# Conditions for State and Control Constraint Activation in Coordination of Connected and Automated Vehicles

## TL;DR

This paper analyzes the conditions under which constraints activate in the optimal coordination of connected and automated vehicles, providing a closed-form solution and simulation validation.

## Contribution

It offers a novel analytical framework to identify when state and control constraints become active in CAV coordination problems.

## Key findings

- Derived conditions for constraint activation in CAV coordination
- Provided a closed-form analytical solution for constrained optimization
- Validated results through numerical simulation

## Abstract

Connected and automated vehicles (CAVs) provide the most intriguing opportunity to reduce pollution, energy consumption, and travel delays. In earlier work, we addressed the optimal coordination of CAVs using Hamiltonian analysis. In this paper, we investigate the nature of the unconstrained problem and provide conditions under which the state and control constraints become active. We derive a closed-form analytical solution of the constrained optimization problem and evaluate the solution using numerical simulation.