S. Liu, J.R.D. Frejo, A. Núñez, B. De Schutter, A. Sadowska, H. Hellendoorn, and E.F. Camacho, "Tractable robust predictive control approaches for freeway networks," Proceedings of the 17th International IEEE Conference on Intelligent Transportation Systems (ITSC 2014), Qingdao, China, pp. 1857-1862, Oct. 2014.
Robust control aims to maintain predefined performance specifications for a wide range of uncertainties. In this paper, we consider the robust control problem for freeway networks, including the uncertainties explicitly in the control design step. We use min-max scheme for handling the uncertainties occurring in freeway networks. In order to reduce the computational complexity of min-max scheme, we propose scenario-based min-max Model Predictive Control (MPC) and scenario-based Receding-Horizon Parametrized Control (RHPC) in this paper, which solve the complete robust problem approximately. In addition, a new objective function is proposed to ensure the satisfaction of queue length constraints. A case study is implemented to assess the effectiveness of the proposed approaches. The results show that nominal MPC and nominal RHPC may result in a better performance than scenario-based min-max MPC and scenario-based min-max RHPC. However, nominal MPC and nominal RHPC cannot ensure the satisfaction of the queue length constraint. By applying scenario-based min-max MPC and scenario-based min-max RHPC, the queue length constraint is satisfied conservatively at the cost of an increase in the performance index.