  The recently emerging multi-mode plug-in hybrid electric vehicle (PHEV)
technology is one of the pathways making contributions to decarbonization, and
its energy management requires multiple-input and multipleoutput (MIMO)
control. At the present, the existing methods usually decouple the MIMO control
into singleoutput (MISO) control and can only achieve its local optimal
performance. To optimize the multi-mode vehicle globally, this paper studies a
MIMO control method for energy management of the multi-mode PHEV based on
multi-agent deep reinforcement learning (MADRL). By introducing a relevance
ratio, a hand-shaking strategy is proposed to enable two learning agents to
work collaboratively under the MADRL framework using the deep deterministic
policy gradient (DDPG) algorithm. Unified settings for the DDPG agents are
obtained through a sensitivity analysis of the influencing factors to the
learning performance. The optimal working mode for the hand-shaking strategy is
attained through a parametric study on the relevance ratio. The advantage of
the proposed energy management method is demonstrated on a software-in-the-loop
testing platform. The result of the study indicates that the learning rate of
the DDPG agents is the greatest influencing factor for learning performance.
Using the unified DDPG settings and a relevance ratio of 0.2, the proposed
MADRL system can save up to 4% energy compared to the single-agent learning
system and up to 23.54% energy compared to the conventional rule-based system.
