Constrained Hierarchical MPC via Zonotopic Waysets

A multi-level hierarchical Model Predictive Control (MPC) formulation is presented for constrained linear systems with finite operation. The control formulation guarantees satisfaction of both state and input constraints during operation and terminal state constraints at the end of operation. Coordination between controllers at different levels is achieved through the use of waysets. These waysets form terminal constraints on lower-level controllers that provide flexibility in short-term operation while guaranteeing the long-term ability to satisfy constraints beyond the prediction horizon of these controllers. The waysets are represented as constrained zonotopes to enable computationally efficient on-line calculation. Constraint satisfaction is proven for a hierarchy with an arbitrary number of levels while a numerical example with a two-level hierarchy demonstrates the key features of the approach.