  This paper proposes a novel hierarchical model predictive control (MPC)
strategy that guarantees overall system stability. This 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, the
method proposed in this paper 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 the method
applicable to systems with reduced levels of time scale separation. This paper
proposes a framework for guaranteeing stability that leverages the use of the
reference model, in conjunction with lambda-contractive constraint sets for
both the inner and outer loops. The effectiveness of the proposed reference
model-based strategy is shown through simulation on an existing stirred tank
reactor problem, where we demonstrate that the MPC optimization problem remains
feasible and that the system remains stable and continues to perform well when
time scale separation between the inner and outer loops is reduced.
