Robust control of bi-modal multi-region urban networks: an LMI optimisation approach

This work concerns the integration of a Three-Dimensional Macroscopic Fundamental Diagram (3D-MFD) modelling for mixed bi-modal traffic (consisting of cars and buses sharing the same infrastructure) in a control framework for congested urban regions. The 3D-MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in a traffic network. A Linear Parameter Varying (LPV) model with uncertain parameters for vehicle composition approximates the original nonlinear system of aggregated dynamics when it is near the equilibrium point for single- and multiple-region cities governed by 3D-MFDs. This model aims at designing a Proportional-Integral (PI) perimeter flow controller that guarantees robust regulation and stability, given that vehicle composition is a slow time-varying parameter. The control gain of the PI regulator is calculated off-line using Linear Matrix Inequality (LMI) optimisation. A simulation-based comparison of the proposed PI control with a pre-timed control plan for an area of San Francisco is carried out. Results show significant improvements in terms of travel delays for cars and buses and schedule reliability of bus services.