### Abstract

Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H
_{∞}
proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.

Original language | English |
---|---|

Number of pages | 27 |

Journal | Transportation Research Part B: Methodological |

DOIs | |

Publication status | Accepted/In press - 21 Mar 2019 |

### Keywords

- Gating
- Network fundamental diagram
- Observer based control
- Robust H-infinity control
- Traffic flow

### Cite this

*H*

_{∞}robust perimeter flow control in urban networks with partial information feedback.

*Transportation Research Part B: Methodological*. https://doi.org/10.1016/j.trb.2019.03.010

}

*H*

_{∞}robust perimeter flow control in urban networks with partial information feedback'

*Transportation Research Part B: Methodological*. https://doi.org/10.1016/j.trb.2019.03.010

** H_{∞} robust perimeter flow control in urban networks with partial information feedback.** / Mohajerpoor, Reza; Saberi, Meead; Vu, Hai L.; Garoni, Timothy M.; Ramezani, Mohsen.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - H∞ robust perimeter flow control in urban networks with partial information feedback

AU - Mohajerpoor, Reza

AU - Saberi, Meead

AU - Vu, Hai L.

AU - Garoni, Timothy M.

AU - Ramezani, Mohsen

PY - 2019/3/21

Y1 - 2019/3/21

N2 - Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H ∞ proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.

AB - Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H ∞ proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.

KW - Gating

KW - Network fundamental diagram

KW - Observer based control

KW - Robust H-infinity control

KW - Traffic flow

UR - http://www.scopus.com/inward/record.url?scp=85063033265&partnerID=8YFLogxK

U2 - 10.1016/j.trb.2019.03.010

DO - 10.1016/j.trb.2019.03.010

M3 - Article

JO - Transportation Research, Series B: Methodological

JF - Transportation Research, Series B: Methodological

SN - 0191-2615

ER -

*H*

_{∞}robust perimeter flow control in urban networks with partial information feedback. Transportation Research Part B: Methodological. 2019 Mar 21. https://doi.org/10.1016/j.trb.2019.03.010