J. Xu, T.J.J. van den Boom, B. De Schutter, and S. Wang, "Irredundant lattice representations of continuous piecewise affine functions," Automatica, vol. 70, pp. 109-120, Aug. 2016.
In this paper, we revisit the lattice piecewise affine (PWA) representation and give a formal proof of its representation ability of continuous PWA functions. Based on this, we derive the irredundant lattice PWA representation through removal of redundant terms and literals. Necessary and sufficient conditions for irredundancy are proposed. Besides, we explain how to remove terms and literals in order to ensure irredundancy. An algorithm is given to obtain an irredundant lattice PWA representation. In the worked examples, the irredundant lattice PWA representation is used to express the optimal solution of the explicit model predictive control, and the results turn out to be much more compact than that given by a state-of-the-art algorithm.