Data driven model free adaptive iterative learning perimeter control for large-scale urban road networks

Highlights

• An iterative form dynamic linearization description is extended.

• A model free adaptive iterative learning perimeter control strategy is proposed.

• A comprehensive comparison is conducted with typical perimeter control strategies.

Abstract

Most perimeter control methods in literature are the model-based schemes designing the controller based on the available accurate macroscopic fundamental diagram (MFD) function with well known techniques of modern control methods. However, accurate modeling of the traffic flow system is hard and time-consuming. On the other hand, macroscopic traffic flow patterns show heavily similarity between days, and data from past days might enable improving the performance of the perimeter controller. Motivated by this observation, a model free adaptive iterative learning perimeter control (MFAILPC) scheme is proposed in this paper. The three features of this method are: (1) No dynamical model is required in the controller design by virtue of dynamic linearization data modeling technique, i.e., it is a data-driven method, (2) the perimeter controller performance will improve iteratively with the help of the repetitive operation pattern of the traffic system, (3) the learning gain is tuned adaptively along the iterative axis. The effectiveness of the proposed scheme is tested comparing with various control methods for a multi-region traffic network considering modeling errors, measurement noise, demand variations, and time-changing MFDs. Simulation results show that the proposed MFAILPC presents a great potential and is more resilient against errors than the standard perimeter control methods such as model predictive control, proportional-integral control, etc.

Introduction

Urban traffic signal control is widely used to alleviate congestion all over the world. In the past decades, a number of methods for urban traffic control systems have been developed, such as SCOOT (Robertson and Bretherton, 1991), SCATS (Lowrie, 1982), TUC (Diakaki et al., 2002), and max pressure (Varaiya, 2013). However, accuracy and computational burden challenge the possible successful application of these optimization and control methods due to the requirement of the detailed models of the controlled urban networks. Moreover, these controllers make decisions at a local level without considering network effects, which may lead to suboptimal solutions due to congestion propagation. Therefore, developing an aggregated model for large-scale road networks is essential for both efficiency and reliability reasons. The macroscopic fundamental diagram (MFD) of urban traffic networks attracts increasing interest in literature owing to its potential in enabling the development of low complexity network-level traffic models, and ultimately the design of real-time management systems for large-scale urban networks.

The idea of MFD was first proposed in Godfrey (1969), but its existence with dynamic features has not been verified until 2008 by the empirical data of Yokohama (Geroliminis and Daganzo, 2008). Thereafter there has been an increased interest in MFD as numerous contributions have been made including theoretical analyses of the MFD, region partitioning via clustering, network-wide traffic modeling and control system design via actuation over perimeter control. Nevertheless, the heterogeneous distribution of congestion and hysteresis phenomena (Geroliminis and Sun, 2011, Gayah and Daganzo, 2011, Mahmassani et al., 2013) may affect the presence of a well-defined MFD. To overcome these drawbacks, one alternative way is to partition the large heterogeneous network into several homogeneous sub-regions. Various clustering algorithms for static and dynamic configuration have been developed to network partitioning, such as (Ji and Geroliminis, 2012, Saeedmanesh and Geroliminis, 2016, Saeedmanesh and Geroliminis, 2017, Lopez et al., 2017, Casadei et al., 2018). Clustering provides the possibility to build multi-region MFD models that can be integrated in perimeter control.

Based on MFD-based dynamical models, traffic control schemes for the perimeter control (i.e., regulating a set of traffic lights on the boundary between two neighbouring regions) are proposed to improve urban traffic conditions. The application of perimeter control to single region networks can be found in Daganzo, 2007, Haddad, 2017a, Haddad and Shraiber, 2014, Keyvan-Ekbatani et al., 2012, Keyvan-Ekbatani et al., 2015a. In Keyvan-Ekbatani et al. (2012), a proportional-integral (PI) feedback controller is involved. These results are extended to the case with time-delays in Keyvan-Ekbatani et al. (2015a). Considering traffic system uncertainty, a robust PI perimeter controller is designed by transforming the plant into a linear parameter-varying model in Haddad and Shraiber (2014). In Haddad, 2017a, the optimal control laws are proposed for both coupled and decoupled perimeter control inputs. Perimeter control is also applied to two-region urban networks with MFD-based dynamics. The two-region perimeter control problem is first formulated in Haddad and Geroliminis (2012) and stability conditions for stable equilibrium are derived. Boundary conditions and controllability issues are investigated in Zhong et al. (2018). In Geroliminis et al., 2013, Haddad, 2017b, model predictive control (MPC) is used to design the perimeter controller for two-region systems.

There are also recent works focusing on multi-region MFD networks. In Aboudolas and Geroliminis (2013), a multivariable linear quadratic regulator (LQR) is designed by linearizing the model at an equilibrium point. A practical multiple concentric PI controller is proposed in Keyvan-Ekbatani et al. (2015b). In order to adapt to different traffic conditions, the controller in Aboudolas and Geroliminis (2013) is enhanced by online adaptive optimization in Kouvelas et al. (2017), which is the first study in the literature where gains are updated based on historical data and performance of the controller from day to day. MPC is also applied to multi-region networks in Ramezani et al., 2015, Fu et al., 2017, Zhou et al., 2017, Sirmatel and Geroliminis, 2018. In Haddad and Mirkin, 2016, Haddad and Mirkin, 2017, the centralized and distributed adaptive perimeter control approaches are proposed, respectively. In the recent work Lei et al. (2019), a decentralized estimation and decentralized MFAC method is applied to perimeter control to solve the strong-coupled interconnections between sub-regions. The other kinds of MFD-based modeling and perimeter control methods could also be found in: integration of agent-based modeling with MFD (Kim et al., 2018a), modeling of macroscopic flows considering link level capacity (Kim et al., 2018b), hybrid PI control (Ding et al., 2018), control via vehicle routing (Menelaou et al., 2017), optimal control (Aalipour et al., 2019), congestion pricing in a connected vehicle environment (Yang et al., 2019), uncertainty modeling (Gao and Gayah, 2018) and robust control (Zhong et al., 2017, Ampountolas et al., 2017, Mohajerpoor et al., 2019).

However, almost all of the aforementioned methods are model-based. Due to the inevitable unmodelled dynamics and unknown demand uncertainty, the mismatch between the model predictions and the plant is a potential source of problems for model-based perimeter control. For this reason, it is worth investigating perimeter control methods independent of the dynamical model. On the other hand, traffic flow patterns usually show similarity from a macroscopic point of view (Hou and Xu, 2003, Hou et al., 2008, Hou and Li, 2016), even if individual roads might have strong daily variations. In such circumstances, the performance of the controller would improve greatly by making full use of the repeatability and similarity of a traffic system.

Iterative learning control is an effective method to deal with repeated control processes. It was originally proposed in Arimoto et al. (1984), and has been extensively developed in the past 30 years with various learning controllers including proportional derivative (PD) type ILC (Saab, 2003), norm optimal ILC (Amann et al., 1996) and Lyapunov-based adaptive ILC (Tayebi, 2004). In Hou and Xu (2003), ILC is first applied to the traffic system to solve the density control problem of freeways. For more detailed reviews of ILC, readers are pleased to read the survey papers (Bristow et al., 2006, Xu, 2011). Although ILC is widely studied, some fundamental limitations still exist. Controller design of the norm optimal or Lyapunov-based adaptive ILC requires model dynamics, and the selection of the learning gain of PD-type ILC is nontrivial. Recently, data-driven model-free adaptive ILC (MFAILC) (Chi and Hou, 2007, Chi et al., 2015, Bu et al., 2019) has been proposed on a new type of dynamic linearization (DL) data modeling technique (Hou and Jin, 2013). Distinguished from the existing other linearization methods, such as Taylor’s, input-output linearization method, etc. (Hou et al., 2017), the DL data modeling technique does not linearize the system at a fixed point but builds an equivalent linearization data model at each operation point. Using only input and output (I/O) data, all the parameters of this dynamic linearization data model can be estimated and then the controller is designed. Considering different memory lengths of the considered system, the DL data model can be classified into three forms: the compact-form dynamic linearization (CFDL) data model, the partial-form dynamic linearization (PFDL) data model, and the full-form dynamic linearization (FFDL) data model (Hou and Jin, 2013). By virtue of the DL data modeling technique, two critical assumptions, identical initial condition and identical trajectory, to traditional ILC, can be relaxed in the MFAILC method. It is also worthwhile pointing out that MFAILC is a branch of model free adaptive control (MFAC), which has been developed into a systematic framework in the past 20 years (see Hou et al., 2017, Hou and Jin, 2013, Hou and Xiong, 2019, Liu and Yang, 2019, Wu et al., 2019 for some recent progress of MFAC). Until now, MFAC has been applied successfully to over 150 different fields (see Hou and Wang, 2013, Hou et al., 2017 for the survey of MFAC approaches). Since the urban traffic network has following outstanding features, that is, repetitive operation pattern is obvious, the traffic system modeling is difficult, and the traffic system data are easy to be obtained, these features motivate us using the MFAILC method in this paper to deal with the perimeter control problem.

The main contributions are as follows.

• (1) The time domain DL description used in Lei et al. (2019) is extended to the multi-input and multi-output (MIMO) iterative form, which presents the relationship of multi-region urban traffic network dynamics between successive iterations.

• (2) Based on the novel iterative DL description, a data-driven model free adaptive iterative learning perimeter control (MFAILPC) strategy is employed in the multi-region urban traffic network in the first time. In particular, the proposed method is compared with other several typical perimeter algorithms in a comprehensive way.

Three attractive properties of this method are as follows.

• (1) The data-driven feature: the controller design and implementation are independent from the traffic plant model, i.e., the system modeling and regional demand profiles are not needed in the perimeter control. Instead, it only requires I/O data of the traffic network, which means complication due to plant-model mismatch is avoided. Note that the critical accumulation used in the algorithm is an input to the method, which is separated from the controller design and not related to the data-driven feature.

• (2) The iterative learning feature: the controller obtains ”experience” from the historical data stored in the data base. In other words, the perimeter control performance will improve over iterations.

• (3) The adaptive feature: by estimating the pseudo Jacobian matrix, the learning gain is updated iteratively, which implies the learning gain selection problem in the tradition ILC method disappears.

The rest of the paper is organized as follows. In Section 2, the urban traffic system dynamics is described using MFD. In Section 3, the MFAILC based perimeter control strategy is introduced in detail. In Section 4, simulation results compared with other typical perimeter control strategies are given. The main conclusions and future works are summarized in Section 5.