.
In one embodiment, " the node power unit is described as node linear model " tool in the step 2
Body includes:
Firstly, controlling gain according to the non-linear lower layer that formula (1) and formula (2) indicate, in general there is τe≈τb, by i-th
The actual acceleration a of vehicleiWith desired acceleration adesBetween relationship description be formula (3):
Wherein, τ=τeFor system time lags, s is Laplace operator；
Then, the quantity of state for taking i-th vehicle includes practical lengthwise position pi, practical longitudinal velocity vi, practical longitudinal acceleration
ai, it is expected acceleration adesFor input quantity, obtaining " node linear model " is that formula (4) pass through such as the entire node of following formula (4) description
The dynamic behavior of power unit 1:
In formula (4), xiFor the quantity of state of the node linear model of i-th vehicle, A is the node linear model of i-th vehicle
State matrix, B are the input matrix of the node linear model of i-th vehicle, and κ indicates the time constant of inertial delay, and the τ of κ=1/；
ui=ades。
The present embodiment only considers vehicle platoon, so for all member's vehicles in vehicle platoon, state matrix A and
Input matrix B corresponds to identical.
In one embodiment, " the higher-dimension closed loop states equation " that step 3 is established considers communication topology time-varying problem.
The information exchange relationship digraph description carried out by wireless communication between member's vehicle in vehicle platoon, then obtains letter
Cease the mathematical description of interactive relation, i.e. communication topology Laplce battle array L (abbreviation Laplce battle array).As described in front of asking, this implementation
Static state-feedback, including position feedback coefficient k are used in example1, velocity feedback coefficient k2, accelerator feedback coefficient k3.This implementation
The vehicle platoon of example is with the target for control of speeding: desired geometry topological structure 2 is maintained, and all vehicle platoons
Member's vehicle speed reaches unanimity with head vehicle, that is, has formula (5):
In formula (5), di,i+1It indicates the expectation spacing between i-th vehicle and i+1 vehicle, is constant.
The expectation acceleration u of i-th vehicleiIt is represented by formula (6):
In formula (6), lijFor the i-th row, the jth column element in Laplce's battle array L, the i.e. adjoint matrix of Laplce's battle array L
I-th of main diagonal element；riFor adjacency matrix, i.e. i-th of main diagonal element of the adjoint matrix of Laplce's battle array L；Di,jIt is i-th
Desired state difference between vehicle and jth vehicle, ideally, velocity and acceleration is all identical, then consider between two vehicles away from
From the distance between adjacent two vehicle is fixed, i.e. di,i-1=const, i=1 ..., N, di,jIndicate i-th vehicle and jth vehicle it
Between expectation spacing, therefore, " state difference " refers to the distance between i-th vehicle and jth vehicle, i.e. Di,j=[di,j 0 0]T；
K is controller gain, K=[k1 k2 k3]；Di,0The desired state difference between i-th Che Yutou vehicle, " state difference " refer to
The distance between i-th Che Yutou vehicle, i.e. Di,0=[di,0 0 0]T, di,0For the expectation spacing between i-th Che Yutou vehicle；xj
For the quantity of state of jth vehicle；xiFor the quantity of state of i-th vehicle；x0For the quantity of state of head vehicle.
In one embodiment, " consider the vehicle platoon of communication topology time-varying with control system of speeding in the step 3
Higher-dimension closed loop states equation " can be described as formula (7):
In formula (7),, absolutely with error of speeding as the total quantity of state of the vehicle platoon of element, to be defined as following using member's vehicle
Formula (9)；For the first derivative to the time；INFor N-dimensional unit matrix；A is the state square of the node linear model of i-th vehicle
Battle array；B is the input matrix of the node linear model of i-th vehicle；For Kronecker product；Hσ(t)For time-varying communication topology battle array,
It is expressed as formula (8):
Hσ(t)=Lσ(t)+Rσ(t) (8)
In formula (8), Lσ(t)For Laplce's battle array of time-varying, Rσ(t)For the traction matrix of time-varying.
It is defined as follows:
In formula (9),ForTransposition,For the absolute with error of speeding of i-th vehicle, quantity of state is expressed as formula (10):
In formula (10), xiFor the node linear model state amount of i-th vehicle, x0For the node linear model state amount of head vehicle,
Di,0For i-th vehicle vehicle to the end expectation with spacing of speeding.
For convenience of stability analysis, below to there are vehicle platoons under communication topology time-varying to carry out mathematical modeling, the modeling
Method specifically includes:
Firstly, time shaft is divided into continuous time series such as following formula (11) to formula (13):
0 < tk-tk-1≤Tup (12)
t0=0 (13)
Formula (11) is into formula (13), tkFor the k moment；tk-1For the k-1 moment；t0For initial time；K is oneself more than or equal to 1
So number；N is nature manifold；TupFor the upper limit of a time interval length, TupIt, can be according to preset for the constant greater than 0
Time interval length random value.
Then, by time interval [tk-1, tk) it is divided into finite continuous, nonoverlapping timeslice, so that each timeslice
In communication topology there is no variation, that is to say, that in a timeslice 0 to N member's vehicle it is constant, be expressed as following formula
(14) to formula (18):
Formula (14) into formula (18),For time interval [tk-1, tk) in the l-1 moment；For time interval
[tk-1, tk) in first of moment；For time interval [tk-1, tk) initial time, with tk-1It is of equal value；For time zone
Between [tk-1, tk) end of time, with tkIt is of equal value；L is time interval [tk-1, tk) in first of moment；mkFor time interval
[tk-1, tk) in mkAt a moment, also correspond to time interval；N is to be divided into mkPart, that is, it is divided into mkA timeslice；
TlowIndicate the lower limit of a time leaf length, TlowIt, can be random according to preset time interval length for the constant greater than 0
Value.
Finally, enabling time interval [ti, tj), communication topology number of transitions is N in 0≤i≤jσ(ti, tj), then average residence
Time π is defined as formula (19):
According to the mathematical modeling of the vehicle platoon of the communication topology of above-mentioned foundation variation, under communication topology variation, that is,
It says, when 0 in Communication topology 3 to N member's vehicle changes, there are controllers to make stable abundant of vehicle platoon system
Condition is: average residence time π is longer than given average residence time lower boundIt is expressed as following formula (20):
In formula (20), ε is obtained with reference to formula (21):
In formula (21), PHσ(t)It is the positive definite solution of communication topology battle array Lyapunov equation, Hσ(t)It is opened up for time-varying communication
Flutter battle array, λ (PHσ(t)) it is matrix PHσ(t)Characteristic value, max [λ (PHσ(t))] it is matrix PHσ(t)Characteristic value maximum value, min [λ
(PHσ(t))] it is matrix PHσ(t)Characteristic value minimum value.
η is obtained with reference to formula (22):
AP+PAT-μBBT+ η P < 0 (22)
In formula (22), P is the positive definite solution of formula (22), and P meets: P > 0；μ meets following linear matrix inequality
(23):
In formula (23), λ1(Hσ(t)) be Communication topology 3 characteristic value,For λ1(Hσ(t)) conjugate complex
Number.
P in formula (21)Hσ(t)Meet following formula (24):
μ is obtained with reference to formula (25):
In formula (25), λg(H) g-th of characteristic value for being communication topology battle array H,For λg(H) conjugate.
In one embodiment, " the low-dimensional Riccati inequality " in step 5 is expressed as formula (26), is asked by formula (26)
Solution object is positive definite matrix P:
AP+PAT-μBBT< 0 (26)
In formula (26), A is vehicle platoon node linear model state matrix；ATFor the transposition of A；B is vehicle platoon node
Linear model input matrix；BTFor the transposition of B；Positive definite matrix P is the symmetric positive definite transformation matrix or Li Kadi of Lyapunov theorem
The positive definite solution of equation, P > 0.
μ is chosen according to range, to solve the solution positive definite matrix P of low-dimensional Riccati inequality.
According to the P that formula (26) acquires, (27) seek controller gain K as the following formula:
The controller gain that above formula is found out substitutes into vehicle platoon shown in Fig. 1 in the distributed director for the system of speeding,
It can guarantee that vehicle platoon allows vehicle platoon to keep in driving process of speeding with the stability for the system of speeding under time-varying communication topology
Desired geometric configuration.
Finally it is noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations.This
The those of ordinary skill in field is it is understood that be possible to modify the technical solutions described in the foregoing embodiments or right
Part of technical characteristic is equivalently replaced；These are modified or replaceed, and it does not separate the essence of the corresponding technical solution originally
Invent the spirit and scope of each embodiment technical solution.
Claims (8)
1. a kind of vehicle platoon considered under communication topology time-varying is with stability control method of speeding, which is characterized in that including following
Step:
Step 1, vehicle platoon includes N+1 member's vehicle, and N is the natural number greater than 1, establishes vehicle platoon with the mathematical modulo speeded
Type: the mathematical model includes node power unit, geometry topological structure, Communication topology and distributed director, and one
Member's vehicle corresponds to a node, wherein the node power unit is according to the expectation acceleration a of inputdes, obtain the phase
Hope accelerator open degree αdesOr desired braking pressure Pdes, control the quantity of state from vehicle；The geometry topological structure is for determining each institute
State longitudinal physics spacing between member's vehicle；The Communication topology is for the information exchange between each member's vehicle；Institute
Distributed director is stated to control using the information of other member's vehicles using static feedback based on the Communication topology,
It is obtained from the expectation acceleration a of vehicledes；
Step 2, in step 1 in the node power unit, increased by the non-linear lower layer's control of feedback linearization constructing tactics
The node power unit is described as node linear model by benefit；
Step 3, according to the specific Communication topology being likely to occur, the vehicle platoon for considering communication topology time-varying is established with speeding
The higher-dimension closed loop states equation of control system；
Step 4, the higher-dimension closed loop states equation provided according to step 3, to there are vehicle platoons under communication topology time-varying to count
Modeling is learned, to calculate the average residence time lower bound during communication topologyThe vehicle for considering communication topology time-varying is provided accordingly
There are the adequate condition of stability controller to be for queue: when average residence time is longer than the average residence time lower boundWhen,
There are feasible solutions for the stability controller of vehicle platoon system；
Wherein, the value of ε can refer to following formula (21):
In formula (21), PHσ(t)Meet following formula (24), Hσ(t)For time-varying communication topology battle array, λ (PHσ(t)) it is matrix PHσ(t)Feature
Value, max [λ (PHσ(t))] it is matrix PHσ(t)Characteristic value maximum value, min [λ (PHσ(t))] it is matrix PHσ(t)Characteristic value most
Small value；
Wherein, the value of η can refer to following formula (22):
AP+PAT-μBBT+ η P < 0 (22)
In formula (22), P is the positive definite solution of formula (22), P >；μ meets following linear matrix inequality (23) and formula (25):
In formula (23), λ1(Hσ(t)) be Communication topology characteristic value,For λ1(Hσ(t)) conjugate complex number；
In formula (25), λg(H) g-th of characteristic value for being communication topology battle array H,For λg(H) conjugate；
Step 5, using the vehicle platoon provided in step 4, there are the adequate condition of stability controller, propose low-dimensional Riccati not
Equation constructs stability controller, acquires controller gain using the solution of the Riccati inequality, to control the distributed control
The static feedback of device processed controls, and vehicle platoon is with the system of speeding with error convergence of speeding under guarantee communication topology time-varying.
2. considering the vehicle platoon under communication topology time-varying with stability control method of speeding, feature as described in claim 1
It is, in step 3, " higher-dimension closed loop states equation " is described as formula (7):
In formula (7),, absolutely with error of speeding as the total quantity of state of the vehicle platoon of element, to be defined as following formula using member's vehicle
(9)；For the first derivative to the time；INFor N-dimensional unit matrix；A is the state matrix of the node linear model of i-th vehicle；B
For the input matrix of the node linear model of i-th vehicle；For Kronecker product；Hσ(t)For time-varying communication topology battle array, indicate
For formula (8):
Hσ(t)=Lσ(t)+Rσ(t) (8)
In formula (8), Lσ(t)For Laplce's battle array of time-varying, Rσ(t)For the traction matrix of time-varying；
In formula (9),ForTransposition,For the absolute with error of speeding of i-th vehicle, quantity of state is expressed as formula (10):
In formula (10), xiFor the node linear model state amount of i-th vehicle, x0For the node linear model state amount of head vehicle, Di,0
For i-th vehicle vehicle to the end expectation with spacing of speeding.
3. considering the vehicle platoon under communication topology time-varying with stability control method of speeding, feature as claimed in claim 2
It is, " the low-dimensional Riccati inequality " in step 5 is expressed as following formula (26), and solving object by formula (26) is positive definite square
Battle array P:
AP+PAT-μBBT< 0 (26)
In formula (26), A is vehicle platoon node linear model state matrix；ATFor the transposition of A；B is vehicle platoon node linear mould
Type input matrix；BTFor the transposition of B；P is the solution of Riccati inequality, P > 0；
According to the P that formula (26) acquires, (27) seek stability controller gain K as the following formula:
4. considering the vehicle platoon under communication topology time-varying with stability control of speeding as claimed any one in claims 1 to 3
Method, which is characterized in that " to there are vehicle platoons under communication topology time-varying to carry out mathematical modeling " in step 4 includes:
Firstly, time shaft is divided into continuous time series such as following formula (11) to formula (13):
0 < tk-tk-1≤Tup (12)
t0=0 (13)
Formula (11) is into formula (13), tkFor the k moment；tk-1For the k-1 moment；t0For initial time；K is the natural number more than or equal to 1；
N is nature manifold；TupFor the upper limit of a time interval length, TupFor the constant greater than 0；
Then, by time interval [tk-1, tk) it is divided into finite continuous, nonoverlapping timeslice, so that in each timeslice
Communication topology is expressed as following formula (14) to formula (18) there is no variation:
mk> 0 (18)
Formula (14) into formula (18),For time interval [tk-1, tk) in the l-1 moment；For time interval [tk-1,
tk) in first of moment；For time interval [tk-1, tk) initial time, with tk-1It is of equal value；For time interval
[tk-1, tk) end of time, with tkIt is of equal value；L is time interval [tk-1, tk) in first of moment；mkFor time interval
[tk-1, tk) in mkAt a moment, also correspond to time interval；N is to be divided into mkPart, that is, it is divided into mkA timeslice；
TlowIndicate the lower limit of a time leaf length, TlowIt, can be random according to preset time interval length for the constant greater than 0
Value；
Finally, enabling time interval [ti, tj), communication topology number of transitions is N in 0≤i≤jσ(ti, tj), then average residence time π
It is defined as formula (19):
5. considering the vehicle platoon under communication topology time-varying with stability control method of speeding, feature as claimed in claim 4
It is, in step 5, the expectation acceleration u of i-th vehicleiIt is represented by formula (6):
In formula (6), lijFor the i-th row, the jth column element in Laplce's battle array L；riFor adjacency matrix；Di,jFor i-th vehicle and jth
Desired state difference between vehicle；K is controller gain, K=[k1 k2 k3]；Di,0It is desired between i-th Che Yutou vehicle
State difference；xjFor the quantity of state of jth vehicle；xiFor the quantity of state of i-th vehicle；x0For the quantity of state of head vehicle.
6. considering the vehicle platoon under communication topology time-varying with stability control method of speeding, feature as claimed in claim 5
Be, in the step 1 " distributed director be based on the Communication topology, utilize other member's vehicles
Information is controlled using static feedback, is obtained from the expectation acceleration a of vehicledes" include the following steps:
In the step 1 " distributed director be based on the Communication topology, utilize the letter of other member's vehicles
Breath, is controlled using static feedback, is obtained from the expectation acceleration a of vehicledes" include the following steps:
Step 11, the quantity of state sought in i-th vehicle and received vehicle platoon between other member's vehicles is poor, the quantity of state
Difference includes that the poor lengthwise position between i-th vehicle and other member's vehicles, longitudinal velocity difference and longitudinal acceleration are poor；
Step 12, i-th vehicle of step 11 acquisition and the sum of the quantity of state difference of other member's vehicles, the sum of quantity of state difference packet are sought
Include the sum of the sum of the sum of lengthwise position difference between i-th vehicle and other member's vehicles, longitudinal velocity difference, longitudinal acceleration difference；
Step 13, the sum of the sum of the sum of lengthwise position difference that step 12 obtains, longitudinal velocity difference, longitudinal acceleration difference are multiplied respectively
With the position feedback coefficient k of corresponding i-th vehicle1, velocity feedback coefficient k2, accelerator feedback coefficient k3, in step 5
Controller gain corresponds to static feedback COEFFICIENT K={ k1, k2, k3}；
Step 14, the quantity of state obtained to step 13 is summed, and the expectation as distributed director output adds
Speed ades；
Wherein, i indicate member's vehicle number, i=0,1,2 ... N.
7. considering the vehicle platoon under communication topology time-varying with stability control method of speeding, feature as claimed in claim 6
It is, " non-linear lower layer controls gain by feedback linearization constructing tactics " in the step 2 specifically includes:
As the expectation acceleration adesWhen >=0, output:
As the expectation acceleration adesWhen < 0, output:
In formula (1) and formula (2), TedesTo guarantee that vehicle reaches desired acceleration adesRequired engine it is expected torque, TbdesFor
Guarantee that vehicle reaches desired acceleration adesRequired wheel side desired braking torque, rwFor vehicle wheel roll radius, m is vehicle mass,
CAFor vehicle air resistance coefficient, v is car speed, τeFor engine response time lag,It is car speed to the derivative of time, g attaches most importance to
Power acceleration, f are wheel rolling frictional resistance, ηTFor vehicle drive system mechanical efficiency, i0For vehicle main retarder speed ratio, igTo become
Fast device speed ratio, M1P-1() indicates that engine is schemed against M1P, τbTime lag, K are responded for electric controlled brake systembFor vehicle wheel side system
Dynamic device gain coefficient.
8. considering the vehicle platoon under communication topology time-varying with stability control method of speeding, feature as claimed in claim 7
It is, " the node power unit is described as node linear model " in the step 2 specifically includes:
Firstly, according to formula (1) and formula (2) and τe≈τb, by the actual acceleration a of i-th vehicleiWith desired acceleration adesBetween
Relationship description be formula (3):
Wherein, τ=τeFor system time lags, s is Laplace operator；
Then, the quantity of state for taking i-th vehicle includes practical lengthwise position pi, practical longitudinal velocity vi, practical longitudinal acceleration ai,
It is expected acceleration adesFor input quantity, then obtaining " node linear model " is formula (4):
In formula (4), xiFor the quantity of state of the node linear model of i-th vehicle, A is the state square of the node linear model of i-th vehicle
Battle array, B are the input matrix of the node linear model of i-th vehicle, and κ indicates the time constant of inertial delay, and the τ of κ=1/；ui=
ades。
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| CN111665843A (en) * | 2020-06-12 | 2020-09-15 | 湖南大学 | Vehicle queue control method and system considering failure of communication part |
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| CN110161854B (en) * | 2019-05-21 | 2021-06-29 | 吉林大学 | Method for controlling longitudinal driving of highway heavy trucks in formation |
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| CN110910012A (en) * | 2019-11-20 | 2020-03-24 | 通号城市轨道交通技术有限公司 | Method and device for detecting train operation diagram overrun rationality |
| CN110910012B (en) * | 2019-11-20 | 2022-08-12 | 通号城市轨道交通技术有限公司 | Method and device for detecting train operation diagram overrun rationality |
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| CN113848941A (en) * | 2021-06-03 | 2021-12-28 | 西南交通大学 | Distributed controller design method for fleet spacing control |
| CN113848941B (en) * | 2021-06-03 | 2023-09-15 | 西南交通大学 | Design method of distributed controller for controlling distance between motorcades |
| CN113341722A (en) * | 2021-06-17 | 2021-09-03 | 西北工业大学 | Vehicle queue collaborative optimal control method under communication topology unconstrained condition |
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| CN113485124A (en) * | 2021-08-11 | 2021-10-08 | 长安大学 | Heterogeneous vehicle queue stability control method and system considering communication time lag |
| CN113485124B (en) * | 2021-08-11 | 2024-02-02 | 长安大学 | Heterogeneous vehicle queue stability control method and system considering communication time lag |
| CN115237118A (en) * | 2022-06-01 | 2022-10-25 | 昆明理工大学 | V2V vehicle queue form strategy optimization method |
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