Time-optimal traffic control synthesis for a signalized isolated intersection

The minimum time optimal control problem for a signalized intersection is defined as finding the green split that dissolves all initial non-zero queue lengths in minimum time. Here, the optimal minimum time control for an isolated intersection is found in explicit state feedback form, where the state is defined as the queue lengths, by the use of a clever modification of D. Gazis´s continuous differential model, and the Pontryagin Maximum Principle. The closed form feedback solution is presented for all types of constraints on the maximal green split values, and on the queue lengths, i.e. with constrained control and state variables. In general, the minimum time optimal solutions are non-unique. It is also demonstrated that the known contribution by D. Gazis, 1964, alleged to solve the minimal “total delay” problem is in fact a minimal time solution in a particular region of the state space.