Optimal Control of Connected and Automated Vehicles at Intersections with State and Control Constraints

This paper addresses the optimal control problem (optimal acceleration and deceleration to minimize fuel consumption) for Connected and Automated Vehicles (CAVs) to cross an intersection with state and control constraints. First, we obtain the crossing time for the CAVs to cross the intersection with Mixed Integer Linear Programming (MILP). Then, the crossing time is used as a terminal time to formulate the optimal control problem and we utilized analytical solution (Hamiltonian analysis) to solve the problem. Finally, we simulated the proposed approach and the results show that, even with the frequently changing crossing time, the controller is capable of providing the solution to the optimal control problem.