Irredundant lattice piecewise affine representations and their applications in explicit model predictive control

In this paper, we derive the irredundant lattice piecewise affine (PWA) representation, which is capable of representing any continuous PWA function. Necessary and sufficient conditions for irredundancy are proposed. Besides, we discuss how to remove redundant terms and literals and propose corresponding necessary and sufficient conditions. In a worked example, the irredundant lattice PWA representation is used to express the explicit model predictive controller of a linear system, and the result turns out to be much more compact than that given by the state-of-the-art algorithm.