This paper proposes a novel cyber-physical traffic signal control system that interconnects physical dynamics and an optimization algorithm in order to reduce the street congestion. We first present a macroscopic traffic flow model that describes time evolution of the vehicle numbers on each road. Using this model, we then formulate an optimization problem to optimize the steady states/inputs in the sense of minimizing the congestion. We then present a (distributed) solution to the problem based on so-called partial primal-dual gradient algorithm. The traffic flow model is then shown to be successfully embedded in the algorithm as a sub-process for optimization, and accordingly a novel cyber-physical system is obtained. We then rigorously prove asymptotic optimality for constant disturbances and input-output stability for time-varying ones. Finally, we demonstrate the present algorithm through simulation on a microscopic traffic simulator, UC-win/Road, capable of the real-time feedback. It is then confirmed that the value of objective function for the optimization problem is reduced by 50% as compared to a fixed-time signal control scheme.
