Stable hierarchical model predictive control using an inner loop reference model and lambda-contractive terminal constraint sets

This paper proposes a novel hierarchical model predictive control (MPC) strategy that guarantees overall system stability. Our method differs significantly from previous approaches to guaranteeing overall stability, which have relied upon a multi-rate framework where the inner loop (low level) is updated at a faster rate than the outer loop (high level), and the inner loop must reach a steady-state within each outer loop time step. In contrast, our approach is aimed at stabilizing the origin of an error system characterized by the difference between the inner loop state and the state specified by a full-order reference model. This makes our method applicable to systems that do not possess the level of time scale separation that is required to apply the multi-rate framework successfully. Stability constraints for the proposed algorithm are derived, and the effectiveness of the proposed reference model-based strategy is shown through simulation on a stirred tank reactor problem, where we demonstrate that the MPC optimization problem remains feasible and the system remains stable and continues to perform well when time scale separation between the inner and outer loops is reduced.