Model Free Adaptive Predictive Perimeter Control for an Urban Traffic
Network
Chunye Xu
1
, Shangtai Jin
1
, Ye Ren
1
,Zhongsheng Hou
1
, Danwei Wang
2
1. Advanced Control Systems Lab, Beijing Jiaotong University, Beijing, China, 100044
1
E-mail: 16125125@bjtu.edu.cn, shtjin@bjtu.edu.cn, 14111048@bjtu.edu.cn,, zhshhou@bjtu.edu.cn
2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
E-mail: edwwang@ntu.edu.sg
Abstract: Most exiting macroscopic fundamental diagram (MFD) based perimeter control methods are regarded as model-based
feedback control methods, whose performance is hard to improve in practice due to the fact that traffic flow model is complex
and has uncertainties. In this paper, a model free adaptive predictive perimeter control strategy is proposed for an urban traffic
network. The control performance is improved by virtue of the prediction data model derived by dynamic linearization technique.
The effectiveness of the proposed perimeter control algorithm is verified by comparing with the traditional PID controller in the
simulation section.
Key Words: perimeter control, macroscopic fundamental diagram (MFD), model free adaptive predictive perimeter control
(MFAPPC)
1 Introduction
In 2008, Geroliminis N. and Daganzo C.F. observed the
traffic experiment data of downtown Yokohama and found
that there was a one-peak and low-dispersion relationship
between the average traffic flow and average vehicle density
of the urban traffic network
[1]
. Moreover, this relationship
was then named macroscopic fundamental diagram (MFD)
which is an inherent attribute of the urban road network. The
MFD can be used to visually observe the operation level of
the urban road network under the current control strategy,
evaluate the quality of the control strategy and facilitate
managers to take different control measures according to the
observed level of road network. Therefore, MFD can be
used to improve road accessibility and ease urban
congestion.
In Ref. [2], Geroliminis N. and Sun J. investigated the
properties of a well-defined MFD of an urban area. In Ref.
[3], Zheng N. and Geroliminis N. proposed a macroscopic
multi-zone road network model based on multi-model MFD.
The total passenger travel time is optimized by tuning the
proportion of various modalities. In Ref. [4], the
heterogeneous area was divided into two approximately
homogenous regions and the corresponding control strategy
was designed. In Ref. [5], the heterogeneous area was
divided into three homogenous regions. Under different
MFD shapes, the feedback perimeter control (FPC) in Ref.
[5] shows the superioty by comparing with bang-bang
control at the boundary. In [6], a three-dimensional MFD is
proposed for mixed bi-modal urban networks with buses and
cars sharing the same road infrastructure. In [7], the MFD
based feedback gating control is applied at junctions located
upstream of the protected network rather than the border.
In addition to model-based control with MFD, model
predictive control (MPC) is also widely used and studied.
Typical MPC methods include model predictive heuristic
1
This work is supported by National Nature Science Foundation under Grant (61573054, 61433002, 61573129)
control (MPHC)
[8]
, dynamic matrix control (DMC)
[9]
, and
generalized predictive control
(GPC)
[10]
. At present, MPC
methods have been successfully applied in the transportation
field. Although the traditional MPC methods have the
advantages of good control effect and robustness, it still
requires that the controlled system model is known and the
modelling accuracy directly affects the control effect. The
existing theoretical research on MPC is mostly aimed at
linear systems
[11-17]
. There is still a lot of work to be done
on predictive control methods of nonlinear system
[18-20]
.
Due to the effects caused by unmodelled dynamics, the
model-based control algorithms have many limitations,
which may lead to the performance degradation in some real
application. In Ref. [21], a model free adaptive predictive
control (MFAPC) was proposed to overcome the above
mentioned limitation. Unlike traditional model based
control methods, MFAPC presents a new way to deal with
the dynamic systems with high uncertainties, and requires
less priori knowledge and computation, which is adaptable
and easy to implement. More importantly, it does not depend
on the accurate system model. In this paper, a model free
adaptive predictive perimeter control (MFAPPC) is applied
to relieve the traffic congestion in the urban traffic network.
The simulation results in different scenarios show the
superiority comparing with PID.
2 Problem Formulation
The MFD of the urban traffic network is defined by
11
(())Gnt
which is the trip completion flow for the region
at
1
()nt
. The trip completion flows of the network consist
of two kinds of trip completion, one of the completion flows
is the transfer flow with internal origin and external
destination, and the other completion flow is the internal
completion with internal origin and internal destination. It is
374
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