  A hierarchical Model Predictive Control (MPC) formulation is presented for
coupled discrete-time linear systems with state and input constraints. Compared
to a centralized approach, a two-level hierarchical controller, with one
controller in the upper-level and one controller per subsystem in the
lower-level, can significantly reduce the computational cost associated with
MPC. Hierarchical coordination is achieved using adjustable tubes, which are
optimized by the upper-level controller and bound permissible lower-level
controller deviations from the system trajectories determined by the
upper-level controller. The size of these adjustable tubes determines the
degree of uncertainty between subsystems and directly affects the required
constraint tightening under a tube-based robust MPC framework. Sets are
represented as zonotopes to enable the ability to optimize the size of these
adjustable tubes and perform the necessary constraint tightening online as part
of the MPC optimization problems. State and input constraint satisfaction is
proven for the two-level hierarchical controller with an arbitrary number of
controllers at the lower-level and a numerical example demonstrates the key
features and performance of the approach.
