# Energy Management in Plug-in Hybrid Electric Vehicles: Convex Optimization Algorithms for Model Predictive Control

## TL;DR

This paper compares convex optimization algorithms for energy management in hybrid electric vehicles, demonstrating that the projected interior point method outperforms ADMM and CVX in accuracy and speed.

## Contribution

It introduces a projected interior point method tailored for energy management optimization, improving computational efficiency for high-accuracy solutions.

## Key findings

- Projected interior point method is faster and more accurate than ADMM and CVX.
- ADMM is preferable for solutions with modest accuracy.
- Both proposed methods outperform general-purpose convex optimization software.

## Abstract

This paper details an investigation into the computational performance of algorithms used for solving a convex formulation of the optimization problem associated with model predictive control for energy management in hybrid electric vehicles with nonlinear losses. A projected interior point method is proposed, where the size and complexity of the Newton step matrix inversion is reduced by applying inequality constraints on the control input as a projection, and its properties are demonstrated through simulation in comparison with an alternating direction method of multipliers (ADMM) algorithm, and general purpose convex optimization software CVX. It is found that the ADMM algorithm has favourable properties when a solution with modest accuracy is required, whereas the projected interior point method is favourable when high accuracy is required, and that both are significantly faster than CVX.