Explicit MPC Solution Using Hasse Diagrams: Construction, Storage and Retrieval

This chapter provides new methods for the construction, storage and retrieval of the explicit MPC solution in the case with quadratic cost and linear constraints. By exploiting the geometric interpretation of the MPC problem, we: (i) construct the explicit solution (i.e., enumerate the critical regions and associated affine laws) in an efficient manner; (ii) store it as a partially ordered set; and (iii) provide a modified graph traversal algorithm for efficient point location (i.e., identifying the currently active critical region and its associated control law).