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

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 λ-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.