Lattice piecewise affine approximation of explicit linear model predictive control

In this paper, the lattice piecewise affine (PWA) approximation of explicit linear model predictive control (MPC) is proposed. The training data consists of the state samples and corresponding affine control laws, based on which the lattice PWA approximation is constructed. The proposed approximation is identical to the explicit MPC control law in unique-order (UO) regions containing the sample points as interior points, thus resemble the explicit MPC control law in a large number of regions. Through simplifying the terms and literals in the lattice PWA approximation, both the storage requirement and online computation complexity are largely decreased. The performance of the proposed approximation strategy is tested through a simulation example, and the result shows that with a moderate number of sample points, the lattice PWA approximation is very close to the explicit MPC control law.