Section: New Results
Vehicular transportation systems
Traffic modelling, estimation and control
Participants : C. Canudas de Wit [Contact person] , C. IrinelConstantin [CRAN] , D. Pisarski, L. Leon Ojeda.
This part is related to the developed work within the Network of Excellence HYCON2 (HighlyComplex and Networked Control Systems). It interested to problems of modelling, estimation and control in traffic.
In [81] , the problem of equilibrium sets for the Cell Transmission Model is studied. The objective is to design the homogeneous distribution of density on the freeway, where the input flows are the decision parameters to be determined. For the proper design of the balanced density the extensive analysis on the structures of equilibria is crucial. The analysis is carried out for the two different cases, where all sections of the freeway are assumed to be free or congested, respectively. The necessary conditions for the existence of balanced equilibria are formulated. These conditions show, that the key for the design of the balanced states may be the variable speed limiting, which strictly cooperates with the ramp metering. The computational algorithm for the input flows in case of free balance is proposed. In order to illustrate the results, the numerical example is provided.
In [39] , the authors are interested to the highway traffic modelbased density estimation. A strategy is proposed for realtime density estimation for trafﬁc networks. To this aim, we introduced a deterministic constrained macroscopic model which reduce the number of possible afﬁne dynamics of the system and preserve the number of vehicles in the network. This model is used to recover the state of the trafﬁc network and precisely localize the eventual congestion front. The state of the network is recovered using what we call forward/backward observers. We pointed out that during unobservable modes the estimation error is preserved due to vehicle conservation law. Numerical simulations show the efﬁciency of the proposed strategy.
In [30] , the problem of front congestions control is treated. For this, we have introduced a new trafﬁc lumped model with only two cells (one free, and another congested) the cells have variable length, and a variation law for the front congestion completes the 3dimensional model. In opposition to ﬁxedlength cell models that are commonly represented by a set of linear statedependent switching systems, our model results in a lower dimensional nonlinear system which solutions are continuous. Based on this model, we have designed a “besteffort” control strategy using variable speed limits. The notion of best effort control is here linked to the physical variable speed limit constraints which limits its size and as well as its rate variation. This results in a relative simple control in closedform that can be implemented by using only information about the front congestion location.
Other work is under development and is related to the traffic show case application and the achievements reached that correspond to the operation of the freeway network around the Grenoble area (Grenoble South Ring). We started by designing the general network architecture, after specifying sensors and actuators locations along the highway and finally setting the platform of an interface between Matlab and our micro simulator "Aimsun". We have also carrying out some simulations from a real life application on Grenoble South ring of a deterministic state estimation technique. Using constrained macroscopic model which in fact reduces the number of dynamic states and preserves the conservation law (number of vehicles in the network).
Vehicle control

Teleoperated control
Participants : C. Canudas de Wit [Contact person] , W. Jiang, J. Dumon, O. Sename.
A mathematical driver model in the spatial equation form has been introduced for analysis of drivers' behavior [31] . In the model, a previewed distance is taken into account. First, optimal control is applied. For the ideal case without driver's reaction delay concerned, for both long distance preview and shorter one, the vehicle tracks well the path. Whereas, when timedelay added into the system, too short preview distance cause the instability of the system. The simulation result corresponds with the real driving experience. Then, LyapunovKrasovskii functional approach is applied deal with stability problem with the driver's delay. In this case, when the delay becomes greater, the longer preview distance will be needed. The average derivation of the steering input is calculated for different preview distance as well as the timedelay cases, which well verifies our driver model. The main contribution of this model is that the preview effect only depends on the path information and it does not affected by the vehicle speed, so the result is more neutral

Electric Power Steering Systems
Participants : C. Canudas de Wit [Contact person] , V. Ciarla, J. Tordesillas Illàn [UJF] .
This part presents several aspects of modeling, observation and control towards a new generation of Electrical Power Steering(EPS) systems [47] . In particular we design an optimal control to reject oscillations of the steering column, then we device a new observer to estimate the internal state variables of the steering column, the driver applied torque (steering wheel torque), and the load torque (tire/ground contact friction). Finally, we also revisited the LuGre tire dynamic friction model by improving the transient behavior between the sticking phases and the dynamic ones. Simulation of the proposed control and observer are shown at the end of the paper using the improved LuGretire friction model. Index Terms—Electric Power Steering systems (EPSs), LQ control, LuGre friction model, observer.