  In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA)
approximations of explicit linear model predictive control (MPC) are proposed.
The training data are generated uniformly in the domain of interest, consisting
of the state samples and corresponding affine control laws, based on which the
lattice PWA approximations are constructed. Re-sampling of data is also
proposed to guarantee that the lattice PWA approximations are identical to
explicit MPC control law in the unique order (UO) regions containing the sample
points as interior points. Additionally, under mild assumptions, the
equivalence of the two lattice PWA approximations guarantees that the
approximations are error-free in the domain of interest. The algorithms for
deriving statistically error-free approximation to the explicit linear MPC are
proposed and the complexity of the entire procedure is analyzed, which is
polynomial with respect to the number of samples. The performance of the
proposed approximation strategy is tested through two simulation examples, and
the result shows that with a moderate number of sample points, we can construct
lattice PWA approximations that are equivalent to optimal control law of the
explicit linear MPC.
