# Consensus-Based Cooperative Control Based on Pollution Sensing and Traffic Information for Urban Traffic Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Review of Pollution and Traffic Sensing Systems

#### 2.1. Pollution Sensing Systems

_{2}, O

_{3}, CO, carbon dioxide (CO

_{2}), mono-nitrogen oxides (NO

_{x}), PM, and volatile organic compounds (VOCs), in different range of sensitivity, selectivity and response time. Depending on the application, the sensor can be chosen with the required specific parameters e.g., in [22] an O

_{2}with a sampling time of 1.6 s and NO

_{2}with a sampling time of 41 s are selected.

#### 2.2. Traffic Sensing Systems

## 3. General Scenario and the Proposed Solution

#### 3.1. Modeling

- ${X}_{M}=\left\{\left(p,v\right)|p\in IPorts,\text{}v\in {X}_{p}\right\}$ is the set of input ports (p) and values (v)
- ${Y}_{M}=\left\{\left(p,v\right)|p\in OPorts,\text{}v\in {Y}_{p}\right\}$ is the set of output ports (p) and values (v)
- $S$ is the set of states
- ${\delta}_{int}:S\to S$ is the internal transition function
- ${\delta}_{ext}:Q\times {X}_{M}^{b}\to S$ is the external transition function
- ${\delta}_{con}:Q\times {X}_{M}^{b}\to S$ is the confluent transition function
- $Q=\left\{\left(s,e\right)|s\in S,\text{}e\in \left[0,{t}_{a}\right]\right\}$ is the total state set and e is the time since the previous transition
- $\lambda :S\to Y$ is the output function
- ${t}_{a}:S\to {R}_{0}^{+}\cup \infty $ is the time advance function

- Traffic-light control unit (TLC)
- Pollution-monitoring service
- Traffic system (i.e., road network, vehicles, traffic lights, etc.)
- Other pollution sources

#### 3.2. Consensus-Based Cooperative Control Design

#### 3.2.1. System Dynamics

- ${\epsilon}_{i}\left(k\right)$ [gNO
_{x}/m^{3}] is the state of the system $i$ at instant $k$. The state of the system is related to the pollution levels and the traffic state at each intersection. The pollutant considered in this study is NO_{x}(mononitrogen oxides). - $\xi \left(k-n\right)$ [gNO
_{x}/m^{3}] is a system input. It contains the pollution information provided to the TLCs at instant $k-n$ where $n$ is the delay between pollution production and pollution information reception by the TLCs. - ${\alpha}_{i}$ is a dimensionless parameter that represents the contribution of intersection $i$ to overall city pollution. It is computed on the basis of the maximum occupancy of intersection $i$ over the total maximum occupancy.
- ${x}_{i}\left(k-m\right)$ [veh] is a system input. It contains the summation of vehicle queues at every approach of the intersection controlled by TLC
_{i}. $m$ represents the delay between traffic queue measurement and traffic information reception at TLC_{i}. - $\beta $ [gNO
_{x}/veh/m^{3}] is the pollutant emissions of a given traffic queue at an intersection. $\beta =\frac{q\xb7F}{{10}^{3}\xb7\mathsf{\Delta}t}$, where $q$ is the emission factor of the pollutant (gNO_{x}/veh/km), $F$ is the dispersion factor of the pollutants (s/m^{2}) and $\mathsf{\Delta}t$ is the simulation step [31]. - $\mathsf{\Delta}{u}_{i}$ [% T.L. cycle] is the consensus-based cooperative control output of TLC
_{i}. The control signal is a percentage change of the cycle length of the traffic lights with respect to the initial cycle length in a limited range. This component is defined later (control law design). - $\gamma $ [gNO
_{x}/m^{3}/% T.L. cycle] represents the influence of the pollutant emissions on traffic-light timing. $\gamma =\beta {\gamma}^{\prime}$, where ${\gamma}^{\prime}$ [veh/% T.L. cycle] is a parameter that represents the queue length with respect to changes in traffic-light cycle lengths. Therefore there is a proportional relationship between $\gamma $ and ${\gamma}^{\prime}$.

#### 3.2.2. Design of a Consensus-Based Control Strategy

- $\lambda $ is a parameter that refers to system stability. If $\lambda \in \left(0,{\theta}^{-1}\right]$, where $\theta $ is the maximum degree of the graph, consensus convergence is guaranteed in a connected graph [32].
- ${a}_{ij}$ is the corresponding value of the adjacency matrix.

#### 3.3. Open-Loop Simulation for Test Scenario: Pollution and Traffic-Based Control Are Switched Off

_{x}emissions of the whole scenario, also in a time window of 20 s. As can be noted, there are no vehicles in the scenario at the beginning of the simulation. Nonetheless, after 100 s from the start of the simulation, the vehicle numbers stabilize.

#### 3.4. Consensus-Based Control Applied to the Test Scenario

- The pollutant considered in this work was NO
_{x}. The NO_{x}produced by vehicles was taken from the HBEFA [37], assuming the vehicles were passenger cars built between 2005 and 2015 (0.35 gNO_{x}/veh/km). - The DEVS model of “Other pollution sources” produces pollution information every 5 s from statistical data of a common urban area, without taking into account the traffic contribution to the pollution. It generates random numbers from the normal distribution with mean: μ
_{Eo}= 30.36 µgNO_{x}/m^{3}and standard deviation σ_{Eo}= 10.48 µgNO_{x}/m^{3}. - The DEVS model “Pollution monitoring” filters the input data by using a moving average filter with a window size of 100 s and outputs a value every 10 s.
- The execution period of TLC DEVS model is 1 s. It filters the input traffic data using a moving average filter with a window size of 100 s.
- The value of $\lambda $ was set to 0.15 to guarantee consensus stability ($\lambda \in \left(0,1/\theta \right]$).
- At each TLC, a threshold value of variation of 1% was defined for $\mathsf{\Delta}{u}_{i}$, in order not to send continuous new ${u}_{i}$ values to the traffic lights when the variation of ${u}_{i}$ is minimal.
- The value of ${\gamma}^{\prime}$ was estimated by applying a linear regression with values obtained via simulation. The adopted value was 12.68 [veh/% T.L. cycle].

## 4. Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 10.**Close-loop simulation results: (

**a**) Consensus variable ($\mathsf{\epsilon}$); (

**b**) Control input ($\mathsf{\Delta}u$); (

**c**) Vehicle queues ($x$); (

**d**) Pollution level ($\mathsf{\xi}$) (closed-loop and open-loop).

Variable | Description |
---|---|

Ev | Vehicle emissions monitoring |

Eo | Other emissions |

$\xi $ | Area-wide air-quality information. Includes current pollution-status details for a given geographic area. |

$\epsilon $ | Consensus variable that represents the TLC dynamics (see Section 3.2.1) |

$x$ | Processed traffic-detector data which allows derivation of traffic-flow variables (density, occupancy, flow measures, etc.). It can be represented as a vector that refers to the signal of each sensor. |

$u$ | Data flow contains the system configuration data for a traffic signal controller. It includes the parameters required to reconfigure its operations. |

Component | Expression | Description |
---|---|---|

1 | ${\alpha}_{i}\xi \left(k-n\right)$ | Feed-forward action related to local pollution data. |

2 | $\beta {x}_{i}\left(k-m\right)$ | Feed-forward action related to local traffic data. |

3 | $\lambda {\displaystyle {\displaystyle \sum}_{j\in {N}_{i}}}{a}_{ij}\left({\epsilon}_{i}-{\epsilon}_{j}\right)$ | Consensus-based control signal that makes use of information from the neighbor of each network node. |

Variable | Value |
---|---|

Length (m) | 5.00 |

Minimum gap (m) | 2.50 |

Maximum speed (m/s) | 55.56 |

Maximum acceleration (m/s^{2}) | 2.60 |

Maximum deceleration (m/s^{2}) | 4.50 |

Imperfection | 0.50 |

Reaction time (s) | 1.00 |

Person capacity | 4 |

KPI | Open-Loop | Closed-Loop | Differences Relative to Open-Loop | |
---|---|---|---|---|

Vehicle queues 1. $\frac{1}{{t}_{f}-{t}_{s}}{\int}_{{t}_{s}}^{{t}_{f}}\parallel x\parallel dt$ | μ | 13.4815 | 12.0382 | 10.70% |

max | 15.0661 | 13.6345 | 9.50% | |

Global pollution 2. $\frac{1}{{t}_{f}-{t}_{s}}{\int}_{{t}_{s}}^{{t}_{f}}\parallel \xi \parallel dt$ | μ | 2.3879×10^{−4} | 2.3791×10^{−4} | 0.37% |

min | 2.2732×10^{−4} | 2.1910×10^{−4} | 3.62% |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Artuñedo, A.; Del Toro, R.M.; Haber, R.E. Consensus-Based Cooperative Control Based on Pollution Sensing and Traffic Information for Urban Traffic Networks. *Sensors* **2017**, *17*, 953.
https://doi.org/10.3390/s17050953

**AMA Style**

Artuñedo A, Del Toro RM, Haber RE. Consensus-Based Cooperative Control Based on Pollution Sensing and Traffic Information for Urban Traffic Networks. *Sensors*. 2017; 17(5):953.
https://doi.org/10.3390/s17050953

**Chicago/Turabian Style**

Artuñedo, Antonio, Raúl M. Del Toro, and Rodolfo E. Haber. 2017. "Consensus-Based Cooperative Control Based on Pollution Sensing and Traffic Information for Urban Traffic Networks" *Sensors* 17, no. 5: 953.
https://doi.org/10.3390/s17050953