Stable hybrid Model Predictive Control for ramp metering

We formulate the Asymmetric Cell Transmission Model (ACTM) as a piecewise affine system defined over regions of the state and input space. We synthesize a hybrid Model Predictive Controller (MPC) for the piecewise affine model such that persistent feasibility and stability are guaranteed. We do so by designing a terminal constraint and terminal cost for the equilibrium state of the system. We include a detailed analysis of the equilibrium point of the piecewise affine system, and define the region of demand under which an equilibrium point exists. We show that our method achieves the same performance in terms of efficiency and exhibits much smoother behavior than that of the commonly used relaxed ACTM controller formulation.