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Many optimal control problems require the simultaneous output of continuousand discrete control variables. Such problems are usually formulated asmixed-integer optimal control (MIOC) problems, which are challenging to solvedue to the complexity of the solution space. Numerical methods such asbranch-and-bound are computationally expensive and unsuitable for real-timecontrol. This brief proposes a novel continuous-discrete reinforcement learning(CDRL) algorithm, twin delayed deep deterministic actor-Q (TD3AQ), for MIOCproblems. TD3AQ combines the advantages of both actor-critic and Q-learningmethods, and can handle the continuous and discrete action spacessimultaneously. The proposed algorithm is evaluated on a plug-in hybridelectric vehicle (PHEV) energy management problem, where real-time control ofthe continuous variable, engine torque, and discrete variables, gear shift andclutch engagement/disengagement is essential to maximize fuel economy whilesatisfying driving constraints. Simulation results on different drive cyclesshow that TD3AQ achieves near-optimal control compared to dynamic programming(DP) and outperforms baseline reinforcement learning algorithms.

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