Modified Dynamic Programming Algorithms for GLOSA Systems with Stochastic Signal Switching Times

TL;DR

This paper introduces a Differential Dynamic Programming (DDP) approach for solving stochastic GLOSA control problems, achieving near-instantaneous solutions suitable for real-time vehicle onboard systems, improving computational efficiency over traditional methods.

Contribution

The paper presents a novel application of DDP to stochastic GLOSA problems, demonstrating faster solutions that enable real-time implementation without discretizing variables.

Findings

DDP achieves extremely fast CPU times suitable for online use.

Solutions are slightly better than traditional SDP due to lack of discretization.

Realistic examples validate the approach's effectiveness.

Abstract

A discrete-time stochastic optimal control problem was recently proposed to address the GLOSA (Green Light Optimal Speed Advisory) problem in cases where the next signal switching time is decided in real time and is therefore uncertain in advance. The corresponding numerical solution via SDP (Stochastic Dynamic Programming) calls for substantial computation time, which excludes problem solution in the vehicle's on-board computer in real time. To overcome the computation time bottleneck, as a first attempt, a modified version of Dynamic Programming, known as Discrete Differential Dynamic Programming (DDDP) was recently employed for the numerical solution of the stochastic optimal control problem. The DDDP algorithm was demonstrated to achieve results equivalent to those obtained with the ordinary SDP algorithm, albeit with significantly reduced computation times. The present work considers a different modified version of Dynamic Programming, known as Differential Dynamic Programming (DDP). For the stochastic GLOSA problem, it is demonstrated that DDP achieves quasi-instantaneous (extremely fast) solutions in terms of CPU times, which allows for the proposed approach to be readily executable online, in an MPC (Model Predictive Control) framework, in the vehicle's on-board computer. The approach is demonstrated by use of realistic examples. It should be noted that DDP does not require discretization of variables, hence the obtained solutions may be slightly superior to the standard SDP solutions.