A chance-constrained tube-based model predictive control for tracking linear systems using data-driven uncertainty sets

This article presents a chance-constrained tube-based model predictive control (MPC) method for tracking linear time-invariant systems based on data-driven uncertainty sets. By defining the terminal admissible set to consider all the possible steady-states and reformulating the stochastic tube-based MPC framework, the proposed method can systematically hedge against the impact of uncertainties and ensure tracking for all reachable operating setpoints. To reduce the conservatism of control performance while enlarging the feasible region, a data-driven polyhedral uncertainty set is constructed by using the principal component analysis technique, which can effectively capture correlations among uncertain variables. Since state constraint violations in a certain probability are allowed, a probability uncertainty set is constructed by using statistic limit and cutting plane methods to formulate a stochastic tube to ensure constraint satisfaction. The recursive feasibility and stability can be guaranteed if the uncertainties are bounded. The effectiveness of the proposed method is verified by numerical examples and tracking problems of a thickening process.