Hierarchical MPC with Coordinating Terminal Costs

Abstract

The performance of hierarchical Model Predictive Control (MPC) is highly dependent on the mechanisms used to coordinate the decisions made by controllers at different levels of the hierarchy. Conventionally, reference tracking serves as the primary coordination mechanism, where optimal state and input trajectories determined by upper-level controllers are communicated down the hierarchy to be tracked by lower-level controllers. As such, significant tuning is required for each controller in the hierarchy to achieve the desired closed-loop system performance. This paper presents a novel terminal cost coordination mechanism using constrained zonotopes, designed to improve system performance under hierarchical control. These terminal costs allow lower-level controllers to balance both short- and long-term control performance without the need for controller tuning. Unlike terminal costs widely used to guarantee MPC stability, the proposed terminal costs are time-varying and computed on-line based on the optimal state trajectory of the upper-level controllers. A numerical example demonstrates the provable performance benefits achieved using the proposed terminal cost coordination mechanism.