S. Liu, A. Sadowska, J.R.D. Frejo, A. Núñez, E.F. Camacho, H. Hellendoorn, and B. De Schutter, "Robust receding horizon parameterized control for multi-class freeway networks: A tractable scenario-based approach," International Journal of Robust and Nonlinear Control, vol. 26, no. 6, pp. 1211-1245, Apr. 2016.
In this paper, we propose a tractable scenario-based Receding Horizon Parameterized Control (RHPC) approach for freeway networks. In this approach, a scenario-based min-max scheme is used to handle uncertainties. This scheme optimizes the worst case among a limited number of scenarios that are considered. The use of parameterized control laws allows us to reduce the computational burden of the robust control problem based on the multi-class METANET model w.r.t. conventional model predictive control. To assess the performance of the proposed approach, a simulation experiment is implemented, in which scenario-based RHPC is compared with nominal RHPC, standard control ignoring uncertainties, and standard control including uncertainties. Here, the standard control approaches refer to state feedback controllers (such as PI-ALINEA for ramp metering). A queue override scheme is included for extra comparison. The results show that nominal RHPC approaches and standard control ignoring uncertainties may lead to high queue length constraint violations, and including a queue override scheme in standard control may not reduce queue length constraint violations to a low level. Including uncertainties in standard control approaches can obviously reduce queue length constraint violations, but the performance improvements are minor. For the given case study, scenario-based RHPC performs best as it is capable of improving control performance without high queue length constraint violations.