Integrating Reinforcement Learning and Model Predictive Control for Mixed- Logical Dynamical Systems

This work proposes an approach that integrates reinforcement learning (RL) and model predictive control (MPC) to solve finite-horizon optimal control problems in mixed-logical dynamical systems efficiently. Optimization-based control of such systems with discrete and continuous decision variables entails the online solution of mixed-integer linear programs, which suffer from the curse of dimensionality. In the proposed approach, by repeated interaction with a simulator of the system, a reinforcement learning agent is trained to provide a policy for the discrete decision variables. During online operation, the RL policy simplifies the online optimization problem of the MPC controller from a mixed-integer linear program to a linear program, significantly reducing the computation time. A fundamental contribution of this work is the definition of the decoupled Q-function, which plays a crucial role in making the learning problem tractable in a combinatorial action space. We motivate the use of recurrent neural networks to approximate the decoupled Q-function and show how they can be employed in a reinforcement learning setting. A microgrid system is used as an illustrative example where real-world data is used to demonstrate that the proposed method substantially reduces the maximum online computation time of MPC (up to $20\times$) while maintaining high feasibility and average optimality gap lower than 1.1% .