*3.2.1 Optimal control method*

This problem is posed as an unconstrained optimization problem [34] and then further extended to also consider the impact of fuel consumption [35]. The output was the ability to derive online an optimal closed-form solution for vehicle coordination at a merge intersection. The importance of safety constraints is also stressed here. Constraints in positioning, maximum velocity and maximum accelerations are imposed. Additionally, the algorithm only allows one vehicle to enter into the merging zone at any time.

The algorithm calculates the time at which each vehicle would enter the merge zone and requires that this time does not conflict with any of the other vehicles.

## *Models and Methods for Intelligent Highway Routing of Human-Driven and Connected… DOI: http://dx.doi.org/10.5772/intechopen.94332*

This ensures that a lateral collision can never happen. Additionally, the algorithm also directs that vehicles maintain at least a specified gap between each other which ensures that rear-end collisions do not occur. Hamiltonian analysis is then used to convert the optimization problem into a system of four equations that can be solved in real time to output the optimal control for each vehicle.

Simulation of this system was then carried out to show that the algorithm performs as desired. It was found that compared to a baseline situation where onramp vehicles always give way to vehicles on the freeway this algorithm performs significantly better. An improvement of 52% in fuel consumption when compared to the baseline situation was also reported.

Disadvantages: Only one lane of the freeway is in use and the benefits obtained from allowing/forcing vehicles to switch lanes in the freeway are ignored (i.e. full capacity of the freeway is not used). Additionally, vehicles are given merging rights based on a simplistic FIFO (First In First Out) queue which can cause additional delays and is definitely sub-optimal.
