Optimal Control of ODE Car-Following Models: Applications to Mixed-Autonomy Platoon Control via Coupled Autonomous Vehicles

TL;DR

This paper develops an optimal control framework for mixed-autonomy vehicle platoons, combining theoretical analysis and numerical methods to improve traffic flow with autonomous and human-driven vehicles.

Contribution

It introduces a novel optimal control formulation for mixed-autonomy platoons with proven well-posedness and a gradient descent algorithm for numerical solutions.

Findings

The control system is well-posed under realistic assumptions.

The numerical algorithm effectively computes optimal controls.

Simulations show improved traffic flow with mixed vehicle types.

Abstract

In this paper, we study the optimal control of a mixed-autonomy platoon driving on a single lane to smooth traffic flow. The platoon consists of autonomous vehicles, whose acceleration is controlled, and human-driven vehicles, whose behavior is described using a microscopic car-following model. We formulate the optimal control problem where the dynamics of the platoon are describing through a system of non-linear ODEs, with explicit constraints on both the state and the control variables. Theoretically, we analyze the well-posedness of the system dynamics under a reasonable set of admissible controls and establish the existence of minimizers for the optimal control problem. To solve the problem numerically, we propose a gradient descent-based algorithm that leverages the adjoint method, along with a penalty approach to handle state constraints. We demonstrate the effectiveness of the proposed numerical scheme through several experiments, exploring various scenarios with different penetration rates and distributions of controlled vehicles within the platoon.