  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.
