Hierarchical MPC Schemes for Periodic Systems using Stochastic Programming

TL;DR

This paper introduces a stochastic programming framework for designing hierarchical MPC schemes for periodic systems, enabling optimal target updates without forecasts and integrating high-level planning with low-level control.

Contribution

It proposes a novel stochastic programming approach for hierarchical MPC, allowing data-driven target updates and handling both linear and nonlinear systems.

Findings

Retroactive optimization approximates stochastic programming for long-term optimal targets.

The approach does not require data forecasts, unlike traditional proactive schemes.

Hierarchical control structure improves performance for periodic systems.

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.