Data-Driven Online Adaptation of the Scenario-Tree in Multistage Model Predictive Control

Abstract

Multistage model predictive control (MPC) is based on the enumeration of scenarios that represent the uncertainty in the system. Scenario selection is important in multistage MPC since the choice of scenarios determines the degree of conservativeness of the optimal solution. We propose a data-driven approach based on principal component analysis (PCA) to dynamically select the scenarios, leading to reduced conservativeness. When time-varying uncertainty is considered, PCA can be performed online to select new scenarios whenever the uncertainty data is updated. The results of the approach are demonstrated for a two-plant system with a thermal storage tank. The solution obtained is less conservative than with standard multistage MPC. This is because the online PCA-based approach accounts for the most recent, and thus more representative, uncertainty realizations.