Distributed data-driven predictive control for cooperatively smoothing mixed trafﬁc ﬂow Jiawei Wangab Yingzhao Lianb Yuning Jiangb Qing Xua Keqiang Lia Colin N. Jonesb

2025-05-03 0 0 8.88MB 28 页 10玖币

侵权投诉

Distributed data-driven predictive control for cooperatively smoothing

mixed trafﬁc ﬂow

Jiawei Wanga,b, Yingzhao Lianb, Yuning Jiangb,∗, Qing Xua, Keqiang Lia, Colin N. Jonesb

aSchool of Vehicle and Mobility, Tsinghua University, 100084 Beijing, China

bAutomatic Control Laboratory, EPFL, 1024 Lausanne, Switzerland

Abstract

Cooperative control of connected and automated vehicles (CAVs) promises smoother trafﬁc ﬂow. In mixed trafﬁc,

where human-driven vehicles with unknown dynamics coexist, data-driven predictive control techniques allow for

CAV safe and optimal control with measurable trafﬁc data. However, the centralized control setting in most exist-

ing strategies limits their scalability for large-scale mixed trafﬁc ﬂow. To address this problem, this paper proposes a

cooperative DeeP-LCC (Data-EnablEd Predictive Leading Cruise Control) formulation and its distributed implemen-

tation algorithm. In cooperative DeeP-LCC, the trafﬁc system is naturally partitioned into multiple subsystems with

one single CAV, which collects local trajectory data for subsystem behavior predictions based on the Willems’ funda-

mental lemma. Meanwhile, the cross-subsystem interaction is formulated as a coupling constraint. Then, we employ

the Alternating Direction Method of Multipliers (ADMM) to design the distributed DeeP-LCC algorithm. This al-

gorithm achieves both computation and communication efﬁciency, as well as trajectory data privacy, through parallel

calculation. Our simulations on different trafﬁc scales verify the real-time wave-dampening potential of distributed

DeeP-LCC, which can reduce fuel consumption by over 31.84% in a large-scale trafﬁc system of 100 vehicles with

only 5% −20% CAVs.

Keywords: Connected and automated vehicles, mixed trafﬁc, data-driven predictive control, distributed optimization.

1. Introduction

Trafﬁc instabilities, in the form of periodic acceleration and deceleration of individual vehicles, cause a great loss

of travel efﬁciency and fuel economy. This phenomenon, also known as trafﬁc waves, is expected to be extensively

eliminated with the emergence of connected and automated vehicles (CAVs). Particularly, with the advances of

vehicle automation and wireless communications, CAV cooperative control promises system-wide trafﬁc optimization

and coordination, contributing to enhanced trafﬁc mobility. One typical technology is Cooperative Adaptive Cruise

Control (CACC), which organizes a group of CAVs into a single-lane platoon and maintains desired spacing and

harmonized velocity, with dissipation of undesired trafﬁc perturbations [1–3].

Despite the highly recognized potential of CAV cooperative control in both academy and industry, existing re-

search mostly focuses on the fully-autonomous scenario with pure CAVs. For real-world implementation, however,

the transition phase of mixed trafﬁc with the coexistence of human-driven vehicles (HDVs) and CAVs may last for

decades, making mixed trafﬁc a more predominant pattern [4–6]. By explicitly considering the behavior of sur-

rounding HDVs that are under human control, recent research has revealed the potential of bringing signiﬁcant trafﬁc

improvement with only a few CAVs. Essentially, the CAVs can be utilized as mobile actuators for trafﬁc control,

leading to a recent notion of trafﬁc Lagrangian control [4,7]. In a closed ring-road setup, the seminal real-world

∗Corresponding author: Yuning Jiang

Email addresses: wang-jw18@mails.tsinghua.edu.cn (Jiawei Wang), yingzhao.lian@epfl.ch (Yingzhao Lian),

yuning.jiang@epfl.ch (Yuning Jiang), qingxu@tsinghua.edu.cn (Qing Xu), likq@tsinghua.edu.cn (Keqiang Li),

colin.jones@epfl.ch (Colin N. Jones)

arXiv:2210.13171v2 [eess.SY] 28 Apr 2023

experiment in [4], followed by a series of theoretical analysis [8,9] and simulation reproductions [10,11], reveals the

capability of one single CAV in stabilizing the entire mixed trafﬁc ﬂow.

Along this direction, multiple strategies have been designed for trafﬁc-oriented CAV control in mixed trafﬁc ﬂow.

One typical method is jam-absorption driving (JAD), which adjusts the CAV motion to leave enough inter-vehicle

spacing for the trafﬁc wave to be dissipated [12,13]. By extending the typical CACC frameworks to the mixed trafﬁc

setup, Connected Cruise Control (CCC) makes control decisions for one CAV at the tail by considering the motion of

one or multiple HDVs ahead [14,15]. By enabling the CAV to respond to one HDV behind, the recent work in [16]

proposes a closed-loop trafﬁc control paradigm to stabilize the upstream trafﬁc. Further, Leading Cruise Control

(LCC) [17] extends the idea in [14–16] to a more general case by incorporating both the HDVs behind and ahead of

the CAV into the system framework, and indicates that one CAV can not only adapt to the downstream trafﬁc ﬂow as

a follower, but also actively regulate the motion of the upstream trafﬁc participants as a leader. The aforementioned

work mostly focuses on the single-CAV case. When multiple CAVs coexist, the very recent work [6] reveals that

rather than organizing all the CAVs into a platoon, one can allow CAVs to be naturally and arbitrarily distributed in

mixed trafﬁc and apply cooperative control decisions, contributing to greater trafﬁc beneﬁts.

1.1. Data-Driven and Distributed Control for Mixed Trafﬁc

Essentially, mixed trafﬁc is a complex human-in-the-loop cyber-physical system. For longitudinal control of CAVs

in mixed trafﬁc, one typical approach is to employ the well-known car-following model, e.g., the optimal velocity

model (OVM) [18] and the intelligent driver model (IDM) [19], to describe the driving behavior of HDVs. Lumping

the dynamics of CAVs and HDVs together, a parametric model of the entire mixed trafﬁc system can be derived,

allowing for model-based controller design. Based on CCC/LCC-type frameworks, multiple model-based methods

have been employed to enable CAVs to dissipate trafﬁc waves, such as optimal control [9,15,20], H∞control [21–23]

and model predictive control (MPC) [24–26]. These model-based methods require prior knowledge of mixed trafﬁc

dynamics for controller synthesis and parameter tuning. In practical trafﬁc ﬂow, however, it is non-trivial to accurately

identify the driving behavior of one particular HDV, which tends to be uncertain and stochastic due to human nature.

To address this problem, model-free approaches that circumvent the model identiﬁcation process in favor of data-

driven techniques have received increasing attention. Reinforcement learning [7,10,27] and adaptive dynamic pro-

gramming [28,29], for example, have shown their potential in learning CAVs’ wave-dampening strategies in mixed

trafﬁc ﬂow. Nevertheless, their lack of interpretability, sample efﬁciency and safety guarantees remains of primal

concern [30]. On the other hand, by integrating learning methods with MPC—a prime methodology for constrained

optimal control problems, data-driven predictive control techniques provide a signiﬁcant opportunity for reliable safe

control with available data. Following this idea, several methods have been applied for CAV control in mixed trafﬁc,

such as data-driven reachability analysis [31] and Koopman operator theory [32]. Very recently, Data-EnablEd Pre-

dictive Leading Cruise Control (DeeP-LCC) [33], which combines Data-EnablEd Predictive Control (DeePC) [34]

with LCC [17], directly utilizes measurable trafﬁc data to design optimal CAV control inputs with collision-free con-

siderations. Both small-scale trafﬁc simulations [33,35] and real-world miniature experiments [36] have validated

its capability in mitigating trafﬁc waves and improving fuel economy.

Despite the effectiveness of the aforementioned model-free methods, one common issue that has signiﬁcantly

prohibited their implementation is the centralized control setting. A central unit is deployed to gather all the available

data, and assign control actions for each CAV. For large-scale mixed trafﬁc systems with multiple CAVs and HDVs,

this process is non-trivial to be completed during the system’s sampling period given the potential delay in both

wireless communications and online computations [37]. As discussed in [33], the number of ofﬂine pre-collected data

samples for centralized DeeP-LCC grows in a quadratic relationship when the trafﬁc system scales up, leading to a

dramatic increase in online computation burden. Moreover, due to the free joining or leaving maneuvers of individual

vehicles (particularly those HDVs under human control), the ﬂexible structure of the mixed trafﬁc system, i.e., the

spatial formation and penetration rates of CAVs [6], could raise signiﬁcant concerns about the excessive burden of

recollecting trafﬁc data and relearning CAV strategies.

As an alternative, distributed control and optimization techniques are believed to be more scalable and feasible

for large-scale trafﬁc control. One particular method is the well-established Alternating Direction Method of Multi-

pliers (ADMM) [38], which separates a large-scale optimization problem into smaller pieces that are easier to handle.

Thanks to its efﬁcient distributed optimization design with guaranteed convergence properties for convex problems,

Figure 1: Schematic of centralized DeeP-LCC for CAVs in mixed trafﬁc. (a) Centralized DeeP-LCC.DeeP-LCC collects the measurable data

from the entire mixed trafﬁc system, including trafﬁc output, control input of the CAVs, and reference input, i.e., the velocity error of the head

vehicle. Then, it utilizes these data to construct Hankel matrices for future trajectory predictions, and design the optimal future trajectory. More

details can be found in [33]. (b) Mixed trafﬁc scenario. The head vehicle is located at the beginning, indexed as 0, behind which there exist nCAVs

and mHDVs. Between CAV iand CAV i+ 1, there exist miHDVs (mi≥0). (c) CF-LCC (Car-Following Leading Cruise Control) subsystem

i, consisting of a leading CAV iand the following miHDVs. More details can be found in [17, Section II-C].

ADMM has seen wide applications in multiple areas, such as distributed learning [39], power control [40], and wire-

less communications [41]. Given the multi-agent nature of trafﬁc ﬂow dynamics, which consists of the motion of

multiple individual vehicles, ADMM has also been widely employed for CAV coordination in trafﬁc ﬂow, by solving

local control problems and sharing information via vehicle-to-vehicle (V2V) or vehicle-to-everything (V2X) interac-

tions; see, e.g., [42–44]. To our best knowledge, however, there has been limited research on data-driven distributed

control for CAVs in the case of large-scale mixed trafﬁc ﬂow, with a very recent exception in [32], which combines

Koopman operator theory with ADMM. Rather than ofﬂine training a neural network as in [32], this paper aims to

develop ADMM-based data-driven distributed control algorithms through the well-established Willems’ fundamental

lemma [45], which directly relies on measurable data for online behavior predictions.

1.2. Contributions

Based on the centralized DeeP-LCC formulation [33], this paper proposes a cooperative DeeP-LCC strategy

for CAVs in large-scale mixed trafﬁc ﬂow, and presents its distributed implementation algorithm via ADMM. As

illustrated in Fig. 1(b), we consider an arbitrary setup of mixed trafﬁc pattern, where there might exist multiple

CAVs and HDVs with arbitrary spatial formations [6]. With local measurable data for each CAV and bidirectional

topology [2] in CAV communications, our method allows CAVs to make cooperative control decisions to reduce trafﬁc

instabilities and mitigate trafﬁc waves in a distributed manner. No prior knowledge of HDVs’ driving dynamics are

required, and safe and optimal guarantees are achieved. Precisely, the contributions of this work are as follows.

We ﬁrst present a cooperative DeeP-LCC formulation with local data for large-scale mixed trafﬁc control. Instead

of establishing a data-centric representation for the entire mixed trafﬁc system [33], we naturally partition it into

multiple CF-LCC (Car-Following Leading Cruise Control) subsystems [17], with one leading CAV and multiple

HDVs following behind (if they exist); see Fig. 1(c) for illustration of one CF-LCC subsystem. Each CAV directly

utilizes measurable trafﬁc data from its own CF-LCC subsystem to design safe and optimal control behaviors. The

interaction between neighbouring subsystems is formulated as a coupling constraint. In the case of linear dynamics

with noise-free data, it is proved that cooperative DeeP-LCC provides the identical optimal control performance

compared with centralized DeeP-LCC [33]. For practical implementation, however, cooperative DeeP-LCC requires

considerably fewer local data for each subsystem.

We then propose a tailored ADMM based distributed implementation algorithm (distributed DeeP-LCC) to solve

the cooperative DeeP-LCC formulation. Particularly, we decompose the coupling constraint between neighbouring

CF-LCC subsystems by introducing a new group of decision variables. In addition, via casting input/output constraints

as trivial projection problems, the algorithm can be implemented quite efﬁciently, leaving no explicit optimization

problems to be numerically solved. A bidirectional information ﬂow topology—common in the pure-CAV platoon

setting [2]—is needed for the ADMM iterations. Each CF-LCC subsystem exchanges only temporary computing data

with its neighbours, contributing to V2V/V2X communication efﬁciency and local trajectory data privacy.

Finally, we carry out two different scales of trafﬁc simulations to validate the performance of distributed DeeP-LCC.

The moderate-scale experiment (15 vehicles with 5CAVs) shows that distributed DeeP-LCC could cost much less

computing time than centralized DeeP-LCC, with a suboptimal performance in smoothing trafﬁc ﬂow. The exper-

iment on the large-scale mixed trafﬁc system (100 vehicles with 5% −20% CAVs), where the computation time

for centralized DeeP-LCC is completely unacceptable, further veriﬁes the capability and scalability of distributed

DeeP-LCC in real-time mitigating trafﬁc waves, saving over 31.84% fuel consumption.

1.3. Paper Organization and Notations

The rest of this paper is organized as follows. Section 2presents the input/output data of mixed trafﬁc ﬂow,

and Section 3brieﬂy reviews the previous results on centralized DeeP-LCC. Section 4presents the cooperative

DeeP-LCC formulation, and Section 5provides a tailored ADMM based distributed DeeP-LCC algorithm. Trafﬁc

simulations are discussed in Section 6, and Section 7concludes this paper.

Notation: We denote Nas the set of all natural numbers, Nj

ias the set of natural numbers in the range of [i, j]

with i≤j,0nas a zero vector of size n,0m×nas a zero matrix of size m×n, and Inas an identity matrix of

size n×n. For a vector aand a symmetric positive deﬁnite matrix X,kak2

Xdenotes the quadratic form a>Xa.

Given vectors a1, a2, . . . , am, we denote col(a1, a2, . . . , am) = a>

1, a>

2, . . . , a>

m>. Given matrices of the same

column size A1, A2, . . . , Am, we denote col(A1, A2, . . . , Am) = A>

1, A>

2, . . . , A>

m>. Denote diag(x1, . . . , xm)as

a diagonal matrix with x1, . . . , xmon its diagonal entries, and diag(D1, . . . , Dm)as a block-diagonal matrix with

matrices D1, . . . , Dmon its diagonal blocks. Finally, ⊗represents the Kronecker product.

2. Input/Output Deﬁnition of Mixed Trafﬁc Flow

Consider a general single-lane mixed trafﬁc system shown in Fig. 1(b), where there exist one head vehicle, n

CAVs, and mHDVs. The head vehicle, indexed as vehicle 0, represents the vehicle immediately ahead of the ﬁrst

CAV. The CAVs are indexed as 1,2, . . . , n from front to end. Behind CAV i(i∈Nn

1), there might exist mi(mi≥0,

i=1 mi=m) HDVs, and they are indexed as 1(i),2(i), . . . , m(i)

iin sequence. We introduce the following notations

for the set consisting of vehicle indices—Ω: all the vehicles; Nn

1: all the CAVs; F: all the HDVs; Fi: those HDVs

following behind CAV i. Precisely, we have

Fi={1(i),2(i), . . . , m(i)

i}, i ∈Nn

1;F=F1∪ F2∪ ··· ∪ Fn; Ω = Nn

1∪ F.

Note that HDV m(i)

i(if it exists) is the vehicle immediately ahead of CAV i+ 1,i∈Nn−1

1, and HDV m(n)

nrepresents

the last vehicle in this mixed trafﬁc system. It is assumed in this paper that all the vehicles, including CAVs and HDVs,

are connected to the V2X communication network. Particularly, the velocity signal of the HDVs can be acquirable by

the cloud unit in the centralized framework, or the CAVs in the distributed framework. Nevertheless, all the results

can be generalized to the case where partial HDVs have connected capabilities, which will be discussed later.

2.1. Deﬁnition for Input, Output and State

We ﬁrst specify the measurable output signals in the mixed trafﬁc system. Denote the velocity and spacing of

vehicle i(i∈Ω) at time tas vi(t)and si(t), respectively. To achieve wave mitigation in mixed trafﬁc, the CAVs

need to stabilize the trafﬁc ﬂow at a certain equilibrium state, where each vehicle moves with an identical equilibrium

velocity v∗,i.e.,vi(t) = v∗, i ∈Ω, whilst maintaining an equilibrium spacing s∗. Here for simplicity, we use a

homogeneous value s∗, but it could be varied for different vehicles.

Deﬁne the error states, including velocity errors ˜vi(t)and spacing errors ˜si(t)from the equilibrium, as follows

˜vi(t) = vi(t)−v∗,˜si(t) = si(t)−s∗, i ∈Ω,(1)

It is worth noting that in practice, not all the error states in (1) are directly measurable. The raw data from V2X

communications are mostly absolute position and velocity signals. To estimate the equilibrium velocity v∗and obtain

the velocity errors ˜vi(t), i ∈Ω, one approach is to utilize the average historical velocity of the head vehicle [36,46].

For the equilibrium spacing s∗, this value for the HDVs is generally unknown and even time-varying; in contrast, the

equilibrium spacing for the CAVs is designed by users, similarly to the desired spacing in typical CACC systems [1].

Accordingly, by appropriate design of the equilibrium spacing, the spacing errors for the CAVs ˜si(t), i ∈Nn

1can be

obtained. In this paper, we assume that the velocity of all the vehicles can be acquired via V2X communication, and

the spacing of all the CAVs can be obtained via on-board sensors. Then, the measurable signals are lumped into the

aggregate output vector y(t)of the mixed trafﬁc system, given by

y(t) = col (y1(t), y2(t), . . . , yn(t)) ∈R2n+m,(2)

where

yi(t) = h˜vi(t),˜v1(i)(t),...,˜vm(i)

(t),˜si(t)i>

∈Rmi+2, i ∈Nn

1.(3)

This output y(t)contains the velocity errors of all the vehicles and the spacing errors of only the CAVs. Regarding

the spacing errors of the HDVs, some existing studies typically assume that these signals are also acquirable; see,

e.g., [5,15,22,28,29]. Then, they consider the underlying state vector, deﬁned as

x(t) = col (x1(t), x2(t), . . . , xn(t)) ∈R2n+2m,(4)

where

xi(t) = h˜vi(t),˜v1(i)(t),...,˜vm(i)

(t),˜si(t),˜s1(i)(t),...,˜sm(i)

(t)i>

∈R2+2mi, i ∈Nn

1,(5)

and design state-feedback control strategies. This is impractical since the equilibrium spacing of the HDVs is in-

deed unknown in real trafﬁc ﬂow. In addition, note that the state (4) and the output (2) are transformed from those

in [33] via row permutation, which has no inﬂuence on the fundamental system properties, such as controllability and

observability.

We next introduce the input signals in mixed trafﬁc control. Denote the control input of each CAV as ui(t), i ∈

1, which could be the desired or actual acceleration of the CAVs [5,15,29]. Lumping all the CAVs’ control inputs,

we deﬁne the aggregate control input of the entire mixed trafﬁc system as

u(t) = u1(t), u2(t), . . . , un(t)>∈Rn.(6)

Finally, the velocity error of the head vehicle from the equilibrium velocity v∗is regarded as an external reference

input signal (t)∈Rinto the mixed trafﬁc system, given by

(t) = ˜v0(t) = v0(t)−v∗∈R.(7)

2.2. Parametric Model of Mixed Trafﬁc Flow

Based on the deﬁnitions of system state (4), input (6), (7) and output (2), model-based strategies from the liter-

ature [15,5,9,21] typically establish a parametric mixed trafﬁc model for CAV controller design. They rely on a

car-following model, e.g., IDM [47] or OVM [18], to describe the driving dynamics of HDVs, whose general form

can be written as

˙vi(t) = Fi(si(t),˙si(t), vi(t)) , i ∈ F,(8)

where ˙si(t) = vi−1(t)−vi(t)denotes the relative velocity of HDV i, and function Fi(·)represents the car-following

dynamics of the HDV index as i. In general, the HDVs have heterogeneous behaviors, which indicates that Fi(·)

could be different for different HDVs. Assume that the CAVs’ acceleration is utilized as the control input, i.e.,

˙vi(t) = ui(t), i ∈Nn

1.(9)

Through linearization around equilibrium (v∗, s∗), a linearized state-space model for the mixed trafﬁc system can be

obtained via combining the driving dynamics (8) and (9) of each individual vehicle, which is in the form of [33,35]

x(k+ 1) = Ax(k) + Bu(k) + H(k),

y(k) = Cx(k),(10)

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Distributeddata-drivenpredictivecontrolforcooperativelysmoothingmixedtrafcowJiaweiWanga,b,YingzhaoLianb,YuningJiangb,,QingXua,KeqiangLia,ColinN.JonesbaSchoolofVehicleandMobility,TsinghuaUniversity,100084Beijing,ChinabAutomaticControlLaboratory,EPFL,1024Lausanne,SwitzerlandAbstractCooperativecontr...

展开>> 收起<<

Distributed data-driven predictive control for cooperatively smoothing mixed trafﬁc ﬂow Jiawei Wangab Yingzhao Lianb Yuning Jiangb Qing Xua Keqiang Lia Colin N. Jonesb.pdf

共28页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Distributed data-driven predictive control for cooperatively smoothing mixed trafﬁc ﬂow Jiawei Wangab Yingzhao Lianb Yuning Jiangb Qing Xua Keqiang Lia Colin N. Jonesb

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: