Distributed control and state estimation in freeway systems

Simona Sacone
Università di Genova

The objective of the presentation is first of all the design of distributed control
schemes for freeway systems. Freeway systems can be controlled in different ways:
the most widely used is ramp metering, which consists of regulating the flows of
vehicles accessing the freeway using traffic lights located at the on-ramps. Several
control schemes devoted to determining and realizing ramp metering can be found
in the literature starting from very simple approaches, up to more sophisticated
techniques as those adopting optimal control techniques. Optimal control schemes
and, specifically, model predictive control (MPC) schemes have shown to be quite
effective for freeway traffic control but their practical applicability is conditioned
by the necessary computational load and communication effort required by such
approaches. Indeed, the complexity of the optimization problem associated with
MPC increases with the dimensions of the freeway system, making the centralized
online application of the control strategies often problematic. In the literature,
several solutions have been proposed in order to address implementation issues.
Some of them are aimed at improving the efficiency of the optimization algorithm,
whereas others are focused on the reduction of the overall computational burden.
An alternative approach consists in breaking the control problem into small
subproblems to be solved locally. This is the basic principle of distributed control.
Distributed control schemes are based on a set of local controllers acting on sub-
sets of freeway cells named clusters. The local controllers are designed to operate
on disjoint nonoverlapping pairs of inputs and outputs, which synergically control
the overall plant. Local controllers can either exchange information or be totally
independent, giving rise to a decentralized control scheme. In this presentation,
the design of a distributed MPC strategy for a freeway system is addressed. The
proposed scheme is described and compared both with a centralized framework
consisting of a classical MPC and with a completely decentralized scheme. Two
different distributed control algorithms are presented and evaluated, one of par-
tially connected noniterative independent type and the other of partially connected
noniterative cooperative type. The centralized and decentralized schemes are used
as a benchmark with respect to which the distributed approaches are compared and
The extension to a multirate decentralized supervised control scheme applying
event-triggered logics is also presented. The control framework is composed of a
high-level supervisor and a set of local controllers, one for each cluster of freeway
cells, which act in a decentralized way. In particular, the local controller present
in each cluster is of event-triggered MPC type, triggering conditions being present
both at the sensor level and at the controller level. The supervisor, thanks to a
detailed prediction model of the plant, is able to predict the evolution of the plant
behaviour over a given time horizon. On the basis of this prediction, the supervisor
decides if the controller of each cluster must be activated or not and, in the former
case, it properly fixes the controller parameters. To do that, the supervisor receives
the plant state measurements from the sensors present in each cluster. Such mea-
surements are not sent at each sampling time but at a lower rate and are used to
initialize the model present in the supervisor.
Since the measurements are not transmitted at each time step, both the con-
troller and the sensors are equipped with a process emulator that is able to repro-
duce the state dynamic evolution of the cluster in an accurate way. Moreover, the
control law generator present in the controller makes a prediction of the cluster
state evolution. The measured state is transmitted to the controller only when the
state provided by the emulator strongly differs from the real state of the cluster.
The control law is computed only when new measurements are received or there is
a significant deviation between the state predicted by the control law generator and
the one provided by the emulator.
Finally, the problem of state estimation, intended as the reconstruction of traf-
fic densities in portions of road links not equipped with sensors is treated in the
presentation. Distributed observers seem to be also suitable for large freeway net-
works where sensors are placed in specific locations and in each location it can be
necessary to estimate the state of the entire freeway system. A distributed switched
observer design method, based on Luenberger-like and consensus strategies is pro-
posed. To this aim, a switching mode model (SMM) is employed, which is a
modified version of the Cell Transmission Model (CTM), representing the freeway
system switching among different sets of linear difference equations. The proposed
scheme allows every observer to estimate the densities of the overall system, with
very limited information exchange requirements between observers. Asymptotic
stability of the overall scheme is proved when the system operates under observ-
able modes, together with L2-gain disturbance rejection capabilities. The solution
is provided in terms of a set of LMIs that makes use of the structure of the SMM
to alleviate the computational requirements.

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