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.

为具有状态和输入约束的耦合离散时间线性系统提出了分层模型预测控制 (MPC) 公式。与集中式方法相比，两级分层控制器（上层一个控制器，下层每个子系统一个控制器）可以显着降低与 MPC 相关的计算成本。分级协调是使用可调管实现的，可调管由上级控制器优化，并限制下级控制器与上级控制器确定的系统轨迹的允许偏差。这些可调节管的尺寸决定了子系统之间的不确定程度，并直接影响在基于管的稳健 MPC 框架下所需的约束收紧。集合表示为 zonotopes，以便能够优化这些可调节管的尺寸并在线执行必要的约束收紧，作为 MPC 优化问题的一部分。状态和输入约束满足证明了两级分层控制器在较低级别具有任意数量的控制器，并且一个数值示例展示了该方法的关键特征和性能。