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Handling Long Horizons in MPC: A Stochastic Programming Approach

We propose an approach to handle long horizons in model predictive control (MPC). The approach is based on the observation that, if periodicity constraints are enforced over short-term stages, the long horizon MPC problem can be cast as a stochastic programming (SP) problem. The SP representation reveals a mechanism to construct a hierarchical MPC scheme under which a high-level (long-horizon) MPC controller provides periodic state targets to guide a low-level (short-term) MPC controller. We show that this hierarchical scheme is optimal under nominal (perfect forecast) conditions and can be extended to handle imperfect forecasts by correcting the targets in real-time. We demonstrate our concepts using a building system with stationary battery storage, where the goal is to use the battery to mitigate monthly demand charges while collecting revenue from hourly frequency regulation markets. We demonstrate that the hierarchical MPC scheme yields improved performance over standard MPC schemes because it can systematically capture long-term effects.