Real-time signalization for an oversaturated intersection via static state feedback control: A switched system approach

In this paper, the traffic-responsive signalization problem for an oversaturated intersection is addressed. A static state feedback control strategy is presented to relieve the waiting vehicles in lanes. By modeling the intersection as a discrete-time switched system and with the aid of quadratic Lyapunov function method, the green time of each phase in signalization is determined by a set of linear state feedback controllers, and moreover, in order to avoid the risk of overflow of waiting vehicles which could lead to the traffic congestion, the boundary of waiting queue length is estimated and further minimized by the state feedback control. Then, linear matrix inequality (LMI) technique is employed to numerically tackle the design problem through solving a set of LMI optimization problems. Furthermore, the design results are extended to the case with unknown disturbance, and H∞ controller is designed to achieve the disturbance attenuation performance. In the end, a simulation study in comparison with traditional Webster method is presented to illustrate the effectiveness of state feedback control in relieving the oversaturated situation for an intersection.