Hierarchical MPC Schemes for Periodic Systems using Stochastic Programming

Abstract: We show that stochastic programming (SP) provides a framework to design hierarchical model predictive control (MPC) schemes for periodic systems. This is based on the observation that, if the state policy of an infinite-horizon problem is periodic, the problem can be cast as a stochastic program (SP). This reveals that it is possible to update periodic state targets by solving a retroactive optimization problem that progressively accumulates historical data. Moreover, we show that the retroactive problem is a statistical approximation of the SP and thus delivers optimal targets in the long run. Notably, this optimality property can be achieved without the need for data forecasts and cannot be achieved by any known proactive receding horizon scheme. The SP setting also reveals that the retroactive problem can be seen as a high-level hierarchical layer that provides targets to guide a low-level MPC controller that operates over a short period at high resolution. We derive a retroactive scheme tailored to linear systems by using cutting plane techniques and suggest strategies to handle nonlinear systems.