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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, consistingof the state samples and corresponding affine control laws, based on which thelattice PWA approximations are constructed. Re-sampling of data is alsoproposed to guarantee that the lattice PWA approximations are identical toexplicit MPC control law in the unique order (UO) regions containing the samplepoints as interior points. Additionally, under mild assumptions, theequivalence of the two lattice PWA approximations guarantees that theapproximations are error-free in the domain of interest. The algorithms forderiving statistically error-free approximation to the explicit linear MPC areproposed and the complexity of the entire procedure is analyzed, which ispolynomial with respect to the number of samples. The performance of theproposed approximation strategy is tested through two simulation examples, andthe result shows that with a moderate number of sample points, we can constructlattice PWA approximations that are equivalent to optimal control law of theexplicit linear MPC.

Error-free approximation of explicit linear MPC through lattice piecewise affine expression