## Section: New Results

### Transportation networks and vehicular systems

#### Traffic estimation and prediction

Participants : C. Canudas de Wit [Contact person] , A. Kibangou, L. Leon Ojeda, F. Morbidi.

In the PhD thesis of Leon Ojeda, we have been concerned with the design of a methodology for the real-time multi-step ahead travel time forecasting using flow and speed measurements from an instrumented freeway. Two main methodologies have been considered. The first one, a signal-based, uses only speed measurements collected from the freeway, where a mean speed is assumed between two consecutive collection points. The travel time is forecasted using a noise Adaptive Kalman Filter (AKF) approach. The process noise statistics are computed using an online unbiased estimator, while the observations and their noise statistics are computed using the clustered historical traffic data. Forecasting problems are reformulated as filtering ones through the use of pseudo-observations built from historical data. The second one, a model-based, uses mainly traffic flow measurements. Its main appealing is the use of a mathematical model in order to reconstruct the internal state (density) in small road portions, and consequently exploits the relation between density and speed to forecast the travel time. The methodology uses only boundary conditions as inputs to a switched Luenberger state observer, based on the “Cell Transmission Model" (CTM), to estimate the road initial states. The boundary conditions are then forecasted using the AKF developed above. Consequently, the CTM model is run using the initial conditions and the forecasted boundaries in order to obtain the future evolution of densities, speeds, and finally travel time. The added innovation in this approach is the space discretization achieved: indeed, portions of the road, called “cells", can be chosen as small as desired and thus allow obtaining a finer tracking of speed variations. The developed methodologies were assessed using the city-lab GTL [31] . Features and activities of this platform are described in [39] .

#### Traffic control

Participants : C. Canudas de Wit [Contact person] , D. Pisarski.

The work was mainly focused on the final design of a distributed controller and its implementation to the model of the south ring of Grenoble in the context of the project Hycon2. For the sake of the controller design, a distributed optimal control method for balancing of freeway traffic density was studied. The optimization was performed in a distributed manner by utilizing the controllability properties of the freeway network represented by the Cell Transmission Model. By using these properties, the subsystems to be controlled by local ramp meters were identified. The optimization problem was then formulated as a non-cooperative Nash game. The game was solved by decomposing it into a set of two-players hierarchical and competitive games. The process of optimization employed the communication channels matching the switching structure of system interconnectivity. By defining the internal model for the boundary flows, local optimal control problems were efficiently solved by utilizing the method of Linear Quadratic Regulator. The developed control strategy was tested via numerical simulations on the macroscopic model in two scenarios for uniformly congested and transient traffic. The controller was also validated through a microscopic simulations with the use of Aimsun software. The controller was implemented through Matlab under which a relevant program simulating distributed architecture was designed. The controller was then plugged to the Aimsun micro-simulator. The simulated scenario was based on real traffic data collected from the south ring of Grenoble. Were examined both, the balancing metric (optimized) and a set of standard traffic metrics (not optimized). The results showed that the balancing has a positive impact on the traffic flow, in particular, by smoothing the vehicle dynamics, it can potentially increase the average velocity (and thus, reduce the travelling time) and reduce the fuel consumption (and related emissions). The proposed modular architecture enabled to perform the optimization for long freeway sections in the real-time.

#### Control of urban traffic networks

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

This work deals with efficient operation of urban traffic networks, by controlling traffic lights. A first contribution has been to devise a model for urban networks, based on the Cell-Transmission-Model adapted to signalized intersections, and then simplified with an average-based approximation. Then, based on this model, a control law has been designed, where the duty cycle of each traffic light is optimized in real time, globally considering the whole network. We have chosen a simple one-step-ahead optimization, which can be formulated as a linear program, thus resulting in simple and fast optimization. This work is part of the PhD thesis of Pietro Grandinetti.

#### Stability of Monotone Dynamical Flow Networks

Participants : E. Lovisari [Contact person] , G. Como [U. Lund] , K. Savla [U. of Southern California] .

The stability properties of monotone dynamical flow networks are studied [22] . Demand and supply functions relate states and flows of the network, and the dynamics at junctions are subject to fixed turning rates. Our main result consists in the characterization of a stability region such that: If the inflow vector in the network lies strictly inside the stability region and a certain graph theoretical condition is satisfied, then a globally asymptotically stable equilibrium exists. In contrast, if the inflow vector lies strictly outside the region, then every trajectory grows unbounded in time. As a special case, our framework allows for the stability analysis of the Cell Transmission Model on networks with arbitrary topologies. These results extend and unify previous work by Gomes et al. on stability of the Cell Transmission Model on a line topology as well as that by the authors on throughput optimality in monotone dynamical flow networks.

#### Control of communicating vehicles in urban environment

Participants : C. Canudas de Wit [Contact person] , G. de Nunzio.

The stability properties analysis of the Variable Length Model (proposed by Prof. Canudas de Wit in 2011), adapted to the urban environment was studied. It has been found that the canonical definition of Lyapunov stability for the equilibrium points does not hold for the system under analysis. A different approach for the analysis of the stability properties of the system has been introduced. Furthermore, an energy map of the equilibrium points has been obtained. Namely, a cost was associated with each feasible equilibrium point of the system, thus obtaining an assessment of the efficiency of any operation point of the system. A Variable-Speed-Limits tracking controller of the desired operation point (i.e. equilibrium) has been also devised, in order to simulate the response of the driver to the energy-efficient speed advisory. This work was submitted and accepted at the IEEE Conference on Decision and Control 2014, with the title “Urban Traffic Eco-Driving: Speed Advisory Tracking”. A previous work on the steady-state analysis of the Variable Length Model in urban environment was carried out in [27] . The effort has been put also on the validation of the macroscopic model (i.e. the Variable Length Model), used for traffic evolution prediction and control synthesis. The validation procedure was run with a microscopic traffic simulator, and aims at proving that the evolution of the state of the mathematical model replicates accurately the true evolution of the traffic conditions. In particular, an important variable modeled by the system is the length of the congested area of the road section under analysis, which may be thought of as the queue length. It has been shown that the macroscopic model is able to depict the evolution in time of the queue length, with only a small error with respect to the real congestion simulated by the highly-detailed microscopic simulator. Furthermore, the validation process aims, not only at confirming the reliability of the dynamical model, but also the accuracy of the energy consumption model and the other macroscopic traffic performance metrics that have been defined in order to formulate the optimization problem. Within the COMFORT project exchange program, the work on bandwidth maximization on signalized arterials by introducing VSL as an additional degree of freedom, and by considering the energetic aspects of the problem was expanded. The canonical bandwidth maximization problem is defined as the maximization of the time interval that the vehicles can use to drive though a sequence of signalized intersections without stopping; this is achieved solely by offset control. The extension of this framework aims at showing that the additional degree of freedom (i.e. variable speed limits) improves in every case the bandwidth. A further simulation campaign in a microscopic simulator shows the benefits of the theoretical bandwidth maximization on the standard traffic performance metrics. In particular, fluidity of traffic and lower number of stops result to be highly beneficial in terms of energy consumption, without losing much in terms of traveling time.