A data-driven robust optimization approach to scenario-based stochastic model predictive control

TL;DR

This paper introduces a data-driven scenario-based stochastic model predictive control method that actively learns and calibrates uncertainty sets from data, reducing conservatism and data requirements while ensuring probabilistic guarantees.

Contribution

It proposes a novel machine learning-based approach to construct and calibrate uncertainty sets for SMPC, improving practicality and robustness over traditional methods.

Findings

Reduces conservatism of control actions.

Requires fewer data samples than traditional SMPC.

Demonstrates effectiveness on systems like two-mass-spring and building energy control.

Abstract

Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive scenarios that are generated to represent uncertainties. In this paper, a novel scenario-based SMPC approach is proposed by actively learning a data-driven uncertainty set from available data with machine learning techniques. A systematical procedure is then proposed to further calibrate the uncertainty set, which gives appropriate probabilistic guarantee. The resulting data-driven uncertainty set is more compact than traditional norm-based sets, and can help reducing conservatism of control actions. Meanwhile, the proposed method requires less data samples than traditional scenario-based SMPC approaches, thereby enhancing the practicability of SMPC. Finally the optimal control problem is cast as a single-stage robust optimization problem, which can be solved efficiently by deriving the robust counterpart problem. The feasibility and stability issue is also discussed in detail. The efficacy of the proposed approach is demonstrated through a two-mass-spring system and a building energy control problem under uncertain disturbances.