Data-driven Scenario Selection for Multistage Robust Model Predictive Control

Abstract

A main assumption in many works considering multistage model predictive control (MPC) is that discrete realizations of the uncertainty are chosen a-priori and that the scenario tree is given. In this work, we focus on choosing the scenarios, which is an important practical aspect of scenario-based multistage MPC. In many applications, the distribution of the uncertain parameters is not available, but instead a finite set of data samples are available. Given this finite set of data samples, we present a data-driven approach to selecting the scenarios using principal component analysis (PCA). Using this approach, the scenarios are carefully selected such that the conservativeness of the solution can be reduced while still maintaining robustness towards constraint feasibility. The effectiveness of the proposed method is demonstrated using a simple example.