۱- Introduction

۲- Basic definitions and setting

۳- Hierarchical MPC schemes

۴- Computational experiments

۵- Conclusions and future work

References

Abstract

We show that stochastic programming 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, the computation of the optimal targets can be achieved without data forecasts. 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 time resolution. We derive a retroactive scheme tailored to linear systems by using cutting plane techniques and suggest strategies to handle nonlinear systems and to analyze stability properties.

Introduction

A well-known challenge arising in model predictive control (MPC) is the computational complexity associated with the length of the planning horizon and with the time resolution of the state and control policies (Rawlings & Mayne, 2009). These issues are often encountered in energy system applications that exhibit phenomena and disturbances emanating at multiple timescales. For instance, in energy systems, long horizons are often required to respond to low-frequency (e.g., seasonal) supply/demand variations and peak electricity costs (e.g., demand charges) while fine time resolutions are needed to modulate high-frequency variations (e.g., from wind/solar supply) and to participate in realtime markets (Braun, 1990; Dowling, Kumar, & Zavala, 2017). Computational complexity issues are often handled using receding horizon (RH) approximations, which are practical but do not provide optimality guarantees (Risbeck, Maravelias, Rawlings, & Turney, 2017).