The present disclosure provides a system and a method for jointly controlling one or multiple connected and automated vehicles (CAVs) and one or multiple human-driven vehicles (HDVs) subject to integer constraints for crossing each of multiple intersections on a road. The method comprises collecting digital representation of states of each of the CAVs, HDVs, and traffic signs, solving an optimization problem jointly optimizing traffic flows based on a macroscopic traffic flow model in a centralized traffic controller (CTC) subject to convex relaxation of the integer constraints, solving a multi-variable mixed-integer programming (MIP) problem in each of multiple intersection traffic controllers (ITCs) optimizing a cost function and minimizing tracking errors in traffic flow values of a microscopic traffic flow model with respect to relaxed traffic flow values from the CTC, and transmitting the optimized values of the control commands to the corresponding CAVs and corresponding traffic signs.