Fast computation of binary search tree for PWA functions representation using intersection classification

Explicit Model Predictive Control (eMPC) aims to overcome the runtime computational effort from Model Predictive Control (MPC) by computing offline the overall optimization procedure. The result from eMPC is a Piecewise Affine (PWA) function that defines a relationship between the system state and the optimal control action. To improve the PWA evaluation during runtime, Binary Search Trees (BST) are employed to represent PWA functions, which may be time prohibitive considering the total time to obtain the tree. This note presents a new classification strategy of polyhedral regions with respect to hyperplanes to build BST for PWA functions. The proposed solution is based on the verification of intersection between regions and hyperplanes, resulting in a decrease by almost half in the number of optimization problems, and consequently, in the total time to build the BST, which is the main time-consuming task. The computational time improvement is verified on numerical examples of different sizes, where the same BST is obtained for the original and the proposed classification methods.