Using a Two‐Level Structure to Manage the Point Location Problem in Explicit Model Predictive Control

The problem of determining the state region in which the current state point lies is referred to as the point location problem in the explicit model predictive control. In this paper, a two‐level structure to store the state regions is proposed and two efficient methods for solving the point‐location problem are developed; these are the two‐level grid (TLG) method and the grid‐BST method. The TLG method uses a tow‐level hash table. Before building the two‐level structure, the synonymy partitions are merged to reduce the memory storage demand. By setting each parameter in a triplet, the two‐level hash table can reach its optimal state and balance the complexity among the memory storage, reprocessing (offline computation) and the online computation. The grid‐BST method uses hash table as the first‐level structure and builds the binary search tree in the hash grid in which there are many partitions. This two‐level structure reduces reprocessing time significantly especially when the state partitions and the piecewise affine control laws (PWA control laws) are in a large number. Using the hyperplane (HP) as the node (not leaf node) of the tree, the method only stores all the different PWA control laws instead of the state partitions. The two proposed methods overcome the quick complexity growth when the number of polyhedral partitions increases and 2 numerical examples show the advantages of the proposed two methods.