Mixed-Integer Optimal Control via Reinforcement Learning: A Case Study on Hybrid Vehicle Energy Management

Many optimal control problems require the simultaneous output of continuous and discrete control variables. Such problems are usually formulated as mixed-integer optimal control (MIOC) problems, which are challenging to solve due to the complexity of the solution space. Numerical methods such as branch-and-bound are computationally expensive and unsuitable for real-time control. This paper proposes a novel continuous-discrete reinforcement learning (CDRL) algorithm, twin delayed deep deterministic actor-Q (TD3AQ), for MIOC problems. TD3AQ combines the advantages of both actor-critic and Q-learning methods, and can handle the continuous and discrete action spaces simultaneously. The proposed algorithm is evaluated on a hybrid electric vehicle (HEV) energy management problem, where real-time control of the continuous variable engine torque and discrete variable gear ratio is essential to maximize fuel economy while satisfying driving constraints. Simulation results on different drive cycles show that TD3AQ can achieve near-optimal solutions compared to dynamic programming (DP) and outperforms the state-of-the-art discrete RL algorithm Rainbow, which is adopted for MIOC by discretizing continuous actions into a finite set of discrete values.