An isolated traffic intersection feedback control using H∞

This paper is concerned with the development of a robust and demand-responsive control model to provide optimum signalization and queue management at an isolated intersection. We formulate the signal control problems for a simple isolated intersection in the H_∞ -control framework. The system is hybrid, in that the the dynamical equations are for a continuous-time model for averaged quantities, while the actual, realizable sequences of traffic signals amounts to a discrete-time, finite state machine. The state space models are valid for both undersaturated and oversaturated intersections. An application of the method of characteristics leads to a solution of the corresponding Hamilton-Jacobi equation with the physical constraints on the control parameters taken into account. The results agree with what one would expect on intuitive grounds. The mathematical foundations are now laid for scaling up the procedure to handle more complicated intersections and networks