N. Groot, B. De Schutter, S. Zegeye, and H. Hellendoorn, "Model-based predictive traffic control: A piecewise-affine approach based on METANET," Proceedings of the 18th IFAC World Congress, Milan, Italy, pp. 10709-10714, Aug.-Sept. 2011.
As an alternative to the rather intensive computations when using the nonlinear traffic flow model METANET in a model-based predictive control context, a piecewise-affine (PWA) approximation of the model is proposed. Here, several model equations amongst which the fundamental diagram are approximated by a PWA function. Some selected methods to determine this approximation are shortly discussed. In addition, we make use of model properties and physical insight to improve the PWA approximation. For the purpose of traffic control, the PWA approximation of the METANET model can be used in a model predictive control (MPC) framework. In view of the on-line optimization used by MPC and the related trade-off between accuracy and computational speed, in a case study the accuracy of various approximations is compared to the original nonlinear formulation of METANET.