Many optimal control problems require the simultaneous output of discrete and continuous control variables. These 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 undesirable for real-time control. This paper proposes a novel hybrid-action reinforcement learning (HARL) 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 discrete and continuous action spaces simultaneously. The proposed algorithm is evaluated on a plug-in hybrid electric vehicle (PHEV) energy management problem, where real-time control of the discrete variables, clutch engagement/disengagement and gear shift, and continuous variable, engine torque, is essential to maximize fuel economy while satisfying driving constraints. Simulation outcomes demonstrate that TD3AQ achieves control results close to optimality when compared with dynamic programming (DP), with just 4.69% difference. Furthermore, it surpasses the performance of baseline reinforcement learning algorithms.
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