Two-class freeway traffic regulation to reduce congestion and emissions via nonlinear optimal control Cecilia Pasquale b,⇑ , Ioannis Papamichail a , Claudio Roncoli a , Simona Sacone b , Silvia Siri b , Markos Papageorgiou a a Dynamic Systems and Simulation Laboratory, Technical University of Crete, Greece b Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Italy article info Article history: Received 15 October 2014 Received in revised form 8 January 2015 Accepted 8 January 2015 Available online xxxx Keywords: Freeway traffic control Two-class traffic model and control Ramp metering Traffic emissions abstract The objective of this paper is the regulation of freeway traffic by means of optimal control techniques. A first innovative aspect of the proposed approach is the adopted objective function in which, besides the reduction of traffic congestion (which is typically considered in traffic control schemes), the minimization of traffic emissions is also included. Moreover, a multi-class framework is defined in which two classes of vehicles (cars and trucks) are explicitly modelled, and specific control actions for each vehicle class are sought. This results in the formulation of a multi-objective optimal control problem which is described in the paper and for which a specific solution algorithm is developed and used. The algo- rithm exploits a specific version of the feasible direction algorithm whose effectiveness is demonstrated in the paper by means of simulation results. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Phenomena of recurrent and nonrecurrent congestion in freeway systems can be relieved by applying proper control techniques, that have been studied by researchers for some decades. A very successful and widespread control measure is ramp metering, which allows to control the traffic flow entering the freeway mainstream by using traffic lights at the on- ramps. Ramp metering is applied to achieve maximum mainline throughput downstream of the ramp (local control) or, more generally, optimal traffic conditions in the freeway network (networkwide approaches) (Papageorgiou and Papamichail, 2008). One of the first effective ramp metering strategies is the local feedback traffic controller ALINEA (Papageorgiou et al., 1991), dating back to the Nineties, that has been applied in many freeways all over the world. It has been shown that ALINEA, despite being a local controller, is quite effective in increasing the motorway throughput (Papageorgiou et al., 2007). During the years, ALINEA has been further extended, resulting in a proportional-integral version, called PI-ALINEA (Wang et al., 2010), or through a coordination of the local ramp-metering actions, thus enabling the linked control of the inflow from consecutive on-ramps (Papamichail and Papageorgiou, 2008). Different traffic control methodologies have been developed in the last decades, also including approaches based on optimization or optimal control algorithms (Kotsialos and Papageorgiou, 2004). In some works, the problem of controlling a freeway is formulated as a discrete-time constrained nonlinear optimal control problem (see Kotsialos et al. (2002) and the references therein), whose numerical solution is often hard to find by directly using the available Nonlinear Program- ming codes, because of the problem dimensions and complexity. A very efficient numerical solution has been adopted in http://dx.doi.org/10.1016/j.trc.2015.01.013 0968-090X/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Transportation Research Part C xxx (2015) xxx–xxx Contents lists available at ScienceDirect Transportation Research Part C journal homepage: www.elsevier.com/locate/trc Please cite this article in press as: Pasquale, C., et al. Two-class freeway traffic regulation to reduce congestion and emissions via nonlinear optimal control. Transport. Res. Part C (2015), http://dx.doi.org/10.1016/j.trc.2015.01.013