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This paper proposes a novel hierarchical model predictive control (MPC)strategy that guarantees overall system stability. This method differssignificantly from previous approaches to guaranteeing overall stability, whichhave relied upon a multi-rate framework where the inner loop (low level) isupdated at a faster rate than the outer loop (high level), and the inner loopmust reach a steady-state within each outer loop time step. In contrast, themethod proposed in this paper is aimed at stabilizing the origin of an errorsystem characterized by the difference between the inner loop state and thestate specified by a full-order reference model. This makes the methodapplicable to systems with reduced levels of time scale separation. This paperproposes a framework for guaranteeing stability that leverages the use of thereference model, in conjunction with lambda-contractive constraint sets forboth the inner and outer loops. The effectiveness of the proposed referencemodel-based strategy is shown through simulation on an existing stirred tankreactor problem, where we demonstrate that the MPC optimization problem remainsfeasible and that the system remains stable and continues to perform well whentime scale separation between the inner and outer loops is reduced.

Stable Hierarchical Model Predictive Control Using an Inner Loop Reference Model and Lambda-Contractive Terminal Constraint Sets