Supervisory Model Predictive Control for Freeway Traffic Systems Antonella Ferrara, Simona Sacone, Silvia Siri Abstract— The application of Model Predictive Control schemes to real world complex plants, such as freeway traffic systems, is sometimes limited because of the necessity of tuning the control action depending on the system operating condition, and the significant computational burden inherent to the methodology. The MPC-based scheme presented in this paper aims at overcoming the mentioned limitations by using a supervisory control approach. The supervisor, at each time step, chooses among three possible actions: i) the controller needs to be changed and the new control action is computed, ii) no change is made to the controller, but it is necessary to recompute the control action, iii) neither is the controller varied, nor it is necessary to recompute the control action and the already determined control law is kept. In other terms, the control sequence is recomputed according to an event-triggered mechanism in which the control action is properly tuned to the system conditions. In the paper, the proposed control scheme is developed with reference to a class of non-linear systems admitting a model of Mixed Logical Dynamical type, which is suitable to describe freeway traffic systems, and the input- to-state practical stability of the controlled system is proved. Finally, the application of the proposed control scheme to a freeway traffic system is discussed and studied via simulation. I. I NTRODUCTION Model Predictive Control (MPC) is nowadays a reliable control technique widely used for process control and ap- plications of different nature [1], [2], [3], among which the control of freeway traffic systems, as evidenced by the numerous papers which have appeared in the literature (see, for instance, [4], [5], [6], [7]). In spite of its effectiveness, MPC has a major drawback since the computational load to solve the optimization prob- lem grows with the system complexity. This significantly limits the on-line usage of MPC algorithms especially in the context of freeway traffic control, where the number of states and control variables can be very high by virtue of the large scale geographical distribution of the system to control. A number of solutions have been proposed to overcome this limitation, leading to the formulation of Fast MPC algorithms [8], with the controller replaced by a look- up table computed off-line, and Plug and Play MPC schemes [9], in which it is possible to use simpler controllers by applying a decentralized synthesis procedure. This work has been supported by the European Union Seventh Framework Programme [FP7/2007-2013] under grant agreement n. 257462 HYCON2 Network of excellence. A. Ferrara is with the Dept. of Electrical, Computer and Biomedical Engineering, University of Pavia, Italy antonella.ferrara@unipv.it S. Sacone and S. Siri are with the Department of Informatics, Bioengi- neering, Robotics and Systems Engineering, University of Genova, Italy simona.sacone@unige.it, silvia.siri@unige.it In this paper, we propose a different way to reduce the computational burden of the MPC algorithms oriented to deal with traffic control systems. The idea is to rely on an event- triggered algorithm inspired by [10], and to include it into a supervisory control scheme, giving rise to a supervisory event-triggered MPC scheme. Event-triggered control strategies ([11], [12]), in which sampling is dictated by the occurrence of events, rather than time-triggered, have become popular in recent years because of the difficulty, in many applications, to apply equidistant sampling for feedback control, due to limited communication resources or inadequate computation power. In our proposal, we design a supervisor so that the asynchronous sampling provided by the event-triggered formulation is exploited to reduce the number of times in which the optimization problem underlying the MPC strategy is solved, i.e. the control law is updated only when it is no longer adequate. On the other hand, a supervisory control scheme (see, for instance, [13], [14], [15], [16]) can be capable of choosing among a family of candidate controllers the one which is more likely to provide the best control performance at the current time step. In our paper, also this feature is effectively exploited. More specifically, relying on the output of a suitable monitoring signal generator, the supervisor not only triggers the recomputations of the control law only when strictly necessary, but also selects, at any sampling time, the appropriate controller to be used. Since our aim is to design a control scheme suitable for on-line usage in freeway traffic systems, we assume that the process dynamics could be affected by interacting physical laws, logical rules and operating constraints. A quite natural way to represent and predict the process behaviour, in such a case, is to adopt a Mixed Logical Dynamical (MLD) model (see [17]). In our proposal the MLD model is used both as a predictor in solving the MPC problem, and as a process emulator to accomplish the generation of an appropriate monitoring signal. The set of controllers, for the sake of uniformity, includes controllers that are all of MPC type, but the scheme is designed to host controllers even of different nature. The stability properties of the controlled system are discussed in the paper while the performance of the proposed scheme when applied to a freeway is analyzed in simulation. This paper is structured as follows. In Section II the proposed supervisory control scheme, with all its modules, is outlined. The stability properties of the controlled system are investigated in Section III. The application of the overall control scheme to freeway traffic systems is described in Section IV, while some conclusive remarks are outlined in Section V.