Robust Traffic Flow Control using Signal Spatio-Temporal Logic

For reliable traffic control at signalized crossings, this study examines the traffic signal optimization problem using formal methods. Our earlier research considered model predictive control (MPC) with signal spatio-temporal logic constraints to optimize traffic signals at an intersection. However, this approach has a restrictive assumption that the number of vehicles arriving at the intersection from unmodeled streets, termed as the disturbance, is known a priori. Moreover, it has a limitation that the control law is suboptimal if any constraint is not feasible. To relax the assumption and overcome the limitation, this article derives satisfaction and minimal-violation requirements for MPC, which takes into account a disturbance set, to fulfill an optimization constraint if it is feasible; otherwise, the constraint is violated as little as possible. In this way, the MPC is robust against all realizations of additive bounded disturbances.