N. Groot, B. De Schutter, S.K. Zegeye, and H. Hellendoorn, "Model-based traffic and emission control using PWA models - A mixed-logical dynamic approach," Proceedings of the 14th International IEEE Conference on Intelligent Transportation Systems (ITSC 2011), Washington, DC, pp. 2142-2147, Oct. 2011.
For the purpose of traffic control a piecewise-affine (PWA) approximation of the METANET model is proposed and tested in a model-based predictive control (MPC) framework. This approximation is provided as an alternative to the rather intensive computations when using the original nonlinear nonconvex METANET traffic flow model extended with a model for vehicular emissions and fuel consumption in an MPC context. As a direct PWA-MPC computation turned out to be intractable for on-line applications due to the size of the final, full PWA model that consists of a large number of PWA regions, the PWA model equations were additionally converted into a mixed-logical dynamic (MLD) model. The resulting MLD-MPC problem - written as a mixed-integer linear program (MILP) - can be solved much more efficiently as it does not explicitly state all model equations for each particular region. In a simple case study on a traffic network including a variable speed limit and an un-metered on-ramp while optimizing the total time spent (TTS), we compared the performance of the approximate MLD-MPC approach to that of model predictive traffic control when using the original nonlinear formulation of the METANET model.