CN113485125B - Time-lapse-containing vehicle queue stability control method and system suitable for arbitrary communication topology - Google Patents
Time-lapse-containing vehicle queue stability control method and system suitable for arbitrary communication topology Download PDFInfo
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Abstract
The invention discloses a time-lag-containing vehicle queue stability control method and a time-lag-containing vehicle queue stability control system suitable for any communication topology, wherein a distributed controller containing communication time lags is established based on the communication topology, a vehicle queue closed-loop control system containing time lags is decoupled into a plurality of subsystems by Jordan transformation of a matrix, the situation that a Laplace matrix of the communication topology simultaneously contains a real number characteristic value and a conjugate complex number characteristic value can be dealt with, and the problem of heavy characteristic values can be solved; by solving the pure virtual root and critical time lag of the subsystem characteristic equation and calculating the root trend of the pure virtual root at the critical time lag, the accurate time lag boundary and stable domain of the subsystem can be obtained; and comprehensively considering all subsystems, taking intersection of stable domains, finally obtaining the stable domain and the accurate time-lag boundary of the vehicle queue, ensuring that the vehicle queue control system stably runs in the calculated time-lag boundary, flexibly controlling sharing interaction of workshop state information, adopting smaller following distance, and increasing road capacity.
Description
Technical Field
The invention belongs to the field of vehicle queue control, and particularly relates to a time-lag-containing vehicle queue stability control method and system suitable for any communication topology.
Background
In recent years, with the increase of the conservation quantity of motor vehicles, people travel is greatly facilitated, and meanwhile, serious problems such as frequent traffic jams, aggravated energy consumption, reduced air quality and the like are brought. Research shows that the intelligent vehicle realizes the 'sharing' interaction of workshop state information through various wireless communication modes such as vehicle-to-vehicle communication, vehicle-to-infrastructure communication and the like, so that the vehicle runs in a queue mode, the driving safety can be improved, the traffic capacity is increased, and the energy consumption is reduced.
However, due to objective factors such as communication bandwidth, channel blocking, etc., there must be a communication time lag in the communication of the vehicle queues. The communication time lag exists so that the rate of change of the state (position, velocity, and acceleration state quantity) of the vehicle queue is related not only to the current time state but also to the past time state. The communication time lag not only has adverse effects on the steady state and transient control performance of the vehicle queue, but also can reduce the stability of the system and influence the driving safety. Therefore, how to ensure that the vehicle queue can stably run under the influence of communication time lag is a difficult problem to be solved in the vehicle queue control technology.
Currently, there are many drawbacks in vehicle fleet control system research involving communication time lags. The existing research is mostly only applicable to several types of special communication topologies, such as a front-vehicle following communication topology, a front-vehicle-pilot vehicle following communication topology, a double front-vehicle-pilot vehicle following communication topology and the like. These special types of communication topologies have a common characteristic that the eigenvalues of the laplace matrix are real numbers and have no complex numbers, so that the stability control and analysis of the vehicle queues under these communication topologies are relatively simple. However, the modes of vehicle-to-vehicle communication, vehicle-to-infrastructure communication, etc. are flexible, and any form of communication topology can be often constructed. Whereas for any form of communication topology, its laplace matrix may contain complex eigenvalues that are conjugate, even both real eigenvalues and complex eigenvalues that are conjugate. More difficult, these real and complex eigenvalues may also be re-roots. These complications with respect to the eigenvalues of the laplace matrix, interleaved with the communication skew, present serious design and analysis difficulties for stability control of the vehicle queues.
Disclosure of Invention
The invention aims to provide a time-lapse vehicle queue stability control method and system suitable for any communication topology, so as to overcome the defects of the prior art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a time-lapse vehicle queue stability control method suitable for any communication topology comprises the following steps:
s1, constructing a vehicle longitudinal dynamics model, a fixed-spacing strategy and a communication topology of a vehicle queue;
s2, establishing a distributed controller containing communication time lag based on a communication topology, establishing a vehicle queue closed-loop control system containing the communication time lag, and decoupling the vehicle queue closed-loop control system containing the time lag into a plurality of subsystems by using Jordan transformation of a matrix;
s3, establishing an auxiliary characteristic equation of the subsystem through Kronecker sum operation and z substitution, solving the auxiliary characteristic equation to obtain a solution set with the root modulus value equal to 1, then solving a pure virtual root set of the subsystem characteristic equation, determining the asymptotic behavior of the pure virtual root at the critical time lag by calculating the root trend, obtaining the stable domain and the accurate time lag boundary of the subsystem, respectively solving the stable domain and the accurate time lag boundary of each subsystem, and obtaining the stable domain and the accurate time lag boundary of the vehicle queue closed-loop control system by taking the intersection set of the stable domains of all subsystems, thereby obtaining the sufficient requirement of the vehicle queue stability.
Further, the vehicle longitudinal dynamics model is:
wherein i represents the number of the vehicle, the number 0 represents the pilot vehicle, and the following vehicles are numbered from front to back in sequence from 1 to N and p i (t)、v i (t)、a i (t) the position, speed and acceleration state quantity of the ith vehicle at the moment t, x i (T) represents the state quantity of the ith vehicle at time T, A, B is the state matrix and input matrix of the ith vehicle, T is the inertia constant of the driving mechanism of the vehicle, u i (t) represents a control input of the ith vehicle.
Further, the fixed spacing strategy is used to make the control target following vehicle of the vehicle train track the state of the pilot vehicle, and make the vehicle train run at a desired fixed spacing, namely:
wherein, I II indicates taking the binary norm, v 0 (t) represents the speed of the pilot vehicle at time t, l i,i-1 For a desired distance from the i-1 th vehicle to the i-th vehicle, there is l i,i-1 ＝-l i-1,i Setting l by adopting a fixed-pitch strategy i,i-1 Is a fixed constant: l (L) i,i-1 ＝l 0 ，l 0 Is constant.
Further, the distributed controller with communication time lag comprises:
where τ is the communication time lag,the position state error, the speed state error and the acceleration state error of the ith vehicle relative to the pilot vehicle at the time t-tau are respectively; k (k) p 、k v 、k a The position, the speed and the acceleration gain of a controller arranged on the ith vehicle are respectively; r is (r) ij Status information indicating whether the ith vehicle can receive the jth vehicle, and if so, r ij =1, otherwise r ij ＝0。
Further, a distributed controller related to the state error is established according to the distributed controller with communication time lag:
wherein k= [ K ] p ,k v ,k a ]For the control gain vector for each vehicle,for the state error of the ith following vehicle relative to the pilot vehicle at time t,/th>Is a position state error, l i,0 Is the desired distance from the pilot vehicle to the ith vehicle; />Is a speed state error; />Is an acceleration state error.
Further, according to the longitudinal dynamics of the vehicle and the distributed controller related to the state error, a closed-loop dynamics equation of the ith vehicle is obtained:
further, the state space expression of the vehicle queue closed-loop control system with communication time lag is as follows:
wherein I is N Is an N-order unit array,representing Kronecker product, matrix +.>Communication topology for describing a train of vehicles, +.>For Laplace matrix, used to describe the communication relationship between all follower vehicles, +.>For the traction matrix, which describes the communication relationship between the pilot vehicle and the following vehicle, X (t- τ) represents the lumped state error of the vehicle train at the time t- τ.
Further, the characteristic equation of the vehicle queue closed-loop control system is:
wherein det (·) represents a determinant operation, I 3N And s is a Laplacian variable, which is a 3N-order unit array.
Further, by Jordan transformation of the matrix Y, the vehicle queue closed-loop control system with communication time lag is equivalently decomposed into a plurality of low-order subsystems, and the auxiliary characteristic equation form of the subsystems is established by using Kronecker sum operation and z substitution as follows:
wherein the matrix Y has q different real eigenvalues and w pairs of different complex conjugate eigenvalues,
z＝e -τs and Z is complex, solve the solution set Z of the auxiliary characteristic equation n ＝{z|g n (z) =0, |z|=1 }; solving the pure virtual root omega of the subsystem characteristic equation, wherein omega is used for the collection of the pure virtual root omega n A representation; the critical time lag set of the subsystem is as follows:
wherein,representing the corner-taking operation,/->Representing a positive number in the real domain;
determining the asymptotic behavior of the pure virtual root of the subsystem characteristic equation at the critical time lag, and solving the pure virtual root omega epsilon omega of the subsystem n Regarding critical time lagIs referred to as the root trend, the expression is as follows:
where Re represents the real part, sgn represents the sign function,representing pair s about->Calculating partial derivatives, wherein i is an imaginary unit; and obtaining a pure virtual root and critical time lag of the subsystem according to the auxiliary characteristic equation of the subsystem and the characteristic equation of the subsystem.
A time-lapse-containing vehicle queue stability control system suitable for any communication topology comprises a vehicle control model and a vehicle queue stability control model;
the method is characterized by comprising the steps of storing a longitudinal dynamics model of a vehicle, a fixed-interval strategy and a communication topology, establishing a distributed controller containing communication time lag based on the communication topology, establishing a vehicle queue closed-loop control system containing the communication time lag, and decoupling the vehicle queue closed-loop control system containing the time lag into a plurality of subsystems by Jordan transformation of a matrix;
the vehicle queue stability control model is used for establishing an auxiliary characteristic equation of a subsystem through Kronecker sum operation and z substitution, solving the auxiliary characteristic equation to obtain a solution set with the root modulus value equal to 1, then solving a pure virtual root set of the subsystem characteristic equation, determining the asymptotic behavior of the pure virtual root at the critical time lag by calculating the root trend, obtaining the stability domain and the accurate time lag boundary of the subsystem, respectively solving the stability domain and the accurate time lag boundary of each subsystem, obtaining the intersection set of the stability domains of all subsystems, and obtaining the stability domain and the accurate time lag boundary of the vehicle queue closed-loop control system and outputting the obtained results.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention relates to a time-lag-containing vehicle queue stability control method suitable for any communication topology, which is characterized in that a distributed controller containing communication time lags is established based on the communication topology, a vehicle queue closed-loop control system containing the communication time lags is established, the vehicle queue closed-loop control system containing the time lags is decoupled into a plurality of subsystems by Jordan transformation of a matrix, the situation that a Laplace matrix of the communication topology simultaneously contains a real number characteristic value and a conjugate complex number characteristic value can be dealt with, and the problem of heavy characteristic values can be solved; constructing an auxiliary characteristic equation of the subsystem, solving a pure virtual root and critical time lag of the characteristic equation of the subsystem, and calculating a root trend of the pure virtual root at the critical time lag to obtain an accurate time lag boundary and a stable domain of the subsystem; comprehensively considering all subsystems, taking the intersection of the stability domains, and finally obtaining the stability domain and the accurate time-lag boundary of the vehicle queue. The method can ensure that the vehicle queue control system stably runs in the calculated time lag boundary, flexibly control the sharing interaction of the workshop state information, and can increase the road capacity by adopting a smaller following distance.
The time-lapse vehicle queue stability control method is applicable to any communication topology, and can meet the flexible adjustment requirement of a workshop state information sharing interaction mode. By means of the train-arranged running of the vehicles, a smaller following distance can be adopted on the premise of ensuring safety, and therefore road capacity is increased. Meanwhile, the stability control problem of the vehicle queue closed-loop control system is converted into the stability control problem of all subsystems, so that the calculated amount of vehicle queue stability control is greatly reduced. By establishing an auxiliary characteristic equation of the subsystem, the infinite characteristic root solving problem is converted into a finite pure virtual root solving problem, and the difficulty of controlling and analyzing the stability of the motorcade is greatly reduced. The invention can calculate the accurate time lag boundary of the vehicle queue, can ensure that the vehicle queue stably runs within the given time lag boundary, and the obtained stability condition is a sufficient and necessary condition.
Furthermore, by the designed distributed controller, the following vehicle automatically tracks the state of the piloting vehicle, thereby achieving the purpose of automatically and longitudinally following the vehicle, increasing traffic capacity and improving driving safety.
Drawings
FIG. 1 is a flow chart of a method for controlling vehicle queue stability according to an example of the present invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
as shown in fig. 1, the method for controlling the stability of the vehicle queue with time lag, which is suitable for any communication topology, mainly includes the following implementation steps:
step 1: the vehicle queue consists of 1 pilot vehicle and N following vehicles, wherein N is a natural number greater than 1, and a mathematical model of a vehicle queue control system is established: the mathematical model comprises a vehicle longitudinal dynamics model, a fixed-spacing strategy, a communication topology and a distributed controller. Wherein the vehicle longitudinal dynamics model describes a longitudinal driving characteristic of the intelligent vehicle. The fixed spacing strategy is used to determine the longitudinal distance between vehicles. The communication topology is used for status information interaction between vehicles. And the distributed controller calculates the expected acceleration of the own vehicle through state feedback by using the state information of the rest vehicles through the communication topology.
Step 2: establishing a longitudinal dynamics model of the vehicle in the step 1:
the number of the vehicle is represented by i, the number 0 represents a pilot vehicle, and the following vehicles are numbered from front to back in sequence1 to N, p i (t)、v i (t)、a i (t) respectively representing the position, speed and acceleration state of the ith vehicle at the time t, and setting the state of the vehicle as x i (t)＝[p i (t),v i (t),a i (t)] T The third-order linear model of the longitudinal dynamics of the vehicle is described as follows:
wherein u is i (t) represents a control input of the ith vehicle, and the state matrix a and the input matrix B are respectively:
where T is the inertia constant of the driving mechanism of the vehicle.
Step 3: determining the fixed-pitch strategy in step 1: the control objective of the vehicle train is to let the following vehicle track the state of the lead vehicle and to let the vehicle train travel at a desired fixed distance, i.e
Wherein, I II indicates taking the binary norm, v 0 (t) represents the speed of the pilot vehicle at time t, l i,i-1 For a desired distance from the i-1 th vehicle to the i-th vehicle, there is l i,i-1 ＝-l i-1,i . Setting l by adopting a fixed-pitch strategy i,i-1 Is a fixed constant: l (L) i,i-1 ＝l 0 ，l 0 Is constant.
Step 4: constructing the communication topology in the step 1: regarding a vehicle as a node, using a directed graphCommunication topology representing a train of vehicles, wherein ∈>For a set of nodes, representing all following vehicles, v i I=1, 2, …, N represents the node represented by the i-th vehicle, ++>Representing a set of edges in the communication topology, each edge representing a j-th vehicle communicating to an i-th vehicle. Adjacency matrix usable for information transfer relation between all following vehiclesRepresentation, wherein->Representing the real number field, r ij Indicating whether the ith vehicle can receive status information of the jth vehicle. If (upsilon) i ,υ j ) Epsilon and r ij =1; if->R is then ij =0; in addition, the vehicle is unable to communicate by itself, i.e. r ij =0. Ith node v i The degree of penetration of (2) is->The ingress matrix consisting of ingress of all nodes is +>And (2) with the picture->The relevant Laplace matrix is +.>Furthermore, the communication relationship between the follower vehicle and the pilot vehicle can be represented by a traction matrix +.>Description. If the ith following vehicle can obtainTaking the state information of the pilot vehicle, then p i =1; otherwise, p i ＝0。
Step 5: designing the distributed controller in the step 1. The embodiment considers that the actual communication is affected by physical conditions such as bandwidth limitation, channel blocking and the like, and time lag exists in information transmission. In order to achieve the control objective in step 3, feedback control is performed on the vehicle state with communication time lag, and a distributed controller with communication time lag is established:
wherein k is p 、k v 、k a The position, the speed and the acceleration of the distributed controller of each vehicle are respectively controlled to gain, tau represents communication time lag, and p i (t-τ)、v i (t-τ)、a i (t- τ) represents the position, speed, and acceleration state of the ith vehicle at time t- τ, respectively.
Step 6: according to the distributed controller with communication time lag in step 5, the distributed controller with state error is provided. Definition of the definitionIs the state error of the ith following vehicle relative to the piloting vehicle at the moment t, wherein,is a position state error, l i,0 Is the desired distance from the pilot vehicle to the ith vehicle;is a speed state error; />For acceleration state errors, the distributed controller for state errors is:
the above can be written in a compact form:
wherein k= [ K ] p ,k v ,k a ]A control gain vector for each vehicle.
Step 7: according to the third-order linear model of the longitudinal dynamics of the vehicle in the step 2 and the distributed controller in the step 6, a closed-loop dynamics equation of the ith vehicle is obtained:
step 8: defining lumped state error vectors for an entire vehicle queueAnd lumped control input +.>Then a state space expression for the closed loop control system for the vehicle queue with communication time lag can be deduced:
wherein I is N Is an N-order unit array,representing Kronecker product, matrix +.>For describing the communication topology of the vehicle consist, X (t- τ) represents the aggregate state error of the vehicle consist at time t- τ.
The characteristic equation of the vehicle queue closed-loop control system is as follows:
wherein det (·) represents a determinant operation, I 3N And s is a Laplacian variable, which is a 3N-order unit array.
For any type of communication topology, there may be both real and conjugated complex eigenvalues in the laplace matrix eigenvalues, and both real and complex eigenvalues may have a strong root. In order to adapt to any type of communication topology, the vehicle queue control system constructed in the embodiment adopts the following steps for control design and analysis.
Step 9: according to the communication topology of step 4, the matrix Y is known to be an nth order matrix. Let lambda be n N=1, 2, …, q is the real eigenvalue of Y, and λ n The weight number of (a) is delta n ，n＝1,2,…,q；λ n ＝α n +iβ n ，Is the conjugate complex eigenvalue of Y, and lambda n The weight of (a) is also delta n N=q+1, q+2, …, q+w, i denotes an imaginary unit. The number of real eigenvalues and the number of conjugate complex eigenvalues satisfy the relationship: />There is a non-singular matrix +.>Make->J is a Jordan matrix having the form:
wherein J is n N=1, 2, …, q is a Jordan block corresponding to the real eigenvalue of matrix Y, in the form:
J n n=q+1, q+2, …, q+w is a Jordan block corresponding to the complex eigenvalue of matrix Y, having the form:
step 10: the vehicle queue closed-loop control system described in step 8 can be equivalently decomposed into a plurality of lower-order subsystems according to the transformation of the matrix Y into a Jordan matrix described in step 9.
Performing linear transformationζ (t) is a state vector of X (t) after linear transformation, ++>To transform the matrix, can obtain
Through the process, the vehicle queue closed-loop control system applicable to any communication topology can be equivalently decomposed into q 3-order subsystems and w 6-order subsystems
The characteristic equation of the subsystem is as follows:
the relationship between the vehicle queue closed-loop control system characteristic equation and the subsystem characteristic equation is as follows:
if the entire vehicle queue control system is stable, each subsystem must be stable. Due to the fact that a subsystem characteristic equation contains a time lag term e -τs Resulting in an infinite number of feature roots for the feature equation. To solve this problem, the present embodiment uses Kronecker sum operation and z substitution (z=e -τs And z is complex), an auxiliary characteristic equation of the subsystem is established, and a pure virtual root of the characteristic equation is obtained by solving the auxiliary characteristic equation. By the method, an infinite characteristic root solving problem is converted into a finite pure virtual root solving problem, and the difficulty of motorcade stability control and analysis is greatly reduced.
Step 11: establishing an auxiliary characteristic equation of the motorcade subsystem in the step 10:
wherein,
solving solution set Z of auxiliary characteristic equation n ＝{z|g n (z) =0, |z|=1 }. Next, a pure set of virtual roots of subsystem characterization equations can be solved, using Ω n The representation is:wherein->Representing positive numbers in the real number domain, ω is the pure imaginary root of the subsystem's characteristic equation.
The critical time-lag set for the subsystem is:
wherein,representing an angular operation.
Step 12: determining the asymptotic behavior of the pure virtual root of the subsystem characteristic equation at the critical time lag, namely determining the traversing behavior of the pure virtual root at the virtual axis of the complex plane, wherein the pure virtual root omega E omega of the subsystem needs to be solved n Regarding critical time lagIs referred to as the root trend, the expression is as follows:
where Re represents the real part, sgn represents the sign function,representing +.>And (5) obtaining a partial derivative.
Step 13: according to the auxiliary characteristic equation of the subsystem in the step 11 and the characteristic equation of the subsystem in the step 10, pure virtual roots and critical time lags of the subsystem can be obtained. The solving sequence is as follows:
and then judging the asymptotic behavior of the pure virtual root at the critical time lag according to the root trend in the step 12, and counting the number of the unstable roots of the area divided by the critical time lag, wherein the area with the number of the unstable roots being zero is the stable domain of the subsystem, and the time lag at the boundary of the stable domain is the accurate time lag boundary of the subsystem.
Step 14: and (3) respectively adopting the stability control process from the step 11 to the step 13 for the state space expressions of all the subsystems in the step 10 to obtain the stability domain and the accurate time lag boundary of each subsystem. And then intersection sets are taken for the stable domains of all subsystems, so that the stable domain and the accurate time-lag boundary of the whole vehicle queue can be finally obtained, and the vehicle queue can be ensured to stably run in the calculated time-lag boundary.
And applying the stability control process to each subsystem to obtain a stability domain and an accurate time lag boundary of each subsystem for the closed-loop control system of the time lag-containing vehicle queue applicable to any communication topology. And intersection sets are taken for the stable domains of all subsystems, so that the stable domain and the accurate time-lag boundary of the whole vehicle queue can be finally obtained, and the vehicle queue can be ensured to stably run in the calculated time-lag boundary.
The invention enables the following vehicle to automatically track the state of the piloting vehicle through the designed distributed controller, thereby achieving the purpose of automatically and longitudinally following the vehicle, increasing traffic capacity and improving driving safety. The designed time-lag-containing vehicle queue stability control method is suitable for any communication topology, and can meet the flexible adjustment requirement of a workshop state information sharing interaction mode. By means of the train-arranged running of the vehicles, a smaller following distance can be adopted on the premise of ensuring safety, and therefore road capacity is increased. Meanwhile, the stability control problem of the vehicle queue closed-loop control system is converted into the stability control problem of all subsystems, so that the calculated amount of vehicle queue stability control is greatly reduced. By establishing an auxiliary characteristic equation of the subsystem, the infinite characteristic root solving problem is converted into a finite pure virtual root solving problem, and the difficulty of controlling and analyzing the stability of the motorcade is greatly reduced. The invention can calculate the accurate time lag boundary of the vehicle queue, can ensure that the vehicle queue stably runs within the given time lag boundary, and the obtained stability condition is a sufficient and necessary condition.
Claims (10)
1. A time-lapse vehicle queue stability control method suitable for any communication topology, comprising the steps of:
s1, constructing a vehicle longitudinal dynamics model, a fixed-spacing strategy and a communication topology of a vehicle queue;
s2, establishing a distributed controller containing communication time lag based on a vehicle longitudinal dynamics model, a fixed-spacing strategy and a communication topology, establishing a vehicle queue closed-loop control system containing the communication time lag, and decoupling the vehicle queue closed-loop control system containing the time lag into a plurality of subsystems by using Jordan transformation of a matrix;
s3, establishing an auxiliary characteristic equation of the subsystem through Kronecker sum operation and z substitution, solving the auxiliary characteristic equation to obtain a solution set with the root modulus value equal to 1, then solving a pure virtual root set of the subsystem characteristic equation, determining the asymptotic behavior of the pure virtual root at a critical time lag by calculating root trend, obtaining a stable domain and an accurate time lag boundary of the subsystem, respectively solving the stable domain and the accurate time lag boundary of each subsystem, and obtaining an intersection set of the stable domains of all subsystems, obtaining the stable domain and the accurate time lag boundary of a vehicle queue closed-loop control system, thereby obtaining the sufficient and necessary conditions of vehicle queue stability;
specific: the form of the auxiliary characteristic equation of the subsystem is established as follows:
wherein the matrix Y has q different real eigenvalues and w pairs of different complex conjugate eigenvalues,
z＝e -τs and Z is complex, solve the solution set Z of the auxiliary characteristic equation n ＝{z|g n (z) =0, |z|=1 }; solving the pure virtual root omega of the subsystem characteristic equation, wherein omega is used for the collection of the pure virtual root omega n A representation; the critical time lag set of the subsystem is as follows:
wherein,representing the corner-taking operation,/->Representing a positive number in the real domain;
determining the asymptotic behavior of the pure virtual root of the subsystem characteristic equation at the critical time lag, and solving the pure virtual root omega epsilon omega of the subsystem n Regarding critical time lagIs referred to as the root trend, the expression is as follows:
where Re represents the real part, sgn represents the sign function,representing pair s about->Calculating partial derivatives, wherein i is an imaginary unit; according to the auxiliary characteristic equation of the subsystem and the characteristic equation of the subsystem, a pure virtual root of the subsystem can be obtainedCritical time lags.
2. The method for controlling the stability of a time-lapse vehicle queue for any communication topology according to claim 1, wherein the vehicle longitudinal dynamics model is:
wherein i represents the number of the vehicle, the number 0 represents the pilot vehicle, and the following vehicles are numbered from front to back in sequence from 1 to N and p i (t)、v i (t)、a i (t) the position, speed and acceleration state quantity of the ith vehicle at the moment t, x i (T) represents the state quantity of the ith vehicle at time T, A, B is the state matrix and input matrix of the ith vehicle, T is the inertia constant of the driving mechanism of the vehicle, u i (t) represents a control input of the ith vehicle.
3. The method for controlling stability of a vehicle train with time lag according to claim 1, wherein a fixed pitch strategy is used to make a control target follower of the vehicle train track the state of a pilot vehicle and make the vehicle train travel at a desired fixed pitch, namely:
wherein, I II indicates taking the binary norm, v 0 (t) represents the speed of the pilot vehicle at time t, l i,i-1 For a desired distance from the i-1 th vehicle to the i-th vehicle, there is l i,i-1 ＝-l i-1,i Setting l by adopting a fixed-pitch strategy i,i-1 Is a fixed constant: l (L) i,i-1 ＝l 0 ，l 0 Is constant.
4. A time-lapse vehicle queue stability control method applicable to any communication topology as claimed in claim 3, wherein the distributed controller with communication time-lapse:
where τ is the communication time lag,the position state error, the speed state error and the acceleration state error of the ith vehicle relative to the pilot vehicle at the time t-tau are respectively; k (k) p 、k v 、k a The position, the speed and the acceleration gain of a controller arranged on the ith vehicle are respectively; r is (r) ij Status information indicating whether the ith vehicle can receive the jth vehicle through the communication topology, and if so, r ij =1, otherwise r ij ＝0。
5. The method for controlling the stability of a vehicle queue with time lags applicable to any communication topology according to claim 4, wherein the distributed controller concerning the state error is established according to the distributed controller with time lags of communication:
wherein k= [ K ] p ,k v ,k a ]For the control gain vector for each vehicle,for the state error of the ith following vehicle relative to the pilot vehicle at time t,/th>Is a position state error, l i,0 Is the desired distance from the pilot vehicle to the ith vehicle; />Is a speed state error; />Is an acceleration state error.
6. The method for controlling the stability of a time-lapse vehicle queue suitable for use in any communication topology according to claim 4, wherein the closed-loop dynamics equation of the i-th vehicle is obtained from the vehicle longitudinal dynamics and the distributed controller with respect to the state error:
7. the method for controlling stability of a vehicle queue with time lag according to claim 4, wherein the state space expression of the closed loop control system of the vehicle queue with time lag is:
wherein I is N Is an N-order unit array,representing Kronecker product, matrix +.>Communication topology for describing a train of vehicles, +.>For Laplace matrix, used to describe the communication relationship between all follower vehicles, +.>For the traction matrix, which describes the communication relationship between the pilot vehicle and the following vehicle, X (t- τ) represents the lumped state error of the vehicle train at the time t- τ.
8. The method for controlling the stability of a vehicle queue with time lags according to claim 7, wherein the characteristic equation of the vehicle queue closed-loop control system is:
wherein det (·) represents a determinant operation, I 3N And s is a Laplacian variable, which is a 3N-order unit array.
9. The method for controlling the stability of a vehicle queue with time lag according to claim 6, wherein the closed loop control system of the vehicle queue with communication time lag is equivalently decomposed into a plurality of low-order subsystems by Jordan transformation of a matrix Y, and Kronecker sum operation and z substitution are utilized.
10. A time-lapse vehicle queue stability control system for any communication topology based on the time-lapse vehicle queue stability control method for any communication topology of claim 1, characterized by comprising a vehicle control model and a vehicle queue stability control model;
the method is characterized by comprising the steps of storing a longitudinal dynamics model of a vehicle, a fixed-interval strategy and a communication topology, establishing a distributed controller containing communication time lag based on the communication topology, establishing a vehicle queue closed-loop control system containing the communication time lag, and decoupling the vehicle queue closed-loop control system containing the time lag into a plurality of subsystems by Jordan transformation of a matrix;
the vehicle queue stability control model is used for establishing an auxiliary characteristic equation of a subsystem through Kronecker sum operation and z substitution, solving the auxiliary characteristic equation to obtain a solution set with the root modulus value equal to 1, then solving a pure virtual root set of the subsystem characteristic equation, determining the asymptotic behavior of the pure virtual root at the critical time lag by calculating the root trend, obtaining the stability domain and the accurate time lag boundary of the subsystem, respectively solving the stability domain and the accurate time lag boundary of each subsystem, obtaining the intersection set of the stability domains of all subsystems, and obtaining the stability domain and the accurate time lag boundary of the vehicle queue closed-loop control system and outputting the obtained results.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105138006A (en) * | 2015-07-09 | 2015-12-09 | 哈尔滨工程大学 | Cooperated tracking control method of time-lag non-linear multi-agent systems |
| CN106502100A (en) * | 2016-12-13 | 2017-03-15 | 浙江工业大学 | Distributed single controller for time delay method for designing of multiple mobile robot |
| CN109241674A (en) * | 2018-10-16 | 2019-01-18 | 长安大学 | A kind of multi-time Delay method for analyzing stability of intelligent network connection platooning |
| CN110568762A (en) * | 2019-10-10 | 2019-12-13 | 厦门大学 | intelligent electric vehicle formation adaptive robust control method capable of resisting communication delay |
| CN111582586A (en) * | 2020-05-11 | 2020-08-25 | 长沙理工大学 | Multi-fleet driving risk prediction system and method for reducing jitter |
| CN111652345A (en) * | 2020-05-29 | 2020-09-11 | 长安大学 | Fleet brake control method based on space-time joint optimization |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US10538174B2 (en) * | 2017-09-29 | 2020-01-21 | Nio Usa, Inc. | Real-time nonlinear receding horizon control of batteries for power systems |
-
2021
- 2021-08-11 CN CN202110921297.5A patent/CN113485125B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105138006A (en) * | 2015-07-09 | 2015-12-09 | 哈尔滨工程大学 | Cooperated tracking control method of time-lag non-linear multi-agent systems |
| CN106502100A (en) * | 2016-12-13 | 2017-03-15 | 浙江工业大学 | Distributed single controller for time delay method for designing of multiple mobile robot |
| CN109241674A (en) * | 2018-10-16 | 2019-01-18 | 长安大学 | A kind of multi-time Delay method for analyzing stability of intelligent network connection platooning |
| CN110568762A (en) * | 2019-10-10 | 2019-12-13 | 厦门大学 | intelligent electric vehicle formation adaptive robust control method capable of resisting communication delay |
| CN111582586A (en) * | 2020-05-11 | 2020-08-25 | 长沙理工大学 | Multi-fleet driving risk prediction system and method for reducing jitter |
| CN111652345A (en) * | 2020-05-29 | 2020-09-11 | 长安大学 | Fleet brake control method based on space-time joint optimization |
Non-Patent Citations (1)
| Title |
|---|
| 考虑时滞的协作式自动驾驶车队的纵向控制方法;李正磊;《汽车安全与节能学报》;第11卷(第2期);第182-189页 * |
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