## Section: New Results

### Transportation networks and vehicular systems

#### Heterogeneity in synchronization: an adaptive control approach, with applications to vehicle platooning

Participants : S. Baldi [Univ. Delft] , P. Frasca [Contact person] .

Heterogeneity is a substantial obstacle to achieve synchronisation of interconnected systems (that is, in control). In order to overcome heterogeneity, advanced control techniques are needed, such as the use of “internal models’’ or of adaptive techniques. In a series of papers motivated by multi-vehicle platooning and coordinated autonomous driving, we have explored the application of adaptive control techniques. Our results cover both the cases of state-feedback [12] and of output-feedback [14], under the assumption that the topology of the interconnections has no circuits. Further investigation on relaxing this restrictive assumption is in progress. We also showed that agents need no leader to synchronise, even in presence of heterogeneity [13].

#### Stability of vehicle platoons with AVs

Participants : V. Giammarino [Univ. Delft] , M. Lv [Univ. Delft] , P. Frasca [Contact person] , M.l. Delle Monache, S. Baldi [TU Delft] .

A key notion to understand the impact of Autonomous Vehicles on traffic is the notion of *stability* of the vehicle collective motion. In this line of research, we have sought criteria to determine when stop-and-go waves form in platoons of human-driven vehicles, and when they can be dissipated by the presence of an autonomous vehicle. Our analysis takes the start from the observation that the standard notion of string/ring stability definition, which requires uniformity with respect to the number of vehicles in the platoon, is too demanding for a mixed traffic scenario. The setting under consideration is the following: the vehicles run along a ring road and the human-driven vehicles obey a combined follow-the-leader and optimal velocity model, while the autonomous vehicle obeys an appropriately designed model. The criteria are tested on a linearized version of the resulting platoon dynamics and simulation tests using nonlinear model are carried out [45].

#### Control and estimation using autonomous vehicles

Participants : R. Stern [Vanderbilt University] , S. Cui [Temple University] , M.l. Delle Monache [Contact person] , T. Liard, Y. Chen [Vanderbilt University] , R. Bhadani [University of Arizona] , M. Bunting [University of Arizona] , M. Churchill [UIUC] , N. Hamilton [Vanderbilt University] , R. Haulcy [Yale University] , H. Pohlmann [Temple University] , F. Wu [UC Berkeley] , B. Piccoli [Rutgers University] , B. Seibold [Temple University] , J. Sprinkle [University of Arizona] , D.b. Work [Vanderbilt University] .

It is anticipated that in the near future, the penetration rate of vehicles with some autonomous capabilities will increase on roadways. In [30], we analyze the potential reduction of vehicular emissions caused by the whole traffic stream, when a small number of autonomous vehicles are designed to stabilize the traffic flow and dampen stop-and-go waves. To demonstrate this, vehicle velocity and acceleration data are collected form a series of field experiments that use a single autonomous-capable vehicle to dampen traffic waves on a circular ring road with 20 to 21 human-piloted vehicles. From the experimental data, vehicle emissions (hydrocarbons, carbon monoxide, carbon dioxide, and nitrogen oxides) are estimated using the MOVES emissions models. We find that vehicle emissions of the entire fleet may be reduced by between 15% (for carbon dioxide) and 73% (for nitrogen oxides) when stop-and-go waves are reduced or eleiminated by the dampening action of the autonomous vehicle in the flow of human drivers. This is possible if a small fraction (5%) of vehicles are autonomous and designed to actively dampen traffic waves. In [57], we look at the problem of traffic control in which an autonomous vehicle is used to regulate human piloted traffic to dissipate stop and go traffic waves. We investigate the controllability of well-known microscopic traffic flow models: i) the Bando model (also known as the optimal velocity model), ii) the follow-the-leader model and iii) a combined optimal velocity – follow the leader model. Based on the controllability results, we propose three control strategies for an autonomous vehicles to stabilize the human piloted traffic. After, we simulate the control effects on the microscopic models of human drivers in numerical experiments to quantify the potential benefits of the controllers. Based on the simulations, finally we conduct a field experiment with 22 human drivers and a fully autonomous-capable vehicle, to assess the feasibility of autonomous vehicle based traffic control on real human piloted traffic. We show that both in simulation and in the field test an autonomous vehicle is able to dampen waves generated by 22 cars, and that as a consequence, the total fuel consumption of all vehicles is reduced by up to 20%. In [17], we consider a partial differential equation – ordinary differential equation system to describe the dynamics of traffic with autonomous vehicles. In the model the bulk flow is represented by a scalar conservation law, while each autonomous vehicle is described by a car following model. The autonomous vehicles act as tracer vehicles in the flow and collect measurements along their trajectory to estimate the bulk flow. The main result is to prove theoretically and show numerically how to reconstruct the correct traffic density using only the measurements from the autonomous vehicles.

#### Two-dimensional traffic flow models

Participants : S. Mollier, M.l. Delle Monache, C. Canudas-de-Wit [Contact person] , B. Seibold [Temple University] .

In [24], we introduce a new traffic flow model for a dense urban area. We consider a two-dimensional conservation law in which the velocity magnitude is given by the fundamental diagram and the velocity direction is constructed following the network geometry. The model is validated using synthetic data from Aimsun and a reconstruction technique to recover the 2D density from the data of individual vehicles is proposed. In [50], [49], we introduce a two dimensional and multi-layer traffic model with a new planning and decision making method in large scale traffic networks for predicting how traffic evolves in special events, emergencies and changes in the city mobility demands. The proposed method is based on a 2-D aggregated traffic model for large scale traffic networks which describes traffic evolution as a fluid in two space dimensions extended with additional state density variables, each one associated to a particular layer describing vehicles evolving in different directions. The model is a 2D-PDE described by a system of conservation laws. For this specific case, the resulting PDE is not anymore hyperbolic as typically the LWR model but results in a hybrid hyperbolic-elliptic PDE depending on the density level. In this case, usual numerical schemes may be not valid and often lead to oscillation in the solution. Thus, we consider a high order numerical scheme to improve the numerical solution. Finally, the model is used to predict how the typical traffic evolution will be impacted in particular scenarios like special events or changes in demands.

#### High-fidelity vehicle trajectory data

Participants : F. Wu [UC Berkeley] , R. Stern [Vanderbilt University] , S. Cui [Temple University] , M.l. Delle Monache [Contact person] , R. Bhadani [University of Arizona] , M. Bunting [University of Arizona] , M. Churchill [UIUC] , N. Hamilton [Vanderbilt University] , R. Haulcy [Yale University] , B. Piccoli [Rutgers University] , J. Sprinkle [University of Arizona] , D.b. Work [Vanderbilt University] , B. Seibold [Temple University] .

High fidelity-vehicle trajectory data is becoming increasingly important in traffic modeling, especially to capture dynamic features such as stop-and-go waves. In [34], we present data collected in a series of eight experiments on a circular track with human drivers. The data contains smooth flowing and stop-and-go traffic conditions. The vehicle trajectories are collected using a panoramic 360-degree camera, and fuel rate data is recorded via an on-board diagnostics scanner installed in each vehicle. The video data from the 360-degree camera is processed with an offline unsupervised algorithm to extract vehicle trajectories from experimental data. The trajectories are highly accurate, with a mean positional bias of less than 0.01 m and a standard deviation of 0.11 m. The velocities are also validated to be highly accurate with a bias of 0.02 m/s and standard deviation of 0.09 m/s.

#### Robust tracking control design for fluid traffic dynamics

Participants : L. Tumash, C. Canudas-de-Wit [contact person] , M.l. Delle Monache.

In [53] we analyze the boundary control of the traffic system described by the LWR model with a triangular fundamental diagram and a space-dependent indomain unknown disturbance, which can be described as an inhomogeneous transport equation. The controller design strategy aims first at stabilizing the deviation from the desired time-dependent trajectory and then at minimizing the deviation in the sense of two possible space-norms.

#### Urban traffic control

Participants : C. Canudas-de-Wit [Contact person] , F. Garin, P. Grandinetti.

In [20] we study near-optimal operation of traffic lights in an urban area, e.g., a town or a neighborhood. The goal is on-line optimization of traffic lights schedule in real time, so as to take into account variable traffic demands, with the objective of obtaining a better use of the road infrastructure. More precisely, we aim at maximizing total travel distance within the network, together with balancing densities across the network. The complexity of optimization over a large area is addressed both in the formulation of the optimization problem, with a suitable choice of the traffic model, and in a distributed solution, which not only parallelizes computations, but also respects the geometry of the town, i.e., it is suitable for an implementation in a smart infrastructure where each intersection can compute its optimal traffic lights by local computations combined with exchanges of information with neighbor intersections.

#### Modeling and control strategies for improving environmental sustainability of road transportation

Participants : B. Othman, G. de Nunzio [IFP Energies nouvelles] , D. Di Domenico [IFP Energies nouvelles] , C. Canudas-de-Wit [Contact person] .

As road transportation energy use and environmental impact are globally rising at an alarming pace, authorities seek in research and technological advancement innovative solutions to increase road traffic sustainability. The unclear and partial correlation between road congestion and environmental impact is promoting new research directions in traffic management. We review the existing modeling approaches to accurately represent traffic behavior and the associated energy consumption and pollutant emissions [26]. The review then covers the transportation problems and control strategies that address directly environmental performance criteria, especially in urban networks. A discussion on the advantages of the different methods and on the future outlook for the eco-traffic management completes the proposed survey.

#### Data analysis for smart multi-modal transportation planning

Participants : A. Kibangou [Contact person] , T. Moyo [Univ. of Johannesburg] , W. Musakwa [Univ. of Johannesburg] .

Modern cities have managed to balance the relationship between supply and demand of services through clear planning strategies which advocate smart solutions to the ever increasing demand for public tranportation services. The end goal is not to prohibit citizens to use their private cars, but to create an enabling smart system at a suitable scale which would lead to citizens not needing to own or drive a car. Having an efficiently and effectively run public transportation system is a crucial and indispensable factor for any developing city region. However as the provision of public transportation is a multifaceted process, with intertwining elements such as culture, politics,finance and shareholder interests, smart means of monitoring and mitigating the challenges faced in the provision of public transportation need to be developed continuously. The Gauteng city region is likewise faced with this challenge. With this region being the economic hub of South Africa, this has greatly affected the operation of the Gautrain system and the BRT systems within the region, as more and more people require a fast and reliable transportation means to move in and out the metropolitan cities. The study relied on a questionnaire-based survey that was administered to 60 respondents. The questionnaire had both closed and open-ended questions which were administered online through Google forms so as to obtain a good response rate from commuters who reside within the study area. The questions centred on identifying factors influencing the commuter’s travelling patterns. Gautrain Management Agency reports and literature were also utilised to supplement infomation gleaned from the questionnaire. Besides the questionnaire, secondary data was collected from Twitter (tweets) concerning the Gaubus and Gautrain (between the period of August to November 2018). Posts from 380 users were analysed. This data was used to spatially identify POI of Gaubus users and also to identify the spatial relationship between land use activities, Gaubus routes, Gaubus stops, Gautrain stations and Guatrain routes. A neighboorhood analysis was run using a focal statistics based tool to map the spatial distribution of commuters of the Gaubus [56].

#### Location of turning ratio and flow sensors for flow reconstruction in large traffic networks

Participants : M. Rodriguez-Vega, C. Canudas-de-Wit [Contact person] , H. Fourati.

We examine the problem of minimizing the number of sensors needed to completely recover the vehicular flow in a steady state traffic network [28]. We consider two possible sensor technologies: one that allows the measurement of turning ratios at a given intersection and the other that directly measures the flow in a road. We formulate an optimization problem that finds the optimal location of both types of sensors, such that a minimum number is required. To solve this problem, we propose a method that relies on the structure of the underlying graph, which has a quasi-linear computational complexity, resulting in less computing time when compared to other works in the literature. We evaluate our results using dynamical traffic simulations in synthetic networks.