Flexible piecewise function evaluation methods with application to explicit model predictive control

This paper addresses efficient evaluation of piecewise functions defined over polyhedral partitions which is a vital problem in many areas such as control applications. As an important application, the explicit model predictive control (eMPC) problem is considered which requires a piecewise affine (PWA) control law to be evaluated online. The proposed method combines an Orthogonal Truncated Binary Search Tree (OTBST) and lattice representation for PWA functions in a unified structure enjoying the advantages of both approaches. The proposed Lattice-based OTBST (LOTBST) method enables the designer to trade-off between preprocessing time, storage requirement and online computation time. Using examples it is shown that the proposed LOTBST leads to a considerably less preprocessing time and memory requirement comparing to the pure BST and less online computation time comparing to the pure lattice representation.